{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## NCAA March Madness\n",
"\n",
"### Pomeroy Ratings and First Round Upset Picks\n",
"\n",
"This notebook continues our examination of strategies for picking first round March Madness upsets. In this notebook, we will look at Ken Pomeroy's [KenPom college basketball ratings](https://kenpom.com/) and see how they can help us predict wins and losses.\n",
"\n",
"We're going to merge the KenPom data with the Washington Post NCAA game history that we [analyzed previously](http://practicallypredictable.com/2018/03/07/march-madness-first-round-upsets/). By combining these data sets, we'll see whether the KenPom data would have helped predict upsets in previous NCAA tournaments."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"pd.options.display.float_format = '{:.3f}'.format\n",
"pd.options.display.max_rows = 100"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import matplotlib as mpl\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"sns.set(context='notebook', palette='colorblind')"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"import math\n",
"import warnings"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"from pathlib import Path"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"PROJECT_DIR = Path.cwd().parent\n",
"SCRAPED_DIR = PROJECT_DIR / 'data' / 'scraped'\n",
"PREPARED_DIR = PROJECT_DIR / 'data' / 'prepared'"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Loading the KenPom Data\n",
"\n",
"First let's read in the previously scraped KenPom data.\n",
"\n",
"See [this notebook](https://nbviewer.jupyter.org/github/practicallypredictable/posts/blob/master/basketball/ncaa/notebooks/ncaa-scrape-kenpom.ipynb) to see how to scrape historical KenPom ratings. "
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"def read_kenpom_csv(filepath):\n",
" \"\"\"Read scraped KenPom CSV file.\"\"\"\n",
" filename = 'kenpom-historical.csv'\n",
" csvfile = filepath.joinpath(filename)\n",
" df = pd.read_csv(csvfile).dropna()\n",
" return df"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"One challenge in combining different data sets is making sure the data are all consistent. It turns out that the KenPom and Washington Post data aren't consistent in how the schools are named. KenPom uses certain abbreviations that the Washington Post doesn't use, and vice versa. I needed to make adjustments to both data sets to make the school names line up. Ultimately, it doesn't matter which naming choice you make, as long as it's consistent in both data sets.\n",
"\n",
"Here's a function which changes certain school names in the KenPom data. A corresponding function for the Washington Post data is below."
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"def fix_kenpom_team_name(s):\n",
" \"\"\"Correct certain team name problems and make consistent with Washington Post team names.\"\"\"\n",
" # Convert \"Saint\" to \"St.\"\n",
" s = s.replace('Saint', 'St.')\n",
" # Add \"St.\" to certain school names\n",
" add_st = {\n",
" 'Middle Tennessee',\n",
" 'Central Connecticut',\n",
" }\n",
" for team in add_st:\n",
" s = s.replace(team, team+' St.')\n",
" # Expand abbreviations for certain school names\n",
" change_abbrs = {\n",
" 'BYU': 'Brigham Young',\n",
" 'SMU': 'Southern Methodist',\n",
" 'UAB': 'Alabama Birmingham',\n",
" 'UCF': 'Central Florida',\n",
" 'UMBC': 'Maryland Baltimore County',\n",
" 'USC': 'Southern California',\n",
" 'UT Arlington': 'Texas Arlington',\n",
" 'UTSA': 'Texas San Antonio',\n",
" 'VCU': 'Virginia Commonwealth',\n",
" }\n",
" for team in change_abbrs:\n",
" s = s.replace(team, change_abbrs[team])\n",
" # Miscellaneous fixes\n",
" fix_misc = {\n",
" 'Southern Miss': 'Southern Mississippi',\n",
" 'Albany': 'Albany (N.Y.)',\n",
" 'Loyola MD': 'Loyola (Md.)',\n",
" 'Miami FL': 'Miami (Fla.)',\n",
" 'Miami OH': 'Miami (Ohio)',\n",
" 'Troy St.': 'Troy',\n",
" 'Corpus Chris': 'Corpus Christi',\n",
" }\n",
" for team in fix_misc:\n",
" s = s.replace(team, fix_misc[team])\n",
" return s"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"def rename_kenpom_cols(df):\n",
" \"\"\"Rename KenPom columns.\"\"\"\n",
" cols = [col.lower().replace(' ', '_').replace('adj', 'adj_').replace('opp', 'opp_') for col in df.columns]\n",
" df.columns = cols\n",
" return df"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"def load_kenpom(filepath=PREPARED_DIR):\n",
" \"\"\"Load Ken Pomeroy data since 2002 and format it.\"\"\"\n",
" df = read_kenpom_csv(filepath)\n",
" df['Seed'] = df['Seed'].astype(int)\n",
" df['Team'] = df['Team'].apply(fix_kenpom_team_name)\n",
" df = rename_kenpom_cols(df)\n",
" return df"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(1061, 24)"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"kenpom = load_kenpom(PREPARED_DIR)\n",
"kenpom.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Understanding KenPom Ratings\n",
"\n",
"Now that we have the KenPom data loaded, let's see what sort of data we have."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Index(['year', 'team', 'conf', 'seed', 'wins', 'losses', 'kenpom', 'adj_em',\n",
" 'adj_o', 'adj_d', 'adj_t', 'luck', 'sos_adj_em', 'opp_o', 'opp_d',\n",
" 'ncsos_adj_em', 'adj_o_rank', 'adj_d_rank', 'adj_t_rank', 'luck_rank',\n",
" 'sos_adj_em_rank', 'opp_o_rank', 'opp_d_rank', 'ncsos_adj_em_rank'],\n",
" dtype='object')"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"kenpom.columns"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>year</th>\n",
" <th>team</th>\n",
" <th>conf</th>\n",
" <th>seed</th>\n",
" <th>wins</th>\n",
" <th>losses</th>\n",
" <th>kenpom</th>\n",
" <th>adj_em</th>\n",
" <th>adj_o</th>\n",
" <th>adj_d</th>\n",
" <th>...</th>\n",
" <th>opp_d</th>\n",
" <th>ncsos_adj_em</th>\n",
" <th>adj_o_rank</th>\n",
" <th>adj_d_rank</th>\n",
" <th>adj_t_rank</th>\n",
" <th>luck_rank</th>\n",
" <th>sos_adj_em_rank</th>\n",
" <th>opp_o_rank</th>\n",
" <th>opp_d_rank</th>\n",
" <th>ncsos_adj_em_rank</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>2002</td>\n",
" <td>Duke</td>\n",
" <td>ACC</td>\n",
" <td>1</td>\n",
" <td>31</td>\n",
" <td>4</td>\n",
" <td>1</td>\n",
" <td>34.190</td>\n",
" <td>121.000</td>\n",
" <td>86.800</td>\n",
" <td>...</td>\n",
" <td>99.500</td>\n",
" <td>6.660</td>\n",
" <td>1</td>\n",
" <td>1</td>\n",
" <td>8</td>\n",
" <td>223</td>\n",
" <td>18</td>\n",
" <td>13</td>\n",
" <td>31</td>\n",
" <td>34</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>2002</td>\n",
" <td>Cincinnati</td>\n",
" <td>CUSA</td>\n",
" <td>1</td>\n",
" <td>31</td>\n",
" <td>4</td>\n",
" <td>2</td>\n",
" <td>30.190</td>\n",
" <td>118.100</td>\n",
" <td>87.900</td>\n",
" <td>...</td>\n",
" <td>100.000</td>\n",
" <td>3.480</td>\n",
" <td>7</td>\n",
" <td>3</td>\n",
" <td>194</td>\n",
" <td>165</td>\n",
" <td>57</td>\n",
" <td>66</td>\n",
" <td>44</td>\n",
" <td>80</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>2002</td>\n",
" <td>Maryland</td>\n",
" <td>ACC</td>\n",
" <td>1</td>\n",
" <td>32</td>\n",
" <td>4</td>\n",
" <td>3</td>\n",
" <td>29.250</td>\n",
" <td>119.200</td>\n",
" <td>89.900</td>\n",
" <td>...</td>\n",
" <td>99.500</td>\n",
" <td>1.620</td>\n",
" <td>4</td>\n",
" <td>7</td>\n",
" <td>15</td>\n",
" <td>104</td>\n",
" <td>16</td>\n",
" <td>11</td>\n",
" <td>32</td>\n",
" <td>120</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>2002</td>\n",
" <td>Kansas</td>\n",
" <td>B12</td>\n",
" <td>1</td>\n",
" <td>33</td>\n",
" <td>4</td>\n",
" <td>4</td>\n",
" <td>28.990</td>\n",
" <td>118.700</td>\n",
" <td>89.700</td>\n",
" <td>...</td>\n",
" <td>99.900</td>\n",
" <td>8.320</td>\n",
" <td>5</td>\n",
" <td>6</td>\n",
" <td>3</td>\n",
" <td>109</td>\n",
" <td>10</td>\n",
" <td>4</td>\n",
" <td>40</td>\n",
" <td>23</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>2002</td>\n",
" <td>Oklahoma</td>\n",
" <td>B12</td>\n",
" <td>2</td>\n",
" <td>31</td>\n",
" <td>5</td>\n",
" <td>5</td>\n",
" <td>26.040</td>\n",
" <td>114.900</td>\n",
" <td>88.900</td>\n",
" <td>...</td>\n",
" <td>100.400</td>\n",
" <td>-0.440</td>\n",
" <td>20</td>\n",
" <td>4</td>\n",
" <td>228</td>\n",
" <td>69</td>\n",
" <td>26</td>\n",
" <td>15</td>\n",
" <td>62</td>\n",
" <td>169</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>5 rows × 24 columns</p>\n",
"</div>"
],
"text/plain": [
" year team conf seed wins losses kenpom adj_em adj_o adj_d \\\n",
"0 2002 Duke ACC 1 31 4 1 34.190 121.000 86.800 \n",
"1 2002 Cincinnati CUSA 1 31 4 2 30.190 118.100 87.900 \n",
"2 2002 Maryland ACC 1 32 4 3 29.250 119.200 89.900 \n",
"3 2002 Kansas B12 1 33 4 4 28.990 118.700 89.700 \n",
"4 2002 Oklahoma B12 2 31 5 5 26.040 114.900 88.900 \n",
"\n",
" ... opp_d ncsos_adj_em adj_o_rank adj_d_rank \\\n",
"0 ... 99.500 6.660 1 1 \n",
"1 ... 100.000 3.480 7 3 \n",
"2 ... 99.500 1.620 4 7 \n",
"3 ... 99.900 8.320 5 6 \n",
"4 ... 100.400 -0.440 20 4 \n",
"\n",
" adj_t_rank luck_rank sos_adj_em_rank opp_o_rank opp_d_rank \\\n",
"0 8 223 18 13 31 \n",
"1 194 165 57 66 44 \n",
"2 15 104 16 11 32 \n",
"3 3 109 10 4 40 \n",
"4 228 69 26 15 62 \n",
"\n",
" ncsos_adj_em_rank \n",
"0 34 \n",
"1 80 \n",
"2 120 \n",
"3 23 \n",
"4 169 \n",
"\n",
"[5 rows x 24 columns]"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"kenpom.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can read about the most recent version of KenPom ratings [here](https://kenpom.com/blog/ratings-methodology-update/).\n",
"\n",
"#### Adjusted Offensive and Defensive Efficiencies\n",
"\n",
"The main building blocks are Adjusted Offensive Efficiency Rating (_AdjO_) and Adjusted Defensive Efficiency Rating (_AdjD_). _AdjO_ is a prediction of the team's points scored per 100 possessions, against an \"average\" team on a neutral court. KenPom defines \"average\" as being an average Division-I opponent.\n",
"\n",
"_AdjD_ is a prediction of how many points per 100 possessions an average opponent will score against the team on a neutral court.\n",
"\n",
"Equivalently, if you divide either rating by 100, it's the predicted points scored by or against the team per possession.\n",
"\n",
"Note that KenPom uses an assumption that home court advantage is worth 3.75 points in estimating the ratings. Since NCAA tournament games are played on neutral courts, no home court adjustment is made for predicting tournament games.\n",
"\n",
"#### Adjusted Efficiency Margin\n",
"\n",
"The Adjusted Efficiency Margin (_AdjEM_) is simply the difference between the offensive and defensive efficiency ratings for the team. It can be positive or negative. If it is negative, it could be because of relatively weak offense or relatively weak defense.\n",
"\n",
"#### KenPom Ranking\n",
"\n",
"In the KenPom methodology, teams are ranked by their _AdjEM_.\n",
"\n",
"Virginia is the top team as of Sunday, March 11 (and a first seed in this year's March Madness), with an _AdjEM_ of +32.15. This is composed of a 116.5 _AdjO_ less its 84.4 _AdjD_. Notice that Virginia's _AdjO_ is only ranked $21^{st}$, while it's _AdjD_ is ranked number 1. In contrast, the number 2 team, Villanova, has the top KenPom _AdjO_ of 127.4, but only the $22^{nd}$ ranked _AdjD_ of 96.0.\n",
"\n",
"#### Tempo\n",
"\n",
"Notice that by estimating points scored or allowed per possession, the KenPom methodology controls for the effect of team pace. In any particular game, both teams get roughly the same number of possessions. This is true whether one or both teams push the ball up the floor or not. You can [read Ken Pomeroy's own post on possessions here](https://kenpom.com/blog/the-possession/).\n",
"\n",
"If you want to predict scores or point differentials, you need to include the effect of pace.\n",
"\n",
"Fortunately, KenPom also helps to predict pace. The Adjusted Tempo (_AdjT_) is a prediction of the number of possessions the team will have against an \"average\" team on a neutral court.\n",
"\n",
"If you want to estimate the number of possessions each team will have in a given game, you can just average the _AdjT_ of each team. So, for example, if Virginia (_AdjT_ of 59.2) were to eventually meet Villanova (_AdjT_ of 68.3) in the 2018 NCAA tournament, KenPom would predict that there would be 127.5 possessions in total (each of average length 18.8 seconds), or equivalently that each team would have roughtly 64 possessions per game.\n",
"\n",
"#### Strength of Schedule Ratings\n",
"\n",
"The strength of schedule (SOS) ratings can be used to get a sense of the average quality of opponents that a team faces during a given season.\n",
"\n",
"The _SOS AdjEM_ is the _AdjEM_ of a hypothetical team that would be predicted to win half of its games against the team's full-season schedule (excluding post-season play). The non-conference strength of schedule measure (_NCSOS AdjEM_) is similar, except that it only looks at the team's non-conference opponents. \n",
"\n",
"#### Luck\n",
"\n",
"The [KenPom ratings glossary](https://kenpom.com/blog/ratings-glossary/) describes the luck rating as:\n",
"\n",
"> A measure of the deviation between a team’s actual winning percentage and what one would expect from its game-by-game efficiencies. It’s a Dean Oliver invention. Essentially, a team involved in a lot of close games should not win (or lose) all of them. Those that do will be viewed as lucky (or unlucky).\n",
"\n",
"You can read more about Dean Oliver and his contributions to basketball analytics [here](https://en.wikipedia.org/wiki/Dean_Oliver_(statistician%29).\n",
"\n",
"Theoretically, once a game is close and goes down to the wire, an average team should win roughly 50% of the time. The luck rating is just measuring historically whether teams have won (or lost) a meaningfully different fraction of these close games.\n",
"\n",
"You can interpret the luck rating in two completely different ways.\n",
"\n",
"1. Teams with high luck ratings have an ability (not captured by other KenPom ratings) to \"win in the clutch.\" You should expect those teams to continue to be \"lucky\" relative to their regular KenPom projections.\n",
"2. Teams with high luck ratings just got very lucky in the past, and you shouldn't rely on that luck to continue in the future in close games. Maybe those teams aren't as good as their records suggest?\n",
"\n",
"You can read about what one researcher learned about these questions [here](http://blog.minitab.com/blog/the-statistics-game/analyzing-luck-in-college-basketball-part-1) and [here](http://blog.minitab.com/blog/the-statistics-game/analyzing-luck-in-college-basketball-part-ii). His conclusion was that you should go with the second interpretation, and be wary of teams with high luck ratings.\n",
"\n",
"#### Ranks\n",
"\n",
"The KenPom data also has the ranks of each team measured by every statistic. Our scraper pulled in this data, but we won't use it in this analysis.\n",
"\n",
"#### One Caveat with Historical KenPom Data\n",
"\n",
"The KenPom data for 2002-2017 that are used in this notebook are as of the end of the respective seasons, and include post-season play. This could be problematic for studyihng historical NCAA tournament results, since the KenPom ratings include the teams' performance in those tournaments. To run a correct analysis, you want to have the KenPom data as it appeared just prior to the tournament start each year. If the tournament results meaningfully changed the final KenPom ratings compared to how they appeared right before tournament, our prediction model would be biased by using the \"incorrect\" KenPom data.\n",
"\n",
"Furthermore, the methodology behind KenPom data changed in 2016. The \"historical\" data shown on the KenPom website for seasons prior to 2016 were computed using the new methodology. Even if we had the KenPom data as it stood just before the previous tournaments, it wouldn't be consistent with how the KenPom data are computed today. To make sure our analysis is using apples-to-apples data, we would need to be sure to get KenPom data, computed using the current methodology, using historical games up to but not including the NCAA tournaments in each year.\n",
"\n",
"Unfortunately, we don't currently have access to such data, so we will use the data we have. This is equivalent to assuming that the final post-season KenPom ratings (computed using the current methodology) in prior years wasn't too different from how it would have looked just prior to the tournaments.\n",
"\n",
"A team plays at most 6 games in the NCAA tournament, and most teams play much fewer than that. Since the KenPom data are based on the entire season, which includes many more games, you might hope that errors introduced by this assumption would be relativley small. We'll proceed with the analysis but we need to keep this potential source of error in mind.\n",
"\n",
"### A First Look at the KenPom Ratings by Seed \n",
"\n",
"Let's look at the average values of these ratings by tournament seed."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"kenpom_cols = ['kenpom', 'adj_em', 'adj_o', 'adj_d', 'adj_t', 'luck', 'sos_adj_em', 'ncsos_adj_em']"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"scrolled": true
},
"outputs": [
{
"data": {
"text/html": [
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" vertical-align: middle;\n",
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" }\n",
"\n",
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" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>kenpom</th>\n",
" <th>adj_em</th>\n",
" <th>adj_o</th>\n",
" <th>adj_d</th>\n",
" <th>adj_t</th>\n",
" <th>luck</th>\n",
" <th>sos_adj_em</th>\n",
" <th>ncsos_adj_em</th>\n",
" </tr>\n",
" <tr>\n",
" <th>seed</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>3.703</td>\n",
" <td>28.848</td>\n",
" <td>119.002</td>\n",
" <td>90.155</td>\n",
" <td>67.161</td>\n",
" <td>0.021</td>\n",
" <td>9.023</td>\n",
" <td>1.739</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>9.188</td>\n",
" <td>24.768</td>\n",
" <td>117.092</td>\n",
" <td>92.333</td>\n",
" <td>66.211</td>\n",
" <td>0.026</td>\n",
" <td>9.033</td>\n",
" <td>1.272</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>15.062</td>\n",
" <td>22.185</td>\n",
" <td>115.855</td>\n",
" <td>93.677</td>\n",
" <td>65.972</td>\n",
" <td>0.020</td>\n",
" <td>8.786</td>\n",
" <td>-0.239</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>16.781</td>\n",
" <td>21.637</td>\n",
" <td>115.041</td>\n",
" <td>93.406</td>\n",
" <td>66.211</td>\n",
" <td>0.002</td>\n",
" <td>8.631</td>\n",
" <td>-0.182</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>21.906</td>\n",
" <td>19.932</td>\n",
" <td>113.461</td>\n",
" <td>93.525</td>\n",
" <td>65.717</td>\n",
" <td>0.004</td>\n",
" <td>7.921</td>\n",
" <td>-0.326</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>27.859</td>\n",
" <td>18.406</td>\n",
" <td>113.277</td>\n",
" <td>94.872</td>\n",
" <td>65.666</td>\n",
" <td>0.010</td>\n",
" <td>7.735</td>\n",
" <td>-0.750</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>31.328</td>\n",
" <td>17.669</td>\n",
" <td>113.355</td>\n",
" <td>95.681</td>\n",
" <td>65.053</td>\n",
" <td>0.009</td>\n",
" <td>6.922</td>\n",
" <td>0.443</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>33.531</td>\n",
" <td>16.792</td>\n",
" <td>112.794</td>\n",
" <td>95.997</td>\n",
" <td>66.384</td>\n",
" <td>0.012</td>\n",
" <td>7.103</td>\n",
" <td>0.159</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>39.531</td>\n",
" <td>15.692</td>\n",
" <td>111.056</td>\n",
" <td>95.372</td>\n",
" <td>65.631</td>\n",
" <td>0.000</td>\n",
" <td>6.647</td>\n",
" <td>0.123</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>40.125</td>\n",
" <td>15.778</td>\n",
" <td>112.144</td>\n",
" <td>96.367</td>\n",
" <td>65.625</td>\n",
" <td>-0.003</td>\n",
" <td>7.147</td>\n",
" <td>0.210</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>46.151</td>\n",
" <td>14.613</td>\n",
" <td>111.632</td>\n",
" <td>97.015</td>\n",
" <td>65.400</td>\n",
" <td>0.003</td>\n",
" <td>4.758</td>\n",
" <td>0.587</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>54.985</td>\n",
" <td>13.131</td>\n",
" <td>110.819</td>\n",
" <td>97.685</td>\n",
" <td>65.110</td>\n",
" <td>0.031</td>\n",
" <td>1.999</td>\n",
" <td>0.215</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>78.769</td>\n",
" <td>9.617</td>\n",
" <td>107.963</td>\n",
" <td>98.354</td>\n",
" <td>66.398</td>\n",
" <td>0.027</td>\n",
" <td>-0.534</td>\n",
" <td>1.849</td>\n",
" </tr>\n",
" <tr>\n",
" <th>14</th>\n",
" <td>95.262</td>\n",
" <td>7.396</td>\n",
" <td>107.888</td>\n",
" <td>100.500</td>\n",
" <td>65.960</td>\n",
" <td>0.030</td>\n",
" <td>-2.054</td>\n",
" <td>1.460</td>\n",
" </tr>\n",
" <tr>\n",
" <th>15</th>\n",
" <td>142.031</td>\n",
" <td>2.276</td>\n",
" <td>104.758</td>\n",
" <td>102.481</td>\n",
" <td>66.195</td>\n",
" <td>0.047</td>\n",
" <td>-4.209</td>\n",
" <td>1.166</td>\n",
" </tr>\n",
" <tr>\n",
" <th>16</th>\n",
" <td>200.011</td>\n",
" <td>-3.355</td>\n",
" <td>101.279</td>\n",
" <td>104.629</td>\n",
" <td>66.360</td>\n",
" <td>0.039</td>\n",
" <td>-6.672</td>\n",
" <td>2.394</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" kenpom adj_em adj_o adj_d adj_t luck sos_adj_em ncsos_adj_em\n",
"seed \n",
"1 3.703 28.848 119.002 90.155 67.161 0.021 9.023 1.739\n",
"2 9.188 24.768 117.092 92.333 66.211 0.026 9.033 1.272\n",
"3 15.062 22.185 115.855 93.677 65.972 0.020 8.786 -0.239\n",
"4 16.781 21.637 115.041 93.406 66.211 0.002 8.631 -0.182\n",
"5 21.906 19.932 113.461 93.525 65.717 0.004 7.921 -0.326\n",
"6 27.859 18.406 113.277 94.872 65.666 0.010 7.735 -0.750\n",
"7 31.328 17.669 113.355 95.681 65.053 0.009 6.922 0.443\n",
"8 33.531 16.792 112.794 95.997 66.384 0.012 7.103 0.159\n",
"9 39.531 15.692 111.056 95.372 65.631 0.000 6.647 0.123\n",
"10 40.125 15.778 112.144 96.367 65.625 -0.003 7.147 0.210\n",
"11 46.151 14.613 111.632 97.015 65.400 0.003 4.758 0.587\n",
"12 54.985 13.131 110.819 97.685 65.110 0.031 1.999 0.215\n",
"13 78.769 9.617 107.963 98.354 66.398 0.027 -0.534 1.849\n",
"14 95.262 7.396 107.888 100.500 65.960 0.030 -2.054 1.460\n",
"15 142.031 2.276 104.758 102.481 66.195 0.047 -4.209 1.166\n",
"16 200.011 -3.355 101.279 104.629 66.360 0.039 -6.672 2.394"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"kenpom.groupby('seed')[kenpom_cols].mean()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We observe the following patterns in the above table:\n",
"\n",
"- Higher seeded teams tend to have better (lower) KenPom rankings and better (higher) _AdjEM_ ratings.\n",
"- The same pattern applies to the underlying _AdjO_ and _AdjD_ ratings. Higher seeded teams have better (higher) _AdjO_ ratings and better (lower) _AdjD_ ratings.\n",
"- There does not appear to be a significant pattern in tempo, as shown by the _AdjT_ ratings.\n",
"- There does not appear to be much of a pattern in the luck rating by seed, although the fact that most seeds have positive average values suggest that these teams have slightly higher win percentages than the underlying KenPom ratings would have projected.\n",
"- Higher seeded teams appear to have played against stronger opponents overall prior to the tournament, although there does not appear to be a pattern in the non-conference SOS ratings.\n",
"\n",
"\n",
"### Loading the Washington Post Tournament Data\n",
"\n",
"Now we will move on to read in the historical tournament game data. This data was previously scraped as demonstrated in [this notebook](https://nbviewer.jupyter.org/github/practicallypredictable/posts/blob/master/basketball/ncaa/notebooks/ncaa-scrape-washpost.ipynb)."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"def read_washpost_csv(filepath):\n",
" \"\"\"Read Washington Post NCAA Tournament games history CSV file.\"\"\"\n",
" filename = 'game_history-washpost-1985_2017.csv'\n",
" csvfile = filepath.joinpath(filename)\n",
" df = pd.read_csv(csvfile)\n",
" return df"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We are going to look only at first round games since 2002 (the first year for which we have KenPom data). So, we will drop all the other historical game information from our analysis."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"def filter_games(df):\n",
" \"\"\"Limit games to first round since 2002 (to match KenPom data).\"\"\"\n",
" df = df[df['Round'] == 1]\n",
" df = df.drop(columns=['Round'])\n",
" df = df[df['Year'] >= 2002]\n",
" return df"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We need to correct a few of the school names to match up with our KenPom data set. This function will do that."
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"def fix_washpost_team_name(s):\n",
" \"\"\"Correct Washington Post team names to match KenPom.\"\"\"\n",
" s = s.replace('State', 'St.')\n",
" s = s.replace('-', ' ')\n",
" fix_misc = {\n",
" 'Long Island': 'LIU Brooklyn',\n",
" 'St. Mary\\'s (Cal.)': 'St. Mary\\'s',\n",
" 'Bakersfied': 'Bakersfield',\n",
" }\n",
" for team in fix_misc:\n",
" s = s.replace(team, fix_misc[team])\n",
" return s"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The Washington Post data has game results (team, seed and score) in terms of the game winner and loser. This isn't what we need for this analysis. The problem is that we want the columns to be consistent by seed. Having winner and loser columns means that some times the higher seed will be in the winner column, and sometimes in the loser column. We want to organize the teams by higher seed versus lower seed.\n",
"\n",
"The next few functions will take care of this for us."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [],
"source": [
"def team_hi(row):\n",
" if row['WinnerSeed'] == row['HigherSeed']:\n",
" return row['Winner']\n",
" else:\n",
" return row['Loser']"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [],
"source": [
"def team_lo(row):\n",
" if row['WinnerSeed'] == row['HigherSeed']:\n",
" return row['Loser']\n",
" else:\n",
" return row['Winner']"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [],
"source": [
"def score_hi(row):\n",
" if row['WinnerSeed'] == row['HigherSeed']:\n",
" return row['WinnerScore']\n",
" else:\n",
" return row['LoserScore'] "
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"def score_lo(row):\n",
" if row['WinnerSeed'] == row['HigherSeed']:\n",
" return row['LoserScore']\n",
" else:\n",
" return row['WinnerScore']"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [],
"source": [
"def fix_washpost_cols(df):\n",
" \"\"\"Adjust columns to reflect high/low seed, not winner/loser.\"\"\"\n",
" df['team_hi'] = df.apply(team_hi, axis=1)\n",
" df['team_lo'] = df.apply(team_lo, axis=1)\n",
" df['seed_hi'] = df['HigherSeed']\n",
" df['seed_lo'] = 17 - df['seed_hi']\n",
" df['score_hi'] = df.apply(score_hi, axis=1)\n",
" df['score_lo'] = df.apply(score_lo, axis=1)\n",
" df = df.drop(columns=['HigherSeed', 'Winner', 'WinnerSeed', 'WinnerScore', 'Loser', 'LoserSeed', 'LoserScore'])\n",
" return df"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we can put everything together to read in the data, filter out the games we don't want, fix the team names and then reorganize the columns."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
"def rename_washpost_cols(df):\n",
" \"\"\"Rename Washington Post game history columns.\"\"\"\n",
" df = df.rename(columns={\n",
" 'Year': 'year',\n",
" })\n",
" cols = ['year'] + [col for col in df.columns if '_hi' in col] + [col for col in df.columns if '_lo' in col]\n",
" return df[cols]"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"def load_first_round_games(filepath):\n",
" \"\"\"Load NCAA first round tournmanet games since 2002.\"\"\"\n",
" df = read_washpost_csv(filepath)\n",
" df = filter_games(df)\n",
" df['Winner'] = df['Winner'].apply(fix_washpost_team_name)\n",
" df['Loser'] = df['Loser'].apply(fix_washpost_team_name)\n",
" df = fix_washpost_cols(df)\n",
" df = rename_washpost_cols(df)\n",
" return df.reset_index(drop=True)"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(512, 7)"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"games = load_first_round_games(PREPARED_DIR)\n",
"games.shape"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>year</th>\n",
" <th>team_hi</th>\n",
" <th>seed_hi</th>\n",
" <th>score_hi</th>\n",
" <th>team_lo</th>\n",
" <th>seed_lo</th>\n",
" <th>score_lo</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>2002</td>\n",
" <td>North Carolina St.</td>\n",
" <td>7</td>\n",
" <td>69</td>\n",
" <td>Michigan St.</td>\n",
" <td>10</td>\n",
" <td>58</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>2002</td>\n",
" <td>Illinois</td>\n",
" <td>4</td>\n",
" <td>93</td>\n",
" <td>San Diego St.</td>\n",
" <td>13</td>\n",
" <td>64</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>2002</td>\n",
" <td>Texas</td>\n",
" <td>6</td>\n",
" <td>70</td>\n",
" <td>Boston College</td>\n",
" <td>11</td>\n",
" <td>57</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>2002</td>\n",
" <td>Cincinnati</td>\n",
" <td>1</td>\n",
" <td>90</td>\n",
" <td>Boston University</td>\n",
" <td>16</td>\n",
" <td>52</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>2002</td>\n",
" <td>Georgia</td>\n",
" <td>3</td>\n",
" <td>85</td>\n",
" <td>Murray St.</td>\n",
" <td>14</td>\n",
" <td>68</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>2002</td>\n",
" <td>Texas Tech</td>\n",
" <td>6</td>\n",
" <td>68</td>\n",
" <td>Southern Illinois</td>\n",
" <td>11</td>\n",
" <td>76</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>2002</td>\n",
" <td>Maryland</td>\n",
" <td>1</td>\n",
" <td>85</td>\n",
" <td>Siena</td>\n",
" <td>16</td>\n",
" <td>70</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>2002</td>\n",
" <td>Oklahoma</td>\n",
" <td>2</td>\n",
" <td>71</td>\n",
" <td>Illinois Chicago</td>\n",
" <td>15</td>\n",
" <td>63</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>2002</td>\n",
" <td>California</td>\n",
" <td>6</td>\n",
" <td>82</td>\n",
" <td>Penn</td>\n",
" <td>11</td>\n",
" <td>75</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>2002</td>\n",
" <td>Xavier</td>\n",
" <td>7</td>\n",
" <td>70</td>\n",
" <td>Hawaii</td>\n",
" <td>10</td>\n",
" <td>58</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" year team_hi seed_hi score_hi team_lo seed_lo \\\n",
"0 2002 North Carolina St. 7 69 Michigan St. 10 \n",
"1 2002 Illinois 4 93 San Diego St. 13 \n",
"2 2002 Texas 6 70 Boston College 11 \n",
"3 2002 Cincinnati 1 90 Boston University 16 \n",
"4 2002 Georgia 3 85 Murray St. 14 \n",
"5 2002 Texas Tech 6 68 Southern Illinois 11 \n",
"6 2002 Maryland 1 85 Siena 16 \n",
"7 2002 Oklahoma 2 71 Illinois Chicago 15 \n",
"8 2002 California 6 82 Penn 11 \n",
"9 2002 Xavier 7 70 Hawaii 10 \n",
"\n",
" score_lo \n",
"0 58 \n",
"1 64 \n",
"2 57 \n",
"3 52 \n",
"4 68 \n",
"5 76 \n",
"6 70 \n",
"7 63 \n",
"8 75 \n",
"9 58 "
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"games.head(10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Perfect, we have 16 years of data, with 32 first round games per year, for 512 total first round NCAA games.\n",
"\n",
"### Checking that the Team Names Match\n",
"\n",
"The code below looks at team names that are in the Washington Post data and don't match a team in the KenPom data, and vice versa. This is the code I used to identify team name mismatches, which were corrected in the code already shown above. I left this code in this notebook to demonstrate the importance of validating data, and how to do it. It's also a useful check when re-running this code in the future."
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
"def first_round_teams(df):\n",
" \"\"\"Get unique team names from Washington Post data set.\"\"\"\n",
" return set(df['team_hi'].unique()) | set(df['team_lo'].unique())"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"237"
]
},
"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"washpost_teams = first_round_teams(games)\n",
"len(washpost_teams)"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"243"
]
},
"execution_count": 29,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"kenpom_teams = set(kenpom['team'].unique())\n",
"len(kenpom_teams)"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"set()"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"washpost_teams - kenpom_teams"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'Alabama A&M',\n",
" 'Alcorn St.',\n",
" 'Coppin St.',\n",
" 'Lamar',\n",
" 'New Orleans',\n",
" 'North Florida'}"
]
},
"execution_count": 31,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"kenpom_teams - washpost_teams"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"These are the only team names that still don't match. They are in the KenPom data, but not the Washington Post historical NCAA tournament data.\n",
"\n",
"Let's look at the specific KenPom rows that have these teams."
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>year</th>\n",
" <th>team</th>\n",
" <th>conf</th>\n",
" <th>seed</th>\n",
" <th>wins</th>\n",
" <th>losses</th>\n",
" <th>kenpom</th>\n",
" <th>adj_em</th>\n",
" <th>adj_o</th>\n",
" <th>adj_d</th>\n",
" <th>...</th>\n",
" <th>opp_d</th>\n",
" <th>ncsos_adj_em</th>\n",
" <th>adj_o_rank</th>\n",
" <th>adj_d_rank</th>\n",
" <th>adj_t_rank</th>\n",
" <th>luck_rank</th>\n",
" <th>sos_adj_em_rank</th>\n",
" <th>opp_o_rank</th>\n",
" <th>opp_d_rank</th>\n",
" <th>ncsos_adj_em_rank</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>251</th>\n",
" <td>2002</td>\n",
" <td>Alcorn St.</td>\n",
" <td>SWAC</td>\n",
" <td>16</td>\n",
" <td>20</td>\n",
" <td>10</td>\n",
" <td>252</td>\n",
" <td>-8.710</td>\n",
" <td>100.100</td>\n",
" <td>108.800</td>\n",
" <td>...</td>\n",
" <td>109.800</td>\n",
" <td>2.600</td>\n",
" <td>213</td>\n",
" <td>268</td>\n",
" <td>23</td>\n",
" <td>8</td>\n",
" <td>325</td>\n",
" <td>325</td>\n",
" <td>325</td>\n",
" <td>101</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1257</th>\n",
" <td>2005</td>\n",
" <td>Alabama A&M</td>\n",
" <td>SWAC</td>\n",
" <td>16</td>\n",
" <td>15</td>\n",
" <td>14</td>\n",
" <td>278</td>\n",
" <td>-12.490</td>\n",
" <td>90.500</td>\n",
" <td>102.900</td>\n",
" <td>...</td>\n",
" <td>106.900</td>\n",
" <td>1.140</td>\n",
" <td>316</td>\n",
" <td>169</td>\n",
" <td>10</td>\n",
" <td>224</td>\n",
" <td>328</td>\n",
" <td>327</td>\n",
" <td>308</td>\n",
" <td>128</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2277</th>\n",
" <td>2008</td>\n",
" <td>Coppin St.</td>\n",
" <td>MEAC</td>\n",
" <td>16</td>\n",
" <td>16</td>\n",
" <td>21</td>\n",
" <td>298</td>\n",
" <td>-14.410</td>\n",
" <td>92.400</td>\n",
" <td>106.800</td>\n",
" <td>...</td>\n",
" <td>105.500</td>\n",
" <td>7.870</td>\n",
" <td>321</td>\n",
" <td>230</td>\n",
" <td>261</td>\n",
" <td>36</td>\n",
" <td>306</td>\n",
" <td>321</td>\n",
" <td>229</td>\n",
" <td>18</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3464</th>\n",
" <td>2012</td>\n",
" <td>Lamar</td>\n",
" <td>Slnd</td>\n",
" <td>16</td>\n",
" <td>23</td>\n",
" <td>12</td>\n",
" <td>108</td>\n",
" <td>6.330</td>\n",
" <td>107.600</td>\n",
" <td>101.300</td>\n",
" <td>...</td>\n",
" <td>103.400</td>\n",
" <td>5.210</td>\n",
" <td>88</td>\n",
" <td>138</td>\n",
" <td>123</td>\n",
" <td>246</td>\n",
" <td>252</td>\n",
" <td>310</td>\n",
" <td>173</td>\n",
" <td>37</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4542</th>\n",
" <td>2015</td>\n",
" <td>North Florida</td>\n",
" <td>ASun</td>\n",
" <td>16</td>\n",
" <td>23</td>\n",
" <td>12</td>\n",
" <td>143</td>\n",
" <td>2.260</td>\n",
" <td>108.400</td>\n",
" <td>106.200</td>\n",
" <td>...</td>\n",
" <td>108.200</td>\n",
" <td>2.230</td>\n",
" <td>88</td>\n",
" <td>204</td>\n",
" <td>51</td>\n",
" <td>230</td>\n",
" <td>331</td>\n",
" <td>312</td>\n",
" <td>321</td>\n",
" <td>91</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5279</th>\n",
" <td>2017</td>\n",
" <td>New Orleans</td>\n",
" <td>Slnd</td>\n",
" <td>16</td>\n",
" <td>20</td>\n",
" <td>12</td>\n",
" <td>178</td>\n",
" <td>-0.520</td>\n",
" <td>101.300</td>\n",
" <td>101.800</td>\n",
" <td>...</td>\n",
" <td>107.600</td>\n",
" <td>8.320</td>\n",
" <td>235</td>\n",
" <td>107</td>\n",
" <td>272</td>\n",
" <td>67</td>\n",
" <td>287</td>\n",
" <td>267</td>\n",
" <td>291</td>\n",
" <td>13</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>6 rows × 24 columns</p>\n",
"</div>"
],
"text/plain": [
" year team conf seed wins losses kenpom adj_em adj_o \\\n",
"251 2002 Alcorn St. SWAC 16 20 10 252 -8.710 100.100 \n",
"1257 2005 Alabama A&M SWAC 16 15 14 278 -12.490 90.500 \n",
"2277 2008 Coppin St. MEAC 16 16 21 298 -14.410 92.400 \n",
"3464 2012 Lamar Slnd 16 23 12 108 6.330 107.600 \n",
"4542 2015 North Florida ASun 16 23 12 143 2.260 108.400 \n",
"5279 2017 New Orleans Slnd 16 20 12 178 -0.520 101.300 \n",
"\n",
" adj_d ... opp_d ncsos_adj_em adj_o_rank adj_d_rank \\\n",
"251 108.800 ... 109.800 2.600 213 268 \n",
"1257 102.900 ... 106.900 1.140 316 169 \n",
"2277 106.800 ... 105.500 7.870 321 230 \n",
"3464 101.300 ... 103.400 5.210 88 138 \n",
"4542 106.200 ... 108.200 2.230 88 204 \n",
"5279 101.800 ... 107.600 8.320 235 107 \n",
"\n",
" adj_t_rank luck_rank sos_adj_em_rank opp_o_rank opp_d_rank \\\n",
"251 23 8 325 325 325 \n",
"1257 10 224 328 327 308 \n",
"2277 261 36 306 321 229 \n",
"3464 123 246 252 310 173 \n",
"4542 51 230 331 312 321 \n",
"5279 272 67 287 267 291 \n",
"\n",
" ncsos_adj_em_rank \n",
"251 101 \n",
"1257 128 \n",
"2277 18 \n",
"3464 37 \n",
"4542 91 \n",
"5279 13 \n",
"\n",
"[6 rows x 24 columns]"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"kenpom[kenpom['team'].isin(kenpom_teams-washpost_teams)]"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>year</th>\n",
" <th>team</th>\n",
" <th>conf</th>\n",
" <th>seed</th>\n",
" <th>wins</th>\n",
" <th>losses</th>\n",
" <th>kenpom</th>\n",
" <th>adj_em</th>\n",
" <th>adj_o</th>\n",
" <th>adj_d</th>\n",
" <th>...</th>\n",
" <th>opp_d</th>\n",
" <th>ncsos_adj_em</th>\n",
" <th>adj_o_rank</th>\n",
" <th>adj_d_rank</th>\n",
" <th>adj_t_rank</th>\n",
" <th>luck_rank</th>\n",
" <th>sos_adj_em_rank</th>\n",
" <th>opp_o_rank</th>\n",
" <th>opp_d_rank</th>\n",
" <th>ncsos_adj_em_rank</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>161</th>\n",
" <td>2002</td>\n",
" <td>Holy Cross</td>\n",
" <td>Pat</td>\n",
" <td>16</td>\n",
" <td>18</td>\n",
" <td>15</td>\n",
" <td>162</td>\n",
" <td>-0.240</td>\n",
" <td>98.100</td>\n",
" <td>98.400</td>\n",
" <td>...</td>\n",
" <td>106.100</td>\n",
" <td>-3.380</td>\n",
" <td>245</td>\n",
" <td>75</td>\n",
" <td>313</td>\n",
" <td>268</td>\n",
" <td>264</td>\n",
" <td>261</td>\n",
" <td>262</td>\n",
" <td>246</td>\n",
" </tr>\n",
" <tr>\n",
" <th>173</th>\n",
" <td>2002</td>\n",
" <td>Siena</td>\n",
" <td>MAAC</td>\n",
" <td>16</td>\n",
" <td>17</td>\n",
" <td>19</td>\n",
" <td>174</td>\n",
" <td>-1.210</td>\n",
" <td>100.800</td>\n",
" <td>102.000</td>\n",
" <td>...</td>\n",
" <td>104.400</td>\n",
" <td>-0.420</td>\n",
" <td>201</td>\n",
" <td>141</td>\n",
" <td>223</td>\n",
" <td>296</td>\n",
" <td>237</td>\n",
" <td>245</td>\n",
" <td>200</td>\n",
" <td>167</td>\n",
" </tr>\n",
" <tr>\n",
" <th>193</th>\n",
" <td>2002</td>\n",
" <td>Boston University</td>\n",
" <td>AE</td>\n",
" <td>16</td>\n",
" <td>22</td>\n",
" <td>10</td>\n",
" <td>194</td>\n",
" <td>-2.740</td>\n",
" <td>101.300</td>\n",
" <td>104.000</td>\n",
" <td>...</td>\n",
" <td>106.900</td>\n",
" <td>0.250</td>\n",
" <td>192</td>\n",
" <td>187</td>\n",
" <td>282</td>\n",
" <td>7</td>\n",
" <td>299</td>\n",
" <td>305</td>\n",
" <td>284</td>\n",
" <td>154</td>\n",
" </tr>\n",
" <tr>\n",
" <th>218</th>\n",
" <td>2002</td>\n",
" <td>Winthrop</td>\n",
" <td>BSth</td>\n",
" <td>16</td>\n",
" <td>17</td>\n",
" <td>12</td>\n",
" <td>219</td>\n",
" <td>-5.310</td>\n",
" <td>97.300</td>\n",
" <td>102.600</td>\n",
" <td>...</td>\n",
" <td>107.900</td>\n",
" <td>-0.980</td>\n",
" <td>258</td>\n",
" <td>155</td>\n",
" <td>243</td>\n",
" <td>79</td>\n",
" <td>311</td>\n",
" <td>313</td>\n",
" <td>304</td>\n",
" <td>188</td>\n",
" </tr>\n",
" <tr>\n",
" <th>251</th>\n",
" <td>2002</td>\n",
" <td>Alcorn St.</td>\n",
" <td>SWAC</td>\n",
" <td>16</td>\n",
" <td>20</td>\n",
" <td>10</td>\n",
" <td>252</td>\n",
" <td>-8.710</td>\n",
" <td>100.100</td>\n",
" <td>108.800</td>\n",
" <td>...</td>\n",
" <td>109.800</td>\n",
" <td>2.600</td>\n",
" <td>213</td>\n",
" <td>268</td>\n",
" <td>23</td>\n",
" <td>8</td>\n",
" <td>325</td>\n",
" <td>325</td>\n",
" <td>325</td>\n",
" <td>101</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>5 rows × 24 columns</p>\n",
"</div>"
],
"text/plain": [
" year team conf seed wins losses kenpom adj_em \\\n",
"161 2002 Holy Cross Pat 16 18 15 162 -0.240 \n",
"173 2002 Siena MAAC 16 17 19 174 -1.210 \n",
"193 2002 Boston University AE 16 22 10 194 -2.740 \n",
"218 2002 Winthrop BSth 16 17 12 219 -5.310 \n",
"251 2002 Alcorn St. SWAC 16 20 10 252 -8.710 \n",
"\n",
" adj_o adj_d ... opp_d ncsos_adj_em adj_o_rank \\\n",
"161 98.100 98.400 ... 106.100 -3.380 245 \n",
"173 100.800 102.000 ... 104.400 -0.420 201 \n",
"193 101.300 104.000 ... 106.900 0.250 192 \n",
"218 97.300 102.600 ... 107.900 -0.980 258 \n",
"251 100.100 108.800 ... 109.800 2.600 213 \n",
"\n",
" adj_d_rank adj_t_rank luck_rank sos_adj_em_rank opp_o_rank \\\n",
"161 75 313 268 264 261 \n",
"173 141 223 296 237 245 \n",
"193 187 282 7 299 305 \n",
"218 155 243 79 311 313 \n",
"251 268 23 8 325 325 \n",
"\n",
" opp_d_rank ncsos_adj_em_rank \n",
"161 262 246 \n",
"173 200 167 \n",
"193 284 154 \n",
"218 304 188 \n",
"251 325 101 \n",
"\n",
"[5 rows x 24 columns]"
]
},
"execution_count": 33,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"kenpom[(kenpom['year'] == 2002) & (kenpom['seed'] == 16)]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see, KenPom has 5 16 seeds for the 2002 tournament. Alcorn St. lost in the play-in game. The other 4 16 seeds played in the first round."
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>year</th>\n",
" <th>team_hi</th>\n",
" <th>seed_hi</th>\n",
" <th>score_hi</th>\n",
" <th>team_lo</th>\n",
" <th>seed_lo</th>\n",
" <th>score_lo</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>2002</td>\n",
" <td>Cincinnati</td>\n",
" <td>1</td>\n",
" <td>90</td>\n",
" <td>Boston University</td>\n",
" <td>16</td>\n",
" <td>52</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>2002</td>\n",
" <td>Maryland</td>\n",
" <td>1</td>\n",
" <td>85</td>\n",
" <td>Siena</td>\n",
" <td>16</td>\n",
" <td>70</td>\n",
" </tr>\n",
" <tr>\n",
" <th>15</th>\n",
" <td>2002</td>\n",
" <td>Duke</td>\n",
" <td>1</td>\n",
" <td>84</td>\n",
" <td>Winthrop</td>\n",
" <td>16</td>\n",
" <td>37</td>\n",
" </tr>\n",
" <tr>\n",
" <th>19</th>\n",
" <td>2002</td>\n",
" <td>Kansas</td>\n",
" <td>1</td>\n",
" <td>70</td>\n",
" <td>Holy Cross</td>\n",
" <td>16</td>\n",
" <td>59</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" year team_hi seed_hi score_hi team_lo seed_lo score_lo\n",
"3 2002 Cincinnati 1 90 Boston University 16 52\n",
"6 2002 Maryland 1 85 Siena 16 70\n",
"15 2002 Duke 1 84 Winthrop 16 37\n",
"19 2002 Kansas 1 70 Holy Cross 16 59"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"games[(games['year'] == 2002) & (games['seed_hi'] == 1)]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can find a list of historical NCAA play-in games [here](https://en.wikipedia.org/wiki/NCAA_Men%27s_Division_I_Basketball_Opening_Round#Single_game_results_(2001%E2%80%932010)). If you look at the list, you will see that the extra KenPom names all correspond to teams that lost in play-in games, and didn't otherwise play in the NCAA tournament. So, it's not a problem that they are missing from the Washington Post data.\n",
"\n",
"### Merging the KenPom and Washington Post Data\n",
"\n",
"The next step is to build a table combining the historical NCAA tournament data with the KenPom data. Each row will correspond to a first round game, with the KenPom data for both teams playing in that game.\n",
"\n",
"Using `pandas`, the way to achieve this is with the `DataFrame` [`merge()`](https://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.merge.html) method. We want to merge the KenPom data as new columns in the NCAA game `DataFrame`.\n",
"\n",
"Since we are going to be merging KenPom data for each team in a game, let's first write a function to merge the data for either the higher seeded teams or the lower seeded teams. We also need to make sure to clean up any unnecessary columns that get added by the `merge()` method, as well as make sure the new columns have the correct names. Each merged KenPom column will have the suffix `'_hi'` or `'_lo'` depending upon which team is being merged."
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [],
"source": [
"def merge_kenpom(games, kenpom, HL):\n",
" \"\"\"Merge KenPom information for one team (high or low seed) with NCAA Tournament games.\"\"\"\n",
" if HL == 'H':\n",
" suffix = '_hi'\n",
" elif HL == 'L':\n",
" suffix = '_lo'\n",
" else:\n",
" raise ValueError('invalid HL', HL)\n",
" df = games.merge(kenpom, left_on=['year', 'team'+suffix], right_on=['year', 'team'], validate='one_to_one')\n",
" df = df.drop(columns=['team', 'seed'])\n",
" cols = [col for col in kenpom.columns if col != 'year']\n",
" new_cols = {col: col+suffix for col in cols}\n",
" df = df.rename(columns=new_cols)\n",
" return df"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, we can just call this function twice: once for the higher seeded teams, and once for the lower seeded teams."
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [],
"source": [
"def merge_ncaa_kenpom(games, kenpom):\n",
" \"\"\"Merge KenPom information with NCAA Tournament games.\"\"\"\n",
" df = merge_kenpom(games, kenpom, 'H')\n",
" df = merge_kenpom(df, kenpom, 'L')\n",
" return df"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(512, 49)"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df = merge_ncaa_kenpom(games, kenpom)\n",
"df.shape"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Since we stil have 512 rows, we know we didn't lose any game information by merging. Let's see what columns we have now."
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Index(['year', 'team_hi', 'seed_hi', 'score_hi', 'team_lo', 'seed_lo',\n",
" 'score_lo', 'conf_hi', 'wins_hi', 'losses_hi', 'kenpom_hi', 'adj_em_hi',\n",
" 'adj_o_hi', 'adj_d_hi', 'adj_t_hi', 'luck_hi', 'sos_adj_em_hi',\n",
" 'opp_o_hi', 'opp_d_hi', 'ncsos_adj_em_hi', 'adj_o_rank_hi',\n",
" 'adj_d_rank_hi', 'adj_t_rank_hi', 'luck_rank_hi', 'sos_adj_em_rank_hi',\n",
" 'opp_o_rank_hi', 'opp_d_rank_hi', 'ncsos_adj_em_rank_hi', 'conf_lo',\n",
" 'wins_lo', 'losses_lo', 'kenpom_lo', 'adj_em_lo', 'adj_o_lo',\n",
" 'adj_d_lo', 'adj_t_lo', 'luck_lo', 'sos_adj_em_lo', 'opp_o_lo',\n",
" 'opp_d_lo', 'ncsos_adj_em_lo', 'adj_o_rank_lo', 'adj_d_rank_lo',\n",
" 'adj_t_rank_lo', 'luck_rank_lo', 'sos_adj_em_rank_lo', 'opp_o_rank_lo',\n",
" 'opp_d_rank_lo', 'ncsos_adj_em_rank_lo'],\n",
" dtype='object')"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.columns"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see, we have all the original game information, plus KenPom information for both the higher seeded and lower seeded teams.\n",
"\n",
"### Preparing the Data for Analysis\n",
"\n",
"We need to do a few more things to the data before we begin our upset analysis.\n",
"\n",
"#### Dummy Variables\n",
"\n",
"First, we will create two new important columns. The first will indicate that the game was an \"upset\", defined as the lower seed winning. The second will flag games where the team with the worse KenPom ranking was actually seeded higher. We will refer to this situation as a \"KenPom inversion\".\n",
"\n",
"These columns will each be \"dummy\" variables, with the value 0 denoting False/No, and 1 denoting True/Yes."
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [],
"source": [
"def is_upset(row):\n",
" if row['score_lo'] > row['score_hi']:\n",
" return 1\n",
" else:\n",
" return 0"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [],
"source": [
"def kenpom_inverted(row):\n",
" if row['kenpom_lo'] < row['kenpom_hi']:\n",
" return 1\n",
" else:\n",
" return 0"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"An upset is simple to determine: the lower seeded team outscores the higher seed team.\n",
"\n",
"On the other hand, you may have to stare at the \"KenPom inversion\" function a bit to convince yourself that it's correct. The best KenPom ranking is 1, so the function is looking for games where the lower seeded team in the tournament has a lower number (higher ranking) from KenPom.\n",
"\n",
"Now we can put these functions together to merge the data and create the dummy variables. Also, since we already know that the first seed has never been upset, we will drop the 64 1-16 games from our data set going forward."
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [],
"source": [
"def merge_data(games, kenpom):\n",
" \"\"\"Merge data and create dummy variables.\"\"\"\n",
" df = merge_ncaa_kenpom(games, kenpom)\n",
" df = df[df['seed_hi'] != 1]\n",
" df['upset'] = df.apply(is_upset, axis=1)\n",
" df['kenpom_inverted'] = df.apply(kenpom_inverted, axis=1)\n",
" start_cols = [\n",
" 'year',\n",
" 'upset',\n",
" 'kenpom_inverted',\n",
" 'team_hi', 'seed_hi', 'kenpom_hi', 'team_lo', 'seed_lo', 'kenpom_lo',\n",
" ]\n",
" cols = (\n",
" start_cols +\n",
" [col for col in df.columns if '_hi' in col and 'rank' not in col and col not in start_cols] +\n",
" [col for col in df.columns if '_lo' in col and 'rank' not in col and col not in start_cols]\n",
" )\n",
" return df[cols].reset_index(drop=True)"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(448, 35)"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df = merge_data(games, kenpom)\n",
"df.shape"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Index(['year', 'upset', 'kenpom_inverted', 'team_hi', 'seed_hi', 'kenpom_hi',\n",
" 'team_lo', 'seed_lo', 'kenpom_lo', 'score_hi', 'conf_hi', 'wins_hi',\n",
" 'losses_hi', 'adj_em_hi', 'adj_o_hi', 'adj_d_hi', 'adj_t_hi', 'luck_hi',\n",
" 'sos_adj_em_hi', 'opp_o_hi', 'opp_d_hi', 'ncsos_adj_em_hi', 'score_lo',\n",
" 'conf_lo', 'wins_lo', 'losses_lo', 'adj_em_lo', 'adj_o_lo', 'adj_d_lo',\n",
" 'adj_t_lo', 'luck_lo', 'sos_adj_em_lo', 'opp_o_lo', 'opp_d_lo',\n",
" 'ncsos_adj_em_lo'],\n",
" dtype='object')"
]
},
"execution_count": 43,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.columns"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### Upsets and KenPom Ranks\n",
"\n",
"Let's take a quick look at how many upsets occurred during the 2002-2017 first round games. In our [prior analysis on first round upsets](http://practicallypredictable.com/2018/03/07/march-madness-first-round-upsets/), we used NCAA tournament data going back to 1985, when the modern 64-team format started. We should make sure that the 2002-2017 sub-period isn't very different from the full data set before we delve too deeply in our analysis.\n",
"\n",
"Since the upset dummy variable is either 0 or 1, we can sum it to get the count of upsets that occurred. If we group by the higher seed, we can compare the upsets in the 2002-2017 period with the full 1985-2017 history."
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"seed_hi\n",
"2 0.062\n",
"3 0.125\n",
"4 0.188\n",
"5 0.422\n",
"6 0.438\n",
"7 0.359\n",
"8 0.406\n",
"Name: upset, dtype: float64"
]
},
"execution_count": 44,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.groupby(['seed_hi'])['upset'].sum() / (4*16)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For the most part, these upset frequencies aren't significantly different from the full 33-year period. The eighth seed upset frequency above is 40.6%, whereas in the full 33-year period it's 49.2%. However, as we discussed in the earlier post, the 8-9 game is never really an upset in the correct meaning of the word, so this shouldn't concern us too much. It's unlikely that there was a meaningful change in the probability of eighth seeds winning these games after 2002 compared to previously.\n",
"\n",
"Overall, there are 128 \"upsets\" (again, including the 8-9 games) in our data set of first round games since 2002."
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0 320\n",
"1 128\n",
"Name: upset, dtype: int64"
]
},
"execution_count": 45,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df['upset'].value_counts()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On the other hand, there are 62 cases where the better-ranked team (by KenPom) was not the higher seeded team in the NCAA tournament first round game."
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0 386\n",
"1 62\n",
"Name: kenpom_inverted, dtype: int64"
]
},
"execution_count": 46,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df['kenpom_inverted'].value_counts()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's look at how these variables interact, using `pandas` [`crosstab()`](https://pandas.pydata.org/pandas-docs/stable/generated/pandas.crosstab.html) function."
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
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"<table border=\"1\" class=\"dataframe\">\n",
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" <th>kenpom_inverted</th>\n",
" <th>0</th>\n",
" <th>1</th>\n",
" </tr>\n",
" <tr>\n",
" <th>upset</th>\n",
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" <td>86</td>\n",
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"</div>"
],
"text/plain": [
"kenpom_inverted 0 1\n",
"upset \n",
"0 300 20\n",
"1 86 42"
]
},
"execution_count": 47,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pd.crosstab(index=df['upset'], columns=df['kenpom_inverted'])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Look first at the \"1\" column for the KenPom inversion dummy variable. Of the 62 times a team with higher KenPom rank was seeded worse in the tournament, 42 (or more than $\\frac 2 3$ of the time) resulted in an \"upset\" (again, including the 8-9 games).\n",
"\n",
"That seems promising. If you see a matchup between teams where the tournament seed and KenPom rankings are inverted, it would suggest you have much better than even odds going with the KenPom ranking in picking the winner.\n",
"\n",
"On the flip side, however, look at the \"1\" row for the upset dummy variable. Of the 128 upsets, only 42 (or roughly $\\frac 1 3$) had the KenPom rankings inverted.\n",
"\n",
"In other words, conditional on seeing a KenPom inversion, an upset is more likely than not. However, if you only focus on KenPom inversions, you'll miss a lot of potential upsets.\n",
"\n",
"We can shed more light on this by looking at the distribution of upsets and KenPom inversions by the seed of the higher seeded team."
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
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" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>kenpom_inverted</th>\n",
" <th>upset</th>\n",
" </tr>\n",
" <tr>\n",
" <th>seed_hi</th>\n",
" <th></th>\n",
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" </tr>\n",
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" <td>23</td>\n",
" <td>26</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" kenpom_inverted upset\n",
"seed_hi \n",
"2 0 4\n",
"3 0 8\n",
"4 0 12\n",
"5 5 27\n",
"6 11 28\n",
"7 23 23\n",
"8 23 26"
]
},
"execution_count": 48,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.groupby(['seed_hi'])['kenpom_inverted', 'upset'].sum()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see that the KenPom inversion is only relevant for the fifth seed or below, and is much more common in the 7-10 and 8-9 matchups. This makes sense, as it's clearly more likely that NCAA seeding would diverge from KenPom rankings for the middle-quality teams.\n",
"\n",
"We can slice the data more finely to better see where the KenPom inversion might be useful in predicting upsets."
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
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"\n",
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"\n",
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"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
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" <th colspan=\"2\" halign=\"left\">0</th>\n",
" <th colspan=\"2\" halign=\"left\">1</th>\n",
" </tr>\n",
" <tr>\n",
" <th>upset</th>\n",
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" <th>1</th>\n",
" <th>0</th>\n",
" <th>1</th>\n",
" </tr>\n",
" <tr>\n",
" <th>seed_hi</th>\n",
" <th></th>\n",
" <th></th>\n",
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" <td>7</td>\n",
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" <th>8</th>\n",
" <td>28</td>\n",
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" <td>10</td>\n",
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" </tr>\n",
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"</table>\n",
"</div>"
],
"text/plain": [
"kenpom_inverted 0 1 \n",
"upset 0 1 0 1\n",
"seed_hi \n",
"2 60 4 0 0\n",
"3 56 8 0 0\n",
"4 52 12 0 0\n",
"5 35 24 2 3\n",
"6 35 18 1 10\n",
"7 34 7 7 16\n",
"8 28 13 10 13"
]
},
"execution_count": 49,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"upset_counts = pd.DataFrame(\n",
" df.groupby(['seed_hi', 'upset', 'kenpom_inverted']\n",
").size()).unstack().unstack().fillna(0).astype(int)\n",
"upset_counts.columns = upset_counts.columns.droplevel()\n",
"upset_counts"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The chance of picking an upset simply using inverted KenPom rankings appears to be most favorable for sixth and seventh seed games. For fifth seed and eighth seed games, the impact doesn't seem as powerful.\n",
"\n",
"#### An Important Note on NCAA Tournament Selection, Seeding and Picking Upsets\n",
"\n",
"There has been a long and fierce debate about the methods and inputs the NCAA tournament committee has used to select teams for March Madness over the years. You can read about the history and some of the issues [here](https://fivethirtyeight.com/features/the-ncaa-is-modernizing-the-way-it-picks-march-madness-teams/), [here](http://www.espn.com/mens-college-basketball/story/_/id/22144913/ncaa-says-year-test-run-new-evaluation-system) and in the underlying linked articles. This year, [the committee has modified its process](https://www.ncaa.com/news/basketball-men/bracketiq/2018-02-15/ncaa-selection-committee-adjusts-team-sheets-emphasizing) to include additional data, including KenPom, into the selection decisions.\n",
"\n",
"I raise this issue here because it's important to note that one reason why KenPom rankings and tournament seeding divered in prior years may have been due (at least in part) to the fact that the tournament committee didn't look at KenPom data. This year, the committee will be looking at many new pieces of information, of which KenPom will be a part.\n",
"\n",
"The point is, the selection process itself is an input into the likelihood of an upset. If the selection and seeding process changes dramatically, historical data may be less useful in picking upsets going forward. This is something to keep an eye on as the committee continues to modify its process going forward.\n",
"\n",
"#### Repeating the Caveat about the Historical KenPom Data\n",
"\n",
"Also, keep in mind that the historical KenPom data include the impact of the NCAA tournament. Suffering an upset in the first round could negatively affect its KenPom ranking, perhaps lowering it enough to actualy cause the inversion in KenPom rankings. If this occurred, rather than _predicting_ the upset, the KenPom inversion would be _because_ of the upset. Until we obtain pre-tournament historical KenPom data, we can't verify whether this situation actually occurred often enough to matter.\n",
"\n",
"### Making Predictions with KenPom Data\n",
"\n",
"Let's see how to use the KenPom data to estimate win probability.\n",
"\n",
"The procedure is relatively simple:\n",
"\n",
"- Estimate the number of possessions in the game for each team.\n",
"- Estimate the points per possession differential between the two teams.\n",
"- Estimate the point spread as the product of the number of possessions per team and the points per possession differential.\n",
"- Convert the point spread into a win probability.\n",
"\n",
"Let's go through this one step at a time.\n",
"\n",
"#### Estimating the Number of Possessions Per Team\n",
"\n",
"Each team has its own Adjusted Tempo measure, $AdjT_H$ and $AdjT_L$, for the higher and lower seed teams, respectively.\n",
"\n",
"Simply average these two tempo measures to estimate the number of possesions each team has (which are assumed to be equal). Call the number of possessions for each team $POSS$:\n",
"\n",
"$$ POSS = \\frac 1 2 (AdjT_H + AdjT_L) $$\n",
"\n",
"#### Estimating the Points Per Possession Differential\n",
"\n",
"We'll need to do a little algebra now.\n",
"\n",
"If we want to predict the offensive output of a team, we need to consider both the team's offensive efficiency and its opponent's defensive efficiency. If the opponent has a good defense (i.e., a low _AdjD_), that should drag down the team's offensive production compared to an average opponent. On the other hand, versus a bad defense (high _AdjD_), the team might put up even better offensive numbers.\n",
"\n",
"Let's focus first on the higher seeded team, with offensive efficiency $AdjO_H$, playing against a lower seeded opponent with defensive efficiency $AdjD_L$.\n",
"\n",
"The predicted KenPom points per possession for the higher seeded team is:\n",
"\n",
"$$ PPP_H = \\frac 1 2 (AdjO_H + AdjD_L) $$\n",
"\n",
"Similarly, the predicted KenPom points per possession for the lower seeded team is:\n",
"\n",
"$$ PPP_L = \\frac 1 2 (AdjO_L + AdjD_H) $$\n",
"\n",
"If you subtract these two, you'll get the points per possession differential. The team with the better (positive) differential is expected to win the game in the KenPom framework.\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"PPP_H - PPP_L &= \\frac 1 2 (AdjO_H + AdjD_L) - \\frac 1 2 (AdjO_L + AdjD_H) \\\\\n",
"&= \\frac 1 2 (AdjO_H + AdjD_L - AdjO_L - AdjD_H) \\\\\n",
"&= \\frac 1 2 (AdjO_H - AdjD_H - AdjO_L + AdjD_L) \\\\\n",
"&= \\frac 1 2 ((AdjO_H - AdjD_H) - (AdjO_L - AdjD_L)) \\\\\n",
"&= \\frac 1 2 (AdjEM_H - AdjEM_L)\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"As you can see, the estimated points per possession differential is just the difference of the efficiency margins for each team.\n",
"\n",
"#### Estimate the Point Spread\n",
"\n",
"To get a spread measured in points, just multiply the differential by the number of possessions per team.\n",
"\n",
"$$ PS_{HL} = POSS \\times (AdjEM_H - AdjEM_L) $$\n",
"\n",
"#### Estimate the Win Probability\n",
"\n",
"Sometimes, the point spread is interesting information in and of itself (for example, if you are comparing the KenPom estimate to a betting line).\n",
"\n",
"Under the KenPom framework, the team with the higher effiency margin is expected to win the game. This is true whether the predicted point spread is 0.1 points or 20 points. To convert the point spread into a win probabilty, use the following rules:\n",
"\n",
"- Divide the point spread by 11 points (see [here](https://www.reddit.com/r/CollegeBasketball/comments/5xir8t/calculating_win_probability_and_margin_of_victory/) and [here](https://www.reddit.com/r/CollegeBasketball/comments/5tl6gj/calculating_probability_based_on_kenpoms_adjusted/))\n",
"- Take this scaled value and plug it into the [standard normal cumulative distribution function](http://www.itl.nist.gov/div898/handbook/eda/section3/eda3661.htm)\n",
"- The result is the estimated win probability\n",
"\n",
"The function below computes the win probability given the KenPom predicted point spread.\n",
"\n",
"It uses the [error function](https://en.wikipedia.org/wiki/Error_function) `erf()` in the Python `math` package to compute the standard normal cumulative distribution function. This is the probability of a standard normal random variable being less than the parameter (in this case, the KenPom point spread divided by 11)."
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {},
"outputs": [],
"source": [
"def kenpom_prob(point_spread, std=11):\n",
" \"\"\"Calculate team win probability using KenPom predicted point spread.\"\"\"\n",
" return 0.5 * (1 + math.erf((point_spread) / (std*math.sqrt(2))))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### A Quick Example\n",
"\n",
"Let's look at the upcoming first round matchup between Virginia and UMBC, using KenPom data as of Monday, March 12, 2018.\n",
"\n",
"| KenPom Value | Virginia | UMBC |\n",
"| :----------- | -------: | --------: |\n",
"| _AdjT_ | 59.1 | 68.1 |\n",
"| _AdjO_ | 116.5 | 103.3 |\n",
"| _AdjD_ | 84.4 | 105.3 |\n",
"| _AdjEM_ | +32.15 | -1.99 |\n",
"\n",
"From these KenPom values, we see that the predicted possessions per game is 63.66 for each team (about 18.9 seconds per possession).\n",
"\n",
"The efficiency margin differential is 34.14 points per 100 possessions in favor of Virginia. This leads to a KenPom prediction that the Cavaliers should beat the Retrievers by 21.7 points.\n",
"\n",
"Plug this point spread into the above function:"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.9757366785052486"
]
},
"execution_count": 51,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"kenpom_prob(21.7)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This formula predicts that Virginia has greater than 97.5% probability of advancing to the second round.\n",
"\n",
"### Analyzing Historical Upsets with KenPom Win Probabilities\n",
"\n",
"Let's apply this method to our historical KenPom data."
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [],
"source": [
"def kenpom_predictions(df):\n",
" \"\"\"Calculate historical KenPom point spread and win probability predictions.\"\"\"\n",
" df = df.copy()\n",
" df['kenpom_poss'] = (df['adj_t_hi'] + df['adj_t_lo']) / 2\n",
" df['kenpom_em_diff'] = df['adj_em_hi'] - df['adj_em_lo']\n",
" df['kenpom_spread'] = df['kenpom_em_diff'] * df['kenpom_poss'] / 100\n",
" df['win_prob_hi'] = df['kenpom_spread'].apply(kenpom_prob)\n",
" df['win_prob_lo'] = 1 - df['win_prob_hi']\n",
" start_cols = [\n",
" 'year', 'upset', 'kenpom_inverted', 'kenpom_spread', 'kenpom_em_diff',\n",
" ]\n",
" end_cols = ['kenpom_poss',]\n",
" cols = start_cols + [col for col in df.columns if col not in start_cols and col not in end_cols] + end_cols\n",
" return df[cols]"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Index(['year', 'upset', 'kenpom_inverted', 'kenpom_spread', 'kenpom_em_diff',\n",
" 'team_hi', 'seed_hi', 'kenpom_hi', 'team_lo', 'seed_lo', 'kenpom_lo',\n",
" 'score_hi', 'conf_hi', 'wins_hi', 'losses_hi', 'adj_em_hi', 'adj_o_hi',\n",
" 'adj_d_hi', 'adj_t_hi', 'luck_hi', 'sos_adj_em_hi', 'opp_o_hi',\n",
" 'opp_d_hi', 'ncsos_adj_em_hi', 'score_lo', 'conf_lo', 'wins_lo',\n",
" 'losses_lo', 'adj_em_lo', 'adj_o_lo', 'adj_d_lo', 'adj_t_lo', 'luck_lo',\n",
" 'sos_adj_em_lo', 'opp_o_lo', 'opp_d_lo', 'ncsos_adj_em_lo',\n",
" 'win_prob_hi', 'win_prob_lo', 'kenpom_poss'],\n",
" dtype='object')"
]
},
"execution_count": 53,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data = kenpom_predictions(df)\n",
"data.columns"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's look at the range of predicted first round NCAA tournament win probabilities for the 2-15 seeds in our historical KenPom data. Remember the caveat that these win probabilities are probably affected by the fact that the KenPom data were retroactively calculated, and include NCAA tournament game results in the calculations."
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
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" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>count</th>\n",
" <th>mean</th>\n",
" <th>std</th>\n",
" <th>min</th>\n",
" <th>25%</th>\n",
" <th>50%</th>\n",
" <th>75%</th>\n",
" <th>max</th>\n",
" </tr>\n",
" <tr>\n",
" <th>seed_hi</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>64.000</td>\n",
" <td>0.904</td>\n",
" <td>0.050</td>\n",
" <td>0.713</td>\n",
" <td>0.887</td>\n",
" <td>0.917</td>\n",
" <td>0.935</td>\n",
" <td>0.983</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>64.000</td>\n",
" <td>0.804</td>\n",
" <td>0.084</td>\n",
" <td>0.561</td>\n",
" <td>0.759</td>\n",
" <td>0.823</td>\n",
" <td>0.866</td>\n",
" <td>0.958</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>64.000</td>\n",
" <td>0.758</td>\n",
" <td>0.088</td>\n",
" <td>0.536</td>\n",
" <td>0.699</td>\n",
" <td>0.779</td>\n",
" <td>0.830</td>\n",
" <td>0.903</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>64.000</td>\n",
" <td>0.652</td>\n",
" <td>0.104</td>\n",
" <td>0.435</td>\n",
" <td>0.565</td>\n",
" <td>0.653</td>\n",
" <td>0.734</td>\n",
" <td>0.844</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>64.000</td>\n",
" <td>0.589</td>\n",
" <td>0.100</td>\n",
" <td>0.270</td>\n",
" <td>0.531</td>\n",
" <td>0.596</td>\n",
" <td>0.664</td>\n",
" <td>0.792</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>64.000</td>\n",
" <td>0.543</td>\n",
" <td>0.110</td>\n",
" <td>0.256</td>\n",
" <td>0.474</td>\n",
" <td>0.541</td>\n",
" <td>0.629</td>\n",
" <td>0.758</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>64.000</td>\n",
" <td>0.526</td>\n",
" <td>0.082</td>\n",
" <td>0.269</td>\n",
" <td>0.480</td>\n",
" <td>0.526</td>\n",
" <td>0.584</td>\n",
" <td>0.709</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" count mean std min 25% 50% 75% max\n",
"seed_hi \n",
"2 64.000 0.904 0.050 0.713 0.887 0.917 0.935 0.983\n",
"3 64.000 0.804 0.084 0.561 0.759 0.823 0.866 0.958\n",
"4 64.000 0.758 0.088 0.536 0.699 0.779 0.830 0.903\n",
"5 64.000 0.652 0.104 0.435 0.565 0.653 0.734 0.844\n",
"6 64.000 0.589 0.100 0.270 0.531 0.596 0.664 0.792\n",
"7 64.000 0.543 0.110 0.256 0.474 0.541 0.629 0.758\n",
"8 64.000 0.526 0.082 0.269 0.480 0.526 0.584 0.709"
]
},
"execution_count": 54,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data.groupby(['seed_hi'])['win_prob_hi'].describe()"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
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" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>count</th>\n",
" <th>mean</th>\n",
" <th>std</th>\n",
" <th>min</th>\n",
" <th>25%</th>\n",
" <th>50%</th>\n",
" <th>75%</th>\n",
" <th>max</th>\n",
" </tr>\n",
" <tr>\n",
" <th>seed_lo</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>64.000</td>\n",
" <td>0.474</td>\n",
" <td>0.082</td>\n",
" <td>0.291</td>\n",
" <td>0.416</td>\n",
" <td>0.474</td>\n",
" <td>0.520</td>\n",
" <td>0.731</td>\n",
" </tr>\n",
" <tr>\n",
" <th>10</th>\n",
" <td>64.000</td>\n",
" <td>0.457</td>\n",
" <td>0.110</td>\n",
" <td>0.242</td>\n",
" <td>0.371</td>\n",
" <td>0.459</td>\n",
" <td>0.526</td>\n",
" <td>0.744</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>64.000</td>\n",
" <td>0.411</td>\n",
" <td>0.100</td>\n",
" <td>0.208</td>\n",
" <td>0.336</td>\n",
" <td>0.404</td>\n",
" <td>0.469</td>\n",
" <td>0.730</td>\n",
" </tr>\n",
" <tr>\n",
" <th>12</th>\n",
" <td>64.000</td>\n",
" <td>0.348</td>\n",
" <td>0.104</td>\n",
" <td>0.156</td>\n",
" <td>0.266</td>\n",
" <td>0.347</td>\n",
" <td>0.435</td>\n",
" <td>0.565</td>\n",
" </tr>\n",
" <tr>\n",
" <th>13</th>\n",
" <td>64.000</td>\n",
" <td>0.242</td>\n",
" <td>0.088</td>\n",
" <td>0.097</td>\n",
" <td>0.170</td>\n",
" <td>0.221</td>\n",
" <td>0.301</td>\n",
" <td>0.464</td>\n",
" </tr>\n",
" <tr>\n",
" <th>14</th>\n",
" <td>64.000</td>\n",
" <td>0.196</td>\n",
" <td>0.084</td>\n",
" <td>0.042</td>\n",
" <td>0.134</td>\n",
" <td>0.177</td>\n",
" <td>0.241</td>\n",
" <td>0.439</td>\n",
" </tr>\n",
" <tr>\n",
" <th>15</th>\n",
" <td>64.000</td>\n",
" <td>0.096</td>\n",
" <td>0.050</td>\n",
" <td>0.017</td>\n",
" <td>0.065</td>\n",
" <td>0.083</td>\n",
" <td>0.113</td>\n",
" <td>0.287</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" count mean std min 25% 50% 75% max\n",
"seed_lo \n",
"9 64.000 0.474 0.082 0.291 0.416 0.474 0.520 0.731\n",
"10 64.000 0.457 0.110 0.242 0.371 0.459 0.526 0.744\n",
"11 64.000 0.411 0.100 0.208 0.336 0.404 0.469 0.730\n",
"12 64.000 0.348 0.104 0.156 0.266 0.347 0.435 0.565\n",
"13 64.000 0.242 0.088 0.097 0.170 0.221 0.301 0.464\n",
"14 64.000 0.196 0.084 0.042 0.134 0.177 0.241 0.439\n",
"15 64.000 0.096 0.050 0.017 0.065 0.083 0.113 0.287"
]
},
"execution_count": 55,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"data.groupby(['seed_lo'])['win_prob_lo'].describe()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Not surprisingly, the average win probabilities drop steadily as a function of the seed. There is quite a range in the values by seed, however.\n",
"\n",
"### Visualizing the Historical Win Probability Distributions\n",
"\n",
"We can create a [violin plot](https://en.wikipedia.org/wiki/Violin_plot) to better understand the distribution of win probability by seed. A violin plot is shows the frequency distribution of data organized by category. We can organize the data by seed and whether the game was an upset or not, and see if there is a pattern in the KenPom win probability distributions."
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [],
"source": [
"def violinplot_kenpom(data, ax, diff, ylabel, legend_loc='upper right'):\n",
" \"\"\"Violin plot of statistics by higher seed, upset vs. no upset.\"\"\"\n",
" ax = sns.violinplot(data=data, x='seed_hi', y=diff, hue='upset', split=True, inner='quart', cut=0, ax=ax)\n",
" ax.set_xlabel('Higher Seed')\n",
" ax.set_ylabel(ylabel)\n",
" ax.legend(loc=legend_loc, title='upset')\n",
" return ax"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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AZjPD8rCxjh49whtvvEEgLR/XyBk9z9jqkf2Dfn+Q+vr2OEUohBCiNz29II7lOlwb0PXOljOJF5qmfQQ8CrxFZDlyO9AQiyDS0tL4xS8epHRsGemn9pNRuT0Wt+mjSPalmGD2bSCeeOIxKirKcQ2bhi9/rNHhJCVd13nssUfQdZ22skXGL5ULIYSIulj+Zt8KXA9wZs/X/s4HVFUtBAo0TVsE/AswCjgQq0CysrL49a/+l5KS4WRW7iStZl+sbtWzMzNfFkviJV+7d+/i9ddfIejMpW3sxUaHk7S2bNnE3r178OaV4s8dbXQ4QgghYiCWazyvAZ9TVfU9IlvNv6aq6neAo8AbQJmqqjsBP3CfpmkxLf2el5fPr3/9v/zzv3wLjm0ko3IH+pkTkN4ilfbSBedcn3tgBTZ309mPgxmFNE++4ZxrOhtwWwOePsWgnDnlaLH0b++a0VyuDh588AFQLDSrV4NV9mXFgs/n47HHHgHFQtvYGLS3EkIIYQoxS740TQsD3/rUpw93ef+eWN27O8OHj+CBX/yGe+/9BpaAh7A9DV2JYyKkR5YcE23Z8bHHHqWhoZ720XMJZhYZHU7SWrbsOerqaukYOZNQWq7R4QghhIiRIbe7eeJElZ/85Bfcf/9/EVasNMy4Cz3F+Znrmqfe3OtYnQ24cw+uxNFU3vvNdR2LJbH28OzZ8wGrV79JID2fjlGze3+CGJDq6ipeeul5wvZ0OkbNMTocIYQQMZRYmUCUXHzxpXz1q1/H6msn9/DbEKeip4quY7EmzpKj3+/nt7/7DaDQOmExJNhyaaLQdZ3f//63BAIBWssuQbdJtwAhhEhmQzL5AvjiF7/M3LnzSW2pJL1qd3xuGtaxWRNnsvEvf3mRmuoqXMOnSxX7GNq0aQM7d27HlzNKmpMLIcQQMGSTL4vFwn33/ZDc3DyyKrdjczXG/J5KWMeaIDNfDQ31vPDCs4TtabSPmdf7E8SAuFwd/P4PvwOLldbxl5uiCLAQQojYGrLJF0BOTi7f+c73IBwi+8j62C8/6nrCFBH985+fxO/30TZmProtMavxJ4Inn1xCc1Mj7aPmEHLmGB2OEEKIOBjSyRfA/PkXc9llV2JvP42z9qOY3ksJJ0byVVVVyZo1bxFIy8NTPMnocJLWwYP7WbnydYJpuXRIj0whhBgyhnzyBXDPPfdit6eSVfE+SigQs/so4XBCJF8vvPAsuh6mY8w8qbAeI36/n4f+99fouk7L+CvlMIMQQgwh8pcVKCws4s4778Lid5F2an/vTxggJaybvnF0Q0M969evJZCWhzd/nNHhJK1ly57jZGUFrmHTCGQPNzocIYQQcWT+aZg4+fzn/4bXl/+VcNUeXMOmQyxOJSbAsuMbb7xOKBTCNeKiuG3+tvg6APinf/p6VArQzp9/MX/3d98wbTHbEyfKeeGFZwmlZtBeutDocIQQQsSZuTOBOMrIyOTmm25j2bLnSKv9CPfwaf0eI2f7UfQPui+2Gll2NO/MVygUYtmy59CBjMqdZFTuHHTrpbMsVupnf/mca5ynD5FRuQOrrx2A4ycrYJB9LxV/kOPHj1FQUMBNN902qLFiIRQK8dBDvyIUCtKqXi41vYQQYgiS5KuL2267k7/8ZRnpNXtxD5sa/ZmfkLmXHffu3UM4HEa3GBNjzefnwiA7AFhdPore2ssf/vB/XHDBZCZMUKMUXXQsX/4qhw8fwlM4AV/+WKPDEUIIYQBJvrrIy8vn8suvYN26tdhbq/DnjOrX81vmjcc7Kv/8D+o6I154z9TJ19atmwFonnIj/pyR3V7Xn9ZLPfGUTMZTMpnibUtQgr7+BduNUHoqTQsnUPDuIX72sx/xxz8uJT09PSpjD1Zt7WmWPrUEPcVBW9mlRocjhBDCILLh/lNuvPFWANJOHYzuwOFIDTEz7/nasWMbui0Vf9Ywo0MZFN/wXNonj+DUqRoeeeQho8MBIi2Efve7h/B5vbSOXUTYnmZ0SEIIIQwiydenTJkyjdGjS3E0HkMJeKI2rhIKA5CSYs49PvX1dZw+fQpf1vCkKHvQduFo/PkZrFu3lnXr3jY6HDZuXM/One/jyxmFp+gCo8MRQghhIEm+PkVRFK677gYUPYyzToveuGdmvlJSzDnzdfhwpMCsP6vE4EiixGKh6eKJ6ClWfvd/D1FXV2tYKB0d7fz+979Dt9hoHX+FtBASQoghTpKv81i8+BqsVitp0ax4H47MfJn1tGNFReSUZjC9wOBIoieU6aRl5lg8bjcPPfQr9Fi3j+rG0qV/oqWlmfZRswk5sw2JQQghhHlI8nUeubm5zJ+/kBRXA7aO+qiMqYQ6Z77MmXzV1FQDEEyy/oLucUV4h+eye/cu1qxZFff7HzmiRVoIOXNxSQshIYQQSPLVrWuuidStSjt9KCrjKWFz7/lqbo7U7QrZzXEyMGoUhZa549BTrDz2+KO0tDTH7da6rvPoow+j6zqt4y5Lir10QgghBk+Sr27MnTuP3Nw80uo1CAUHP6DJ93y1t7ejW6xgNefM3GCE0lNpnT4aV0cHS5cuidt93333HQ4dOoinYDz+3P6VLRFCCJG8JPnqhtVq45prrkMJ+nA2Hu39Cb34ZObLnMlNMBhM6pkZ18RhBLLTWL36TY4dG/y/Z2/8fh9PPPE4WKy0j5UWQkIIIT5hzmkYk7juuptYtux5nKcODro8QOeeL2ssekZGizH70ePDotA6s5SCdw/x1FNL+PnP/yemt1u+/FXq62vpGDmTkEM22cdLKBTiyScf4/Tp031+TmpqKl/96tcpKUns+nZCiMRh4kzAeMOHj2DmzNns3r0Lm6uRYHo31ev74szMl91uzj1fTqcTQgHQ9aQtheAbloOvKIvt27ehaR+hqpNich+Xy8ULLz6LbkulY+SsmNxDnN+mTe/yl78s6/fzxo+fwB133BWDiIQQ4rMk+erFTTfdxu7du0g7tZ+28ZcPeJzOmS+zVrjPyMhEQUcJ+tBTHEaHExuKQvu0UaSuO8hLL73Aj370s5jcZsWKV+lob6djzPzk/VqaUDgc5vnnnwFFof6iuwjbM3p9TmpLBTnaWsLhZJ72FUKYjez56sWCBQspLCwire7woPoPKrq563wVFhYBYPW1GxxJbPmKs/HnprN16ybq6+uiPr7X6+WVV15Ct6XiGn5h1McX3du8eQMVFeW4C1WCGYWE7c7e36ypRocthBiCJPnqhdVq46abbkUJBXAOpuiqyU87lpREKtvbvK0GRxJjioJrYgnhcJi3314d9eHXrl1NW1srHcOmodvMucScjEKhEM888xQoCh2j5xodjhBC9MicmYDJXH/9TTz73NNk1OzDPXw6KP3PWc3e23HMmLEA2FxNkDxF7s/LM7qAnF3lrF//Nnff/ZWojavrOq+//lcA0moPn21P5S1SaS9dcM61uQdWYHM3nf04mFFI8+Qbzrkm8/gWHA1dTmZarNTP/vI51zijVIcu0W3YsI7KyhO4iydJFwEhhOnJzFcfZGfncNXiq7F6W0ltLB/QGJ29Hc2652vcuPEApLiivxRnNrrdhndYDpWVFVRVnYzauAcP7qey8gRhiw09SQ8tmFEwGOSZZ5aCYpFZLyFEQjBnJmBCt9/+Bd56ayXp1R/iKxjX/wHC5m4vVFBQSEFBIXWtp5P6xGMn74hcnFVN7N69i5Ejo1MAtbN9UfOUG/Hn9Dxm89Sbex2vvWwR7WWLerzGUzKZnKPv9j3IJLRmzSpqaqpxDZtGyJFldDhCCNErSb76qLR0LLNnz2XXrh3Y2usIZhb16/nK2cba5v2ST506jQ0b1lO04yn0HpZWm6fcTDA9r8exPrNkdh6e4sl0jDFmpsJfFFma2r9/LzfffNugxwsEAmzevJGQPQN/9shBjyf6xufz8eyzT6FbbHSMnmN0OEII0SfmzQRM6I477mLXrh1kVO+h5YJr+vXcT5YdzTnzBTBjxmw2bFiPEg6iW+O/N614xe6z73tKC2m7aMw5j+e/ewhbq/vsx4HcdJouO7dWV9bucpyVjWc/1i0KdTefW2sr7VgtmftPErbbOHJEi0rse/fuweXqwDP8oqSfNTST119/hcbGBlwjZxFOtr6kQoikJclXP8yaNYcxY8ZSUXmUNt/FhFN7ryN0Vsjcy44As2dHZqH8mcU0T71lUGP1ZcnMaIHsNGpO1eD3+wdd/Hb79vcA8OWPjUZoog/a29tZtuz5SDHbUVLMVgiROCT56gdFUbj99jt5+OEHST+1/zMn2Hp8bgIsOxYVFVNWNp5jJ8pRgv64l0qovXkmWLpf7my8YnKvY7TNHEvbzJ4TIPe4YtzjisnZdgS9vo26utOMHDm63/F2tXvPB+gWG/4saVETLy+99DwdHe20j70Y3Sb1uoQQiUNOO/bTlVdeTUZGJmmnD0I41Ofnmf20Y6eLL74EJRwitemE0aHEXMgZSS4bGxt7ubJnbW1tVFacwJ9VktTNyc2krq6WV1/7C6HUDFzDphsdjhBC9Iu5MwETcjgcXH/9jbz88os4Go7iLVL79sQEmPkCuPTSK3j22adwNnyMt2ii0eHEVNgRWQJua2sb1Did+8YCmSWDjmmgqqurePzx33f7eEnJMG655fY4RhRbzz77FAG/n/YJl4CZm9ULIcR5yG+tAbjhhlt4+eUXSTt1oM/Jl3K21IQ5i6x2Ki0dy9ixZRyvqEAJeJO6N6Fui0z8er2eQY1z4sRxAALpBlSn1cPoRGaCXnml54bSc+bMY/jwEfGJK4ZOnChnzZq3CKbl4Sm+wOhwhBCi3yT5GoDhw0cwY8Ys9uz5AKunpW9PMnl7oa4WL76a8icew9lwFPewqUaHEzP6mf1lwWBwUON0FmoNpuUOOqaBUAB/fgYtc8rO+3j60VrSj9Zy+vSppEi+li5dgq6HaStdOKBuE0IIYTT5zTVAV199HcDZFjK96WwvZOZSE50WL74aRbHgrE3y1jVnKkLoZ5qeD1RtbS0AoVTjCnyGU6wE8jPP++bPj5zKbWxsMCy+aDlwYB/btm3BlzUcX16p0eEIIcSASPI1QBdffAkpdjvO+o/7dL1i8gr3XRUUFDJ79lzs7bXYXIPbjG5mSuSfBMsgN8m3tDShW2ymbaQdrYMFRtN1nSeeeAyA9rELpZ6aECJhSfI1QE5nGvPmLsDmaUEJuHt/QtjcjbU/7brrIk2ek7pxc5QOQXR0dBA2camDsCPyPdfUlNjJ1/bt73Hw4H68+WMJSEkPIUQCi9kGJFVVLcAfgAsBH/ANTdOOdnn8u8AXgTDwgKZpr8UqllhZsOBitmzZSIq7uddrlQTa8wWwYMEisnNy0es+itQzS8ITZZ1LwYMtsOrz+dAt5v36hJyR2dbm5iaDIxm4cDjM0qV/AqB9TN/r6wkhhBnFcubrVsChadoC4PvAQ50PqKqaA/wzsAC4GvhtDOOImVmzIr3kLCF/r9d2/qFPlJkvm83GdddejxL04Ww4YnQ4MaEEI/8mqanmnbWKhnBqJPlqbe3j4RAT2rBhPeXlx3AXqQTT840ORwghBiWWydciYDWApmnvA7O7POYCKoD0M2+D2/FskPz8gj5XRlfOLjuaf89XpxtuuAVFUUg7td/oUGLik5mvwSVfNpsNBrlpP6asFvQUa8ImX6FQkD8/8yQoFjpGzzM6HCGEGLRYrpVkAa1dPg6pqmrTNK3zXP9J4BBgBX7Z22C5uWnYbOarHj5r1gyqqip7vU4J6dhsNoqLs+MQVXQUFmayaNEiNm/ejK29jmBmkdEhRVVn8lVUlENhYeaAx8nISMfS1Nr7hQYKpdpob28b1P+nUZYvX05NdRWukqmEnLH5+cnISE3Ir40QIjHFMvlqA7r+NrN0SbyuA4YBnU341qiqulXTtB3dDdbc3IdN7QYYNer8tZU+IxQmJcVOfX17bAOKsmuvvZnNmzeTfmofrZlXGR1OVHXuw3O7g4P6d0lPz8QS9EZmv0xadypsT6G1tS3hvv+CwSB/fOxxsFjpGD279ycMUEeHL+G+NkIIc+vpBV0s/1JsBa4HUFV1PtB17aoZ8AA+TdO8QAuQE8NYYqa0tOcmzp2UUHjQG7uNMHv2XIYNG4Gz/ghKYHCV4E3QaEbYAAAgAElEQVTnTPJltQ5uRrWgoBAAi8816JBiJWy34ff78Pt9RofSL+vXr+X0qRpcxZMJp8rMlBmFQqFz3sJhEy/BC2ESsZz5eg34nKqq7xEpZ/k1VVW/AxzVNG2FqqpXAe+rqhoGtgBrYxhLzIwcOers+znbj6J/UA6Ap7SQtovGnH1MCYVJTU+8jd0Wi4VbbrmNxx57lLTTh3CNmmV0SFEUSb6UQc5WlZREyh7YvK34HeZMEML2SILZ3t5Ofn5ifB+GQiFeeOHZyF6vkcn0fZc83nprJQ//9kH0LglXSkoKP//5/zBzZuxmKoVIdDFLvjRNCwPf+tSnD3d5/MfAj2N1/3jJy+vbyatEnfkCuOaa63nqqT+Rfmo/rpEzTLu01n+RIp2DfaU+alTk0IXN3YQ/Z+Sgo4oF3R75Ue/oaCc/34AelAOwZcsmqqtP4i6eTDjGSa3f78Pl6jjvY2lp6ShS0PW8jhzR0MNh/PkZhG1WLIEQNHWwb9+HknwJ0QPzFidKEF1/KbfMG4931PmTMUsoPOhTdUbJyMjkqquu5c03l5PaWI6vYJzRIUWFbon82w22t+P48RMASOmoH3RMsRI+m3ydP8EwG13Xeeml5wHoGDkzZvex+NrRgaeffoKnn37ivNcsXLiI++/v9UzQkNa8YALB7DSsHV5Kln/A6dOnjA5JCFOT5CteguGErid166138Oaby0mv2Zc8yZctMoPn9Q5uL9vo0WNITXWg1x3G3nKyx2ubp9xMMD2vx2syj2/B0XC0x2s8xZPpGDO3zzF2Jl8ul3n3pXW1b9+HHDmi4ckfRyiGDcutfjcKEMh2Esx0fuZxe2MH27Ztpbm5idzcnv/dBITS7OgK1NaeNjoUIUxNkq94CIdRdD2hk6/S0rFcdNFMPvxwNzZXY0wKXRav2N3j441XTCaYndbjNVm7y3FW9txGxz2uiPZpo9FTopOQWK02Jk2azIcf7kbRdXQTLlGFuyw7JoJXX30ZILLMHQfuccV0TBrxmc+nf1RNzu4TbN26mRtvvCUusSQ0i4WwM1VmvoTohSRfcdBZSd3h+Owr60Ry66138OGHu0mr2UfbhCuMDmfQwqmRb/+2tsHX6OpMTNvKFuEtnDCosdrLFtFetmjQMXWlp3yy4d7sTp2qYdu2rfgzighklhgai3dUPuw+waZN70ry1UfBjFQa6xsIBAIJVVRaiHgaUPKlqmqJpmkyr9xHSjAEgMPhMDiSwZk//2KKioqprT9Me+kC9JTo/v/U3jwTLIPbzN82cyxtM/tW/iPkiPxhaGnpvTdnb2bPnsfTTz9BatOJQSdfsdCZaLa3txkcSe9WrVqBruu4h18IBs8ihjIc+PMz+HDvHpqbm8nNjd0SaLIIZjjQ69qoq6tlxAhzHkARwmgD/Uv3VlSjSHKWszNfiZ18Wa1WbrnldpRQkLTaj4wOZ9DCzsjp0/r6wW+UnzBhInn5BTiaTkA4NOjxoi1Rlh2DwSBvrV5F2ObAUzje6HAAcJcWoofDbNr0rtGhJITQmZI6p07VGByJEOY1oORL07T4bMRIEL0dQ++c+XI6e96vlAiuvfZGUux20k/tA103OpxBCZ75I1FXN/hJXIvFwiWLLsUS9GJvrRr0eNH2SXNtc7dB2r79PVpbmvEUqWAxx64Iz5hIaY716982OJLEEMyIvMiU5EuI7vUp+VJVdbqqqt9WVfVbqqqqsQ4q0Vh6WSpTAp3JV2Lv+QLIyspi8ZWfw+ptI7X5hNHhDIput6GnWKO2OfjyyxcD4KzTojJeNCVK8rV27WoA3MWTDI7kE2GnHW9JNocOHaSmptrocEwvlBlJvk6fluRLiO70mnypqvrPwCtAKaACb6iq+tUYx5VQek2+kmjmC+CWW+4AIK1mfy9XmpyiEMhwUFNTgx6FWbwpU6ZRMmw4zsZjKEF/FAKMHt1mQbdaorK/LVY6OtrZvv19Amn5BDMKjQ7nHO6xkaby77yzxuBIzK9z5qumRpIvIbrTl5mvbwKzNE37d03T/g2YB3w3tmEllt6WHS1nZr7S0pIj+Ro/fgJTpkzD0VxB0falFO54msIdT5N5Yttnrs09sOLs44U7nib30JufuUYJDa7I6WAEMx34/T4aGxsGPZaiKFx7zfUooSCO+o+jEF0UKQohRwpNzT2X4TDSe+9tIRgM4DHhgQXvqHx0m5W3335Lehf2IuxIQbdZZZZQiB70JflyAYFPfeyNTTjJqXPZMT093eBIoufmm28HQAkFernS3EJnCmtWV0dnn9Y111yPxWIh/dQB0+2JCzntNDc1EQqZ70AAwHvvbQbAW2COjfZd6SlW3KPzqa09zd69e4wOx9wUhUCmg+qaqqjMKAuRjLrd0aqq6o/OvNsIbFVVdRkQBO4EjsQhtqRhCURmdtLSkif5WrToUrJzcmnpcFM/60tgPf+3UvPUm3sdS7fazi7Nxlsws3OJpJoLLxz8OZKCgkIWLryELVs2ktJ+mkDWsEGPGS2hNDvhhnaam5spKDBXf0e/38euXTsJOnNjWtF+MNzjikg/Xsfq1W8yY4Y0+u5JKMOBr7mRpqbGhOklKkQ89XScqHMtbceZ/3aumcmRn35S/Mk382W327nu2htYtuw5nA1H8Jhog3R/dO5PiWZF7ltuuZ0tWzaSXrOXFjMlX2dPd9aaLvk6cGA/Pp8X74gLjA6lW/7CLIKZTjZv3sC99/4rWVlZRocUF6FQkFdffeW8ZUoOHz503ud0vqiprq6S5EuI8+g2+dI07f7O91VVLSSy18sGbNM0rTYOsSWM3qbWO2e+MjIy4hFO3Nxww8289NLzpJ3an7DJV2dCEs1edBdeOIOxY8soP3GUNl874dTMqI09GKH0yB/E2tpTTJ48xeBozrV79y4AfLmjDY6kB4qCa3wxtj0neOedNdx+++eNjigu1q9/hyVLft+v5wS7LOdPn35RLMISIqH1WkhHVdVrgKXA+0T2iD2uqurXNU1bGevgEkWvydeZma+MDHP8EY6WkpJhzJkzjx073sfWUW+6E2p9ETpTaDUaG+47KYrC7bd/gYce+hXp1Xuj3ipooD45hWa+jdD79+8FIOfIevQzk+7eIpX20gXnXJd7YAU2d9PZj4MZhTRPvuGcaz7TmNxipX72l8+5xnn6EBmVO7AEff2K011WRNbeSt58czm33XZnr4dtksFbb0V+1TdNvoGw7dxC0TnaWmy+z3ZNCGZFrquq6rnR/FCxZ88HbNu29byPzZo1h3nzFpz3MZG8+lLF8BfAIk3TygFUVS0DXgUk+Tqjt9NPFn/nzFdyJV8AN9xwCzt2vE/a6YO0jb/c6HD6z2pBT7FFpb9jV1de+TmWLl2CfvogHaPnoNuMb6pu1j+Ifr8f7ePD6IrlbOJlVmFHCp5ReVRWVLBv34dR2SdoZpWVFezfvxdf9kh8+WWfeVzvZq9nMKtz5stc32tGCIfD/OrXP6epmxd427e/J8nXENSX5CulM/EC0DTtuKqqg2vAl2T6knxZbbakKLL6afPmzScvvwC9XqN97MXo1sRrpBtKsdLR0RHVMe12O7fddidLly4h7fRBXCNnRnX8gQilO9CtFioqThgdyjnKy48RCgZxD5vWawLflwMcfWlM7imZjKdkMhkn3ifz5M7+hItrYglpFQ2sXPl60idfK1cuB8A9bGq/nhdOTSGcYqOysiIWYSWUQ4cO0NTYgKdgPB2jZp/zWN7BNwgGjSu1I4zTlySqUlXVf1VVNfPM278B8hPVDxZfgMyMzKRcorBabVx37Q0oQf+5Sz2JxKrgD0S/KOqNN96Kw+Eko/pDc/R7tCgEspxUVJwwVbmJY8cih6cDCbJs7S/MIpCdxubNG6O6XG02breb1WveJGxPx3ueWa8eKQrBLAc1p2oIGVjHzwzWr38HAHfJZIIZhee86YrV4OiEUfqSfH0dWAAcB8rPvP8PsQwq2Vj8waQ+GXXttTegKApppw8aHcqAWS3R/yWYmZnJDTfchMXvwmmSoquB3HT8fp+plh47Z+KCafnGBtJXikLHxBJCoRCrVr1hdDQxs3r1m3jcblzDpsIAfj6CWU5CweCQ7vEYCATYuHE94ZQ0/DmjjA5HmEhfkq9/1jTtLk3TCjVNK9A07QuapkXvXH6yC+so/iDZ2TlGRxIzJSXDmDFjFva2U1jd5m1f0x0lECI1NTZ7sm6//QuRoqtVu01RdDWQGyl3cuSIefpPdha4DToT52fEM7YIPcXKypXLCQQSu9Dw+UTKS7yMbrHhLpk2oDECWZHqRJWVldEMLaHs3Pk+bW2tuAsngiK7dcQn+rLn6yZVVf9b0zTj/3IkIIs/iKJDVla20aHE1DXX3MDu3btIq/2I9rELBzRG8YrdZ9/3lBbSdtGYcx7Pf/cQtlb32Y8Duek0XXZuiYus3eU4Kz9poaNbFOpuPrcgZtqxWjL3fzLzY/EFycmJTWHPoqJirrhiMevWrSW1uQJfXmlM7tNXgfxIuZPDhw9x1VXXGBpLp9OnT6HbUtFTHL1fbBJ6ihVXWRGKdootWzZyxRVXGR1SVG3c+C61tadxD5tG2D6wvarB7MjzTp6sAMxx4jfeVq9eBYCn2Lz164Qx+pKKNwKHVVV9UVXVpZ1vsQ4sWVh8kVfF2dnJnXxdfPElpKWn46zTQE+c3ndKWEfRdYqKimN2jzvv/CIA6VXGt6Xx52WgWxQOHjxgdChnNTQ0ELQnXgHijomRArqvv/5XgyOJrnA4zAsvPBupazZy4AcKOpMvsx3wiJeGhga2b3+PwJn9XUJ01ZeZrz/HPIokZvF2Jl+Js6QyEKmpqVx+2ZWsWvUG9pYq/AMolll780ywdP96oPGKyb2O0TZzLG0zx/Z4jXtcMe5xkWTLUdVI/sbDlJb2/JzBGD9+AjNmzGLPng+Mr4dmteDPz+TY8aO4XB2kpxtb+Nfv9+NydRDOHmloHAMRynLiHZ7LoUMH0LTDqGpyzG5s3ryRiopy3MWTCDkG/qIxmOFEtyhnZr6GntWrVxIOh3GX9O+kqBgaepz5UlVVBdqAdzVN+3PXt/iEl/g6Z75itaxlJp3LWM468+wn6o29PtIy5YILek/sBuOOO74AQHrN3pjepy98xVno4TD79hkfi8vlAiCcQEuOXXWokdmv5cuTY/YrFArx52eejBwq+FRZhH6zKAQznZyoODHkGmyHQkFWrlyObk3BUzjR6HCECfXUWPte4FfAYWCcqqrf1DQtOX7DxEje1o/xjDg3yUo7s/8oNzf5k68pU6ZRWFRMXeNxWkPBbpttm4mjppmUlBQmT47tq9M5c+YzfMRIqqs/IrX5JLoS5Sru/eAryYEDVezevZMFCy4e0BjR4vV6ABKyPhyAb1gOwSwn7777Dt/4xrfIy0uQE5vdeOedNZysrMBdPJlQFA5ABHLS8FY0UFdXS3FxSRQiTAxbt26msbEB97Dp6Da70eEIE+pp5uufgHGaps0BrgC+G5+QEkvnKzodUEJh0iobz3kDsNpslJWNNzDK+LBYLCy+8iqUkB9H8wmjw+mVrdVNSoubWbPmxLwArsVi4dZb7kABlJCxp+P8BZnoNis7drxvaBzA2QKTeqKeBFMUOtRhBINB3nxzhdHRDIrP5+PpPz+JbrHRPmZuVMYMZkdOPJ44Ud7LlcnltddeAcA1fGAnRUXy62lqwq9pWh2Apml7VVVNvB2xceD1egFQgPvu+wFz5sz/zDUOhwOnMy3OkRnj8suvYtmy53HUfYy3wNwJZ9qxSH/4xYuvjsv9rr76Wp588jHc2Kmf85Vuj573q4p7OMiwrX/sXyBWC95hOdScrKaysoLRo8f0/pwYCZ8tPpu4BYjdY4vI3lvJijde46677sZuT8yZjldffZmG+jpcI2dGrRl84GzydXzItNA5fPgQBw7sw5s7mlBantHhCJPq6eXmpxfph3aZ4m50dLSffT8jI5Pc3LzPvA2VxAugrGwcI0eOxtFcgRKKftX4aFECQTKO1ZGTm8vChZfE5Z7p6RksXnw1Vl87qc3G1j7yjoz8UXjvvc2GxmG1Rop3KiTOCdlP01OsdIwroqW5mY0b1xsdzoA0NTXy4ovPEU5xDn6vVxeBnMjvvqF04vGVV14CwDXC+JZiwrx6Sr7yVVX9SufbeT4WnJt8CVAUhcsuuwIlHCS1ybynnDIOn0LxB7nt1jvjOlNx/fWRWS2juwF4RuSCRWHz5o2GxmG3R4rbKiZqdzQQronDQImUnUjEzeVLly7B43HTPnpeVJvAhzIi/UTLy49FbUwzq6mpZtOmDQTSC/HnJN4JXhE/PSVf64ns9ep86/rx5TGPLEG0t0vy9WmXXHI5AI5Gc/7CtXj9ZH5UTVZWNrfcckdc7z1xokpZ2XgcTSew+N29PyFG9NQUvMXZfPzxYUPbv6SlRWZGzDxL2hehDAeeEXl8/PFhDh0yTw21vjh06CBr1qwikJ6Pe9iU6A5uUQhkO6morBgSPR5feul5dD1Mx6iZkIS9fEX0dLvnS9O0r8UzkETV0dFhdAimU1Y2juLiEk43VEQaSsegb+JgZO2pQAmE+Mo9f096eny3MiqKwjXXXM8f//h/OOo/xj3iorjevyvPmAIcp1pYv34td9/9VUNicDrTUCwWLEGvIfePpg51GM6qJl5//a9MmZIYG61DoSCPPPIQAK3jLo9JC5xATjqBpjqqq6sN3V8Ya/X1daxZ8xZBZ47p97sK4yXoESPzcLtdRodgOoqisHDhJSghP/bWaqPDOUfq6RbSj9dRVjaeG2/sfWN7LFx55VVYrVbSag8bcv9OnlH56FYL77zztmFLZVarlezsbENnAaPFX5xNIDuNzZs30NDQYHQ4fbJ8+WscPXoEd9EFBLKHx+QewTP7vpJ96fGll54nFArSMXKW9HEUvZLvkEHyeDxGh2BK8+dH+js6msxzxFzxB8l9/ygWi4V///fvYzWoDllOTi5z5swjxVV/Tj2veNPtNjwj86iqquTw4UOGxVFYUIjV7zJF4/FBOVN2IhQKsXLl60ZH06v6+jqeeupP6LZU2sfGrvdiICcyu1xefjxm9zBaQ0M9q1a9QciRhadINTockQAk+Rokny/xl0tiYdq0C3E4nebZdK/r5Ow4htXl44tf/DITJxr7C/LKKz8HgKPuY0PjcJcVAbBmzVuGxVBcPAwlHMQSSPzZL8/YQnS7jZVvLsfvN+8+Nl3XeeSRh/F6PbSOvXjAzbP7IpAbmfk6dmxgRYETwYsvPkcgEKB91GzTbbMQ5tRr8qWq6gxVVf+iquo6VVXXd77FI7hEEAgYWzDTrFJSUpg1czY2bytWT4vR4ZB25DRpFQ1MnjyFL33p74wOh/nzL8ZuT8XZcMTQGR9fSQ6hNDvr1681bBZ3+PARAFg9rYbcP5p0W6TsRGtLC5s3bzA6nG5t3ryBbdu24Msegac4tq21wg47IUcKx8uTM/mqq6tl1aoVZ2a9kqO/p4i9vsx8PQNsBH4G3N/lTRDphSbOb9asOQCkNp80NI6UhnZyPzhBZlYW//mf92OzGd/2yOl0Mm/efGyeFmzuRuMCsSi4xhXj8bjZsGGdISGMGhVpwm7kEmw0uSZE+j2uWPGqwZGcX1tbG4888jC6xUbrhCvjciovkJtOXW1tUpbmee65pwkGg7SPniuzXqLP+vJXyK1p2qMxjyRBdR6Vh0gRTfGJmTMjyZe95SRug9psWNw+CjYdRtF1/vOHP6GoqNiQOM7nkksuZ/PmjTgajtGRXmBYHO5xxWQdOMnKlcu57rob437/0tKxAGSVbyHj5K4er22ecjPB9J6rhvel76WneDIdUWqh82mhTAfe4bkcOnSQo0c/Zvx4czVWfuyxR2hpaaa9dEFU+jf2RSAnHcepFo4fP8b06cad8I22qqpK1qxZRTAtV/Z6iX7pS/K1RlXVbwNrgLMbnDRNM7ZEt0nccMMtFBYW43A4mDbtQqPDMZXhw0dQWFRMbVN1ZGmtl1fYVpcPLFHchhjWyduiYfH4+eY/3Ht2Js4s5s1biM2WgqPxOB1j5hkWRyg99WyNKk37CFWdFNf7l5aWoSgWlHDiVrn/tI6JJThqmlmx4jW+853/MDqcs3bu3M7atasJpBfiGhm/Cuyd+76OHz+aVMnX008/STgcpn3MfDnhGAfHjh3l+PFPXlhZrTbmzp1HRkZ02mHFU1+Sry+f+e93unxOB8qiH07iSU1N5ZJLLjM6DFNSFIWLLpzB2rWrsbkbCXY7uxNJykpW7I5JHNdccz133nlXTMYejLS0NGbMmMXOne9j9bYRcmQZFotrQgnOqiaWL3+V733vP+N6b4fDwZgxYyivPNljz8u+Otv30kC+YbmE0lNZv34t99xzrylmxT0eN7/97YOgKLRMXBzXZCGQG/n/T6ZN9x9/rLFx43r8GUV488cZHU7S03Wd7973L3S0t53z+S984Yt885v/ZFBUA9dr8qVp2th4BCKS0/TpF7F27WrsrTXdJl/B1EzsQS+LF38OJcp/EEpKhvG3f/sVFJNWm164cBE7d75PamM57hHGzZz6huUQzHSwYcM67rnnXrKz47Mc1emCCyZz4kQ5NlcjwYzCuN47JiwKHeNLsO6tYO3aNdx6a3w7KZzP0qV/oq6ulo5Rs+P+NQ5mOdGtlqRJvnRd54knIg3t28culGr2cdDQUE9Hexv+zBLcJZOx+t1kVryPy5WYp6S7Tb5UVf2Jpmk/UVV16fke1zTt73saWFVVC/AH4ELAB3xD07SjZx67CPhtl8vnA7dqmra6n/ELk5s6dToA9rYa3MOnn/caPcUBwHe/+0NTbIaPp/nzF/K730XqoRmZfKEodEwchu2Dct56ayV/8zdfiuvtp0yZxurVb2JvO5UcyRfgHldE9v5KVq1awS233G7oC4BDhw6yfPlfCTpzaR9twPL7mTZDJ04cJxgMJvzP+a5dO9iz5wO8uaPx54wyOpwhoaoqcnDLlzMST8kUrO4mMiveNziqgetpmqFz5+vGbt56cyvg0DRtAfB94KHOBzRN+1DTtMs1Tbsc+D3wqiReyWnEiJFkZWVjbzttdCimVFBQyPjxE7G3VqMEja0L5S4rQrdZWbHitbj34TubpJusI8JghJ12PCPzKC8/zkcfGVfENhAI8PDDv0bXdVomXAEWYxKfQG46gUCAkydNUvtvgEKhEH/605lZr9KFBkczdFRXVwHE7ZBIrPX0U3iHqqqZwJuapg2kV8YiYDWApmnvq6o6+9MXqKqaTqRsxaW9DZabm4bNJsd4E9FFF13Ipk2bsPhdhO3d91IsKMggJSUljpGZwxVXXMbRox9jbzmJr8C4vSO63YZrbCH1R05z8OBuFi9eHLd7FxRMorCoiNrmvh3OSBSu8SU4Kxt5993VXHbZfENiePLJJzlxohxXyVQC2SMMiQE6933VUV9fzdy5ibvpfvny5ZSXH8NddEFUZmktFoXCwsTbMB5vTU21AAQ/lXw5nSkJ+fXrKfnaBlwPPKCqajPwNrAW2KxpWl9eomcBXasmhlRVtWma1vUl9deBv/QluWtuTsx1XQGlpePZtGkTKe11+PK730LY0NCR8MsRAzF1auTUWWpzhaHJF4BLHUbGkdM888xzTJ8em1IM3blw+gzeeWcNNldD0iw9+kqyCaWn8tbq1Xzta/94TmmaeDh1qobHH19COCUtsjfJQIHcyAuv3bv3MXdur6+3Tcnr9fJ///cIusVGe2l0kulwWKe+Pvnqn0Xb0aORVnUhx7nJl8cTMO3Xr6eksNtlR03Tlmia9uUzG+5vAfYDdwI7VFXtyxJhG9D1zpZPJV4AdwNP9GEskcA6SxekdNQZHIk5qeokMjOzcDRXGN7fMJidhrc4m71793DiRHz7cp4tyttibFHeqFIUXOOK8Hm9bNr0btxv/8c/PoLf76O1bBG6LTXu9++qa7mJRPXqqy/T2NiAa8SFhFMTb7YlkVVXn0S3pRI+s0c40fWlvVAGMAOYDUwnUutrXx/G3kpk5gxVVecTSd66jpsNpGqalkS/acX5TJgQKTIpydf5Wa1WZs2ag9XXYYoq7y7VmArtZ5Mvs/QDjRJ3WaSw75o1q+J63x073j/bQshbaHyhVz3FRjDDwdFjR9ATsIl6c3MTL774HOEUJx0jZxkdzpASCoWoqakh4MhOmi0J3SZfqqr+QFXVDUSSptuJbMC/TdO0+Zqmfa8PY78GeFVVfQ94GPg3VVW/o6rqzWcenwicGEzwIjHk5uaRm5tHisvANjomN2dOpMhqarPxtYu9I/IIpaWy9p01uN3xW+7Pzc1j4sQLSG2rQQn64nbfWAulp+ItyebAgX1nNw3HWjAY5LHHHgEU2sZdapo/WIHcdNrb2mhoqDc6lH579tmn8Ho9tI+ea/gs4lBTX19HMBhIms320POer58C7wD/CGzQNM3bw7WfoWlaGPjWpz59uMvjO4mciBRDwLhx42netQMl4D1bWkJ84pM+mJW4Rs4wNhiLgmt8MdZ9laxb9zY33RS/H9P58xfy8ceHSW2uxFs4IW73jTX32CIcp1tZt+5tvvKVHqv0RMVbb63k5MlKXCVTeihuHH+B3HScJxs5fvwohYVFRofTZ5WVFbz55gqCzhzcJVOMDmfIqamJnIIOOrMNjiR6elp2zAf+BNwGfKiq6lpVVe9TVVV66Ih+Gzs20hDBDMtqZpSfX0BZ2TjsbTUQ5zIP5+MaXwyKwqpVb8T1vgsWRCrTOxqPx/W+seYdlY9us/DOO2tivuTm9Xp55pml6NYUQ9tWnU/npvujR48YHEn/PPHEY4TDYdpKF0rzbAN01vhKppmvnjbct2ma9qqmafdomnYB8P8AP/C8qqqn4hahSApjxkROOUry1b3Zs+eihIPY24yvdRV22vGMyOXo0Y/5+GMtbvcdN248hUXFkcMH4VDc7htregdP/xMAACAASURBVIoVz8g8Tp2q4fDh2Nb8euON12hpaaZj+EU9lnYxQmfylUiV7vft+5Bt27bgzxqGL1+66hmhM/n6dJmJRNbjuf4zm+3nAxcTqds1DvgAWBf70EQyGT16DAA2T7PBkZjXrFlzefnlF0ltPok/d0y/npta10bx65G6yJ7SQtouOvf5+e8ewtb6yf6tQG46TZed20A7a3c5zspP9uUp4cgMzZo1q5g4Ue1XPAOlKAqLLr6U1177C/bWqn5/HczMXVpI2okGNmxYx6RJsVm68vl8vPTyi+g2O64R5qulFUqzE7bbEubEo67rLFnyBwDaxi4yzd65oaaqKrIXNujMNTiS6Olpw/0e4CTwr0AHcJ+maWWapn1e07TH4hWgSA6jRo0GwOaW5Ks7U6dOI8VuN8Wme4CwzULYkcL6d9cSCATidt9FiyI1oJwNx+J2z3jwleQQttvYsHE94XA4Jvd4++1VtLY04xo2zZx7KxWFQG4aNTXVeDzmr924efMGNO0jPAXjCWSVGB3OkHXyZCXhlLSkOujQ08zXvcCO89TmEqLfMjIyyc7OIehpMToU07LbU7lw+kXs2rUDi6+DcGpGn5/rK8qicfHUbh9vvGJyr2O0zRxL28xzi+Bmf1CO5XANO3duZ+HCRX2OZzCmTJlGTm4u4cbjtI6/HKLcbN0wVguekXk0Ha/jo48OMmXKtKgOHw6HefXVV9AtVlzDzbs1N5CTTmptG+Xlx5k8ufvvWaMFg0GeXLoEFAvtpQuMDmfI8vl81NaeJpA13OhQoqqnPV/vSeIlomnEiJFYfW2gx+ZVfzIwW6FRd2mk0vy7774Tt3tarVYuWXQZloAHe4vx+9+iyTM6H4DNm/vSHrd/PvxwN1VVlXgKxptur1dXibLva82aVdRUV+EqmZJUG70TzcmTFei6TjAtz+hQoipJXlKKRDBs2DAUXcfqM2crCDP4pOSEOZKvQF46wQwH297fis8Xv9pbl112JQCOhsQ6FdcbX0kOus3K1vc2R/3U41tvrQTAPSy6M2rR1pl8lZeb90Sr3+/j2WefQrfY6Bg9x+hwhrTOThvJlnwNvUZ6wjAlJZFpY6u3jZAjeeq1RFNpaRm5uXmEW06ao8G0ouAZnY/tUDW7d+9iwYKL43LbqVOnn1l6PEZbHJYeMw+cJF2LHOKO1oEF3aJQd/O5ldDTTtSj6zqnT9VQWXni7CngwfJ43GzYsA5dUcg5vAYAb5H6meWy3AMrzjlxHMwopHnyDedck3l8C46GLrNSFiv1s798zjXO04fIqNyB1e/qd6yB7DR0BcrLzbunb+XKFZE2QiNnmnoWcSjo/D4JpucbHEl09aW90CWqqv5VVdX1Xd/iEZxILsXFkQ2rVl+HwZGYl6IozJ49F0vAjc3Va7/5uPCOiLzi3L79vbjd02q1cuklV2AJeLG3xKcqfLzotsiv3fffj97Xs3Ms3ZIStTFjxmohmOnk+PGjpmwz5PP5WLbsuUidtJEzjQ5nyOtcng6kJVfy1ZeZr6eB+4Hkargm4q6oKNLjzuptMzgSc5s5czZr164mtbmSYEah0eHgL8gknGpjx4730XUdJU6zcZdddgUrVryKs/4I/tzRMb1X+9RRdEwa0e3jAz2w8GnuccV4R+Qy7K872bVrB3fddXe/Yz2fbdu2RuK88I4eK9o3T72528c6tZctor2s58MVnpLJeEomU/DB86QMoHZfICcNd2UjdXW1Z1+UmcWqVW/Q3NyEa9Qs9BSn0eEMabquc+zYUUKpmeY8vTsIfUm+qjVNeybmkYik19lOxOqXma+ezJw5G4hsuneNMkEDX4uCtzib+so6qqtPMnJkbBOhTlOnTicvv4Bw4zFaw5cnTWXxsMOOPzedAwf24fV6cTgG90clHA6z64MdhFIzCCbI7EAgNx0qG/n/7N13fBzXdejx35Tt6J0dbBgWgAQ7KVEs6r04tmNbtiw7tuOXxO/Fdp6fnZcocZJP/FKc5ihWbMcljnviIiVxl2VbklUoSqTEMmwgwYZeFgts33l/DBYsIoAFsDt3FrjfzwcfkcBi5ghccs/ee+45bW0nXZV8JZNJvvGNr9irXgsEj/mS6OnpZmCgn0T1ctGh5F0uydc/GIbxb8CTwNjpR5mQSVNVW2uv4qhy23FCVVXVLFu2gpOn2+xRQ5r40sxEfTnB9l4OHnzFseRLVVV279rLd77zLXwDZ4lXNTpyXyfEG8rx9l/g8OHXxpLt6WprO8VQOEy8bpX4GsEcpSqCgF1MvX27M3WEuXjyyR/btV7zWx1Z9VJTMXp6hnnooV+/8vOqyrvf/T527dpb8Bjc7Ngxexx08lo7AKOn5p955hecPHntgzmlpWV87GOPUFpaWrAYpyuXKtZ3A/OBG4C9ox97ChiTNEsFAkECgSBawv3NFUXbvHkLSiZtz3p0gXhdGQCHDr3m6H1377ZffK4oAJ8F4vX2gZMDB16e8bUOH34VgET5+NumbpMst4vYT592z4lHy7L493//OiiqY9MBlHSStJXm3GDPFR/nz5/jxz/+oSMxuFl2FFeytP51X8uemu8f7OfI8aOv/zCP8OKLz/Hss790NOZc5fKWusE0TVl1KOVFVVUVw129kz9wjtu4ccvoqKH2gtc75SJVFsTSNUzziKP3Xb16LbW1dXT1nmIwk541W4+J2mwy++qMr5WdvXmtFyi3Spf4sHTNVe0mXnllP6dPtxGtXUnG79xKSTrgo/OBK1c/5/3HC64+DeqUw4cPAZAsHX9remR5PQPbVrzu8/rACPX/9TL79+/jttvuLFiM05VL8vW8YRh3A983TXP2TLqVhKisrOLc+fP2kvFs6VxeAM3N6/B4PPgG2smlK9rlsx2vpXfvGlLlwQmvcXWrhKslKoO0n20nHo/j8zkz5kNVVXbt2st//Mc38A20E6/KT2sG0SyvTrI8yFHzCOl0Gk2bflLZ1nYKS9GKa+iwopAsC9DefoZ0OoXmgq31J574LoArpgMkKoJ0dnQwMjJCMDjx39vZKplMcvToEZLBaizdO+XvT5UHSAe8vPzyS44eFMpVLq9+9wOPA0nDMDKjHzIJk6aloqISBQs1GRMdiqv5fD5aWtbjGe5Fdck2bbIihJXJcO6csw1gs3Uv/u7ZtfWYqC4hHouNDQ2eDsuyOHu2nVSgvOhWBZMVQVKpFBcuiN9aHxjo59lnf0kyWD3hKotTUhXZRrRzd/Xr+PFjJBJxEuXTHCukKMTry+nv7xtr1Oomk77dME1znhOBSHNDebn97lxNxsh45+Y7ulxt3LiZ/fv34R04S6zOmPCxk812zMVkrRJCR+0XyXPnzrJ8+euX+Qtl9eo19tZjX9us2nq8fMzOdJuthsODjIwMk66uy2dojsiuxJ4+fYpFi8RurT/55E9Ip9OMNKxxxaGF5OiBhLa2U3mfAVosDh58BWD6yRf2wZbg6W5efvklli5dlq/Q8iKXJqtBwzD+wjCMfYZhvGIYxt8YhiFb/krTUl5uFxqrqajgSNzv0qih6a+M5FM6ZG81dnQ4u1KhKAq7du1BScVdM/MyHy6N2Zn+6kZPj92IN+1132muySTL7dOE7e3iW0g+9dRPAYVYbZPoUIBLz41Tp2bXau9UHDxoH0aZyUGSeIP9Zv/ll1/KS0z5lMu24z8CIexTj+8EvMBjhQxKmr2yR34Vue04qWXLVlBWVo5v4Jw9akiwdNBOvrIv+E7auXM3AP7e2bMNkyqzk4+zZ6efXPf12TV6xbiKnF35OnPmtNA4uru7OHLkEPHyBa75OdojmBROnZo9z/epSCaTHHz1AMlA5YzGO6VDPlIlfg4efJl0OjX5NzgolyrHTaZpXl6B+DuGYRwuVEDS7FZaap/yUlPODWkuVqqqsnHjJp566km0aD9pwYNl0wF7dE04POj4vdesabZnXva2MbhidhzWyPg9WB6NCxfOT/saQ0P2tIhMEXb/Tod8WJoqfOXrhReeA8Az3E3tC18EnJmLaRvnTZWmkirzc+rUSTKZDKpa/M/3qTh8+DXisRiJ+TNfiYw3lDNyopPjx4+xatXkkyqcksufqGoYxtgxmtFfuyuFlIpGSUkJIJOvXG3YYHe497lgvqHltd+rDQ3lcv4yv1RV5frrb0BNRvEOXnT8/gWhKKRCPjo6OqZ9iZER+zBGRpv6aTDhRk88nj3bTiaTERbGSy+9CIClij9xeblkRYhodITOzuk/P4pV9s8kXjHzWsBsT71sDZlb5PJs+xvgRcMwHh/9/b3AJwoXkjSbhUJ28qWkE4IjKQ6trXby5R04x8j8dUJjsTT7vVosJqZe77rrbuA///N7+HtPkqgonoaiE0kHfUQH+qfdUiAet7fv3ZY45CpVFiDR30NXVycNDc6f7bIsi4OvHiDtLaFr68MTFtvney4mQMMv/3HcxyUrQ3Cmh5MnTzBv3vSLzovRiy8+j6Woefl7nm0QfeDAy7z5zW+b8fXyZdKVL9M0vwA8AJwCTgNvME3z8wWOS5qlgkF7/14mX7mZN28+dXUN+AZdUPelKFiKQjotptPM+vUbCASC+PvaxP8s8iS7lZut3ZqqZHJ0E6JIT4Dmo+5tJrq6Ohkc6CdR1uCKU46Xm6tF9319vZw4cYxE+XysPKzoZoI+UqV+Xjv0qrB/u65l3OTLMAzVMIz3Gobx98Ba0zQfNU3zU6ZpzrwlszRnBQL2P7ZqOik4kuKgKAqtrRtQU3H0YecL3d3E6/Wydet2tFj4itqbYpYZ3cqNRKa3lWuNzrezXJY45CqbfDndOy4rOxPwmrMDBbvUiuTacwtnq2wNXryyMW/XjNeVMTI87KqJChOtfH0a+A0gAfy+YRiPOBOSNJtlky9FJl85a221p3sJr/uyLBTLQtfFbXFt22YXQfv6TguLIZ8sj/2zHB4entb3Z7t2K0W6EphNvs6fF5N8ZVfcUoFKIfefSMbvIeP3cPLk3Fr5eu65ZwCIVTXm7ZrZcV6HDzs7m3YiEyVfu4Adpmn+b+BG4NecCUmazXw++1SWkpFnNnK1fv0GALyD0z8Vlw9Kyl5l8fvFnazbunU7iqLMnuRLt/8JztZuTdXYWKJiTb5K7eeSqJWvrq4uANL+MiH3n5CikKgM0dnZMe2V0WKTSMTZt+9FUoEK0sH8JcSJWrvFUXYIvRtMlHzFTNO0AEzT7GXcM7GSlDufz97Dlytfuaurq6ehYR7e8AWhL7Jqwk6Ys73aRCgvr8AwVuMbuogyC07MWqq9cjXdWhRdt2vGlIx7almmwvLopANeYclXf3+2T5o7+4ZfPgVhLti/fx/xeIxYdX670adKA2S8+tigbjeYaP/g6n/lxZ0FlmYNj2e0gLJIXyxEWbeulY4ffR99pJdUqEZIDGrMTpjLysQOcN66dTtHjx7GN3CWWI1zY44Kw06+MpnpJdXZAeeiV5JrfnpoLJGMNtYSbl1yxderf3YYffDSjNJkZYi+3asBSJX46eruIplM4vF4nAuaS9u9Gd2ZQfFTdXndV3YFfDZ75plfAhCrmt64rXEpConqEi5evMDg4MDYmDuRJlr5WmIYxuezH9f4vSRNmaIoeDwe4S8Wxaalxe5z7B0UN4RYi9onVKurq4XFALBp01YAvC4ZuzQjoyuZY9uHU+T3F38NZarUj5XJ0NHhfP+2ZHL05+bS06LZ5OvEidlfdJ9Op3j22afJeIMky/LfdiRRbbc5OnbMzPu1p2Oila8PXfX7nxcyEGnu8Hi8KJZcSJ2K5ma7x5d38IKwfl/asF2XVFdXL+T+WYZhEAyFSIk+gJAHStr+ezDdFZ9QKDh6HbGtW3puWjs2LuhaeveO31k8W/d18eIFcQO2Lct1rSbA3i6zdHVOnHg8cOAVwuFBog3NBfmzSF6WfG3Zsi3v15+qcZMv0zS/5GQg0tyh6zok5bbjVCxYsJDy8grSQ+K6u+tDdvI1f/5CYTEAaJpO6/oNPPvs02ixsDuLpXOkpOy/B9M9xFBSYtfflZzdR/Di+MXE/WvvJRWaeDzV60bjXEO0fg2RJVunHugE0iX2//tMxixNl9c7WgZhpUFxYaNaVSFZEeLMmdMkEolL8c5Cv/jFUwDEagtTSpCospOvkyePFeT6UzXps80wjHcCnwSyRw8UwDJN053rtJLr6bqOkpDbjlOhKArNzS0888wvUeNDZHzOF73rg3Zn+4ULFzl+76u1tm7i2Wefpublb5DR7FWj6c7jAyh97Swhc/zEtnfvmglXdgDK9rcRaJ+4WerI8jqGWi6t7qgJO/nKTn6YqmzyVaynHcGu+QLo6HB+Sz37c1dT8bGea26TqAzh7RnizJk2Vq40RIdTEKlUil/88mdkvEES5YWZXpEJeMn4dNccXsjl2fYIsMc0Tfc0yJCKmsfjAUt2uJ+q1avX8swzv8Qb7iBW63zy5RkYpraunlBI/Mmw9etb7V9kUqA5W6SdT2o8e4hheqt35eX23Lp45WIG1tw5o1hyGY1TCOmx5Mv5Vd2qKns1UE2MuP7E44kTx2dt8rV//z6GwmGi89aBUqAh4oq9injx4gWi0RECgamP88qnXJKvCzLxkvJJVVVZ8zUNa9Y0A+AZ6iBWu9LRe6vRBFosycqNzt53PI2NywiFShhMa3RveWjcx+Uyjw9gqHkRkdUze8cd3riU8MapndLKniCtqJheT6PS0jIURUFNipm3mQ8Zn46la1y86Hzyla1f1GJhUi7scg+QrLKTr+PHj3HHHYKDKZAnn/wRANG6poLeJ1kRxNc5SHv7GQxjdUHvNZlckq+XDMP4d+BHwFgnQNM0/7VgUUmzmqZpRduRW6SVKw1UVcU71On4vb09Q2MxuIGqqjQ3t/D8879CTQy7dtViMlo0QWlZ2bRreTRNo7y8gmR8ZPIHu5WikAp56ezscPzW8+fbCbce7cetXeOSFSEsRZm1RffR6AhPP/1LUv5ykqUNBb1XcnSiwpkzp4UnX7ms75UDQ8AOYO/ox54CxiTNcqqqInv2Tp3f72fp0uV4It2O90nLJl/Z1Tc3yMbiDYs7hDAjloU+Eqd+hqdHq6qq0RLTG0/kFumQn+HhCMPDEUfv29hoN/P0DLt4VqimkioPcOLEcVcNhs6Xn//8Z8TjMaJ1RsFPnGbrNkUNcr/cpCtfpmm+C8AwjErTNPsLH5I026mqBnLbcVoMYxUnTx5HH+lzdJvE2xVGVVVWrRq/ZYDTLm3DdhZls1U1nkRJZaivn9m7/erqGk6dOoGSSmDpxXkaLhWym5x2dXWydOn0Dh9Mx7x58wkGQ6QiXY7dczoSVSV4Bro4d+4sS5Y0ig4nr37wg/8CIFpf+JUo0YPcL5fLacf1wDeAoGEY24FfAG82TXN/oYOTZidVVXBfR53i0NS0iv/+7yfwDHVekXz5usLUf3cfMPUO41lXn9azVIWuezehJNN4eyOsbFpFMCi2SPVyTU2r7Ka9ArZh8yHbumPevJnVmtXW2s8DLR4hpU/cTsKt0sFs8tXF0qXLHbuvqqo0NRm88sp+lGQMyyNubulEklUhOAXHj5uzKvk6c6aNQ4deJV6x2JGWMRm/B0vXuHBBfI/AXLYdPwU8APSapnkB+B/AYwWNSprVFEUt6qPxIjU12TVXnki3Y/f0dg2iWBYbNmx07J65CAaDLFq0GG+kuyifT9nka6atO8aKxuPFO3w5HbJX7Lq7nV+BWru2BQCvwB56k0lW2quBJ064o0dVvjzxxHcBGJm31pkbKgqpEh/nL5zHEvxvRi4F90HTNI8Yhv2PvmmaPzYM468n+ybDMFTgn4D1QBx4j2maJy77+h3AH43+dj/w29lB3tLspqqq3HacpsbGZWi6jueqbZJ4XRm9N41fjzVRh/Gs8U7r+S8OALBx45YpRlt4K1c20d5+Bi06QDo4vRODomRXImeafGW3LbV4eMYxiZJd+erpce5NRda6da185StfouLojyad8SiqWW223YRbRuPkw/DwMD/60Q/IeEP5n+U4gVSJn/hAH0NDYcrKyh2779VyWfnqG916tAAMw3gQyKU68X7Ab5rmDuCj2I1aGb1GKfBXwN2maW4HTgNipgVLjrML7qXp8Hg8LG1ciifSRd3zn6fuhQIPorAs/Bf68QcCYyOO3GT5cvtoume4R3AkU6eH7fYQM91Gamiw5+BpsWJOvuyVLxHJ19q1La6fN2t5NJJldtF9JjM73rj+6EffJxodYXhei6OzNdOj9YUiWptcLpeVr/8BfAlYaxjGAHAceDCH79sJ/ADANM3nDMPYfNnXrgNeBT5pGMYy4HOmaTr/t04SQq58zczdd9/PN7/5NcDCsiwuXixcmwE9HEUfirF55+5pzx8spKVL7dNq+nAvONz7bKY8AyOUl1dMu8dX1qV2CQP5CEuIdEBc8uXz+WhpWc/+/fvobX3TjNuWFKpZbbKqhOjpbi5cOMfChYJmYOZJOp3m29/+JpaqM9Lg7AnqbPLV09OFYaxy9N6XGzf5MgwjaJrmiGmaJ4GdhmGEAM00zbBhGLkcLSoDBi/7fdowDN00zRT2KtdeoBWIAL80DONXpmmOu6FdWRlE1+VEo9nA5/Ncs89XTU2JK1/g3ebhhx/k4Yft9z+pVIrNmzdP8h3T5z9nL3LfcsuN1Aroqj+ZzZvt1bjLRwgVAyWZQo/EMLaum/HPtaamhEAwSLKIky90DcurEw4PCHme7dmzi/379+Hrb3fk1N10JKpCBE9309HRzoYNDtVIFcgPf/hDOjouMtLQTMYbcPTe2UQ/Gg0L/TdtopWv/zIM43bTNOMApmkOw9isx78HKia5dhi4/P9MHU28AHqBF03T7Bi95i+wE7Fxk6/+/iJuIihdIZ22AMsukr6sr0tPT8Qeui3lLJ0u7FZJ4Gwvqqqydu1GurvdV9BtWT5CoRJSIxPPVHQbz0C23mtJXn6uixYuxjx+3F5RLtR4lgJL+T10dHYKeZ6tWbMBAF/fadcmX8lqu+h+375X2LzZ+TFQ+ZLJZHjssc8ACsMLnT/Ek60vPHPmXMGfaxMldxP9LT0M/KdhGD6w67QMw/gq8HHs04+TeQa4c/R7t2NvM2a9BDQbhlFjGIYObB+9nzQHaFp2BVOer3AzdSSOtzfCunWtlJdP9l5LDEVRWLx4iV3v5HDj2Znw9NtNUZcvz89W6ZIljShWuqjrvjIBD0PhMKmU87VXixcvob6+AX9/u2ufR9kTj8ePF3fR/bPPPk1b20mitStJB5wveM+ufPX2in3DNm7yZZrmb2MnRN8zDGM3cABIA+tN0/xZDtf+DhAzDONZ4G+BDxqG8SHDMO4dre/6GPBD4Hng23J+5NwxlnzJui9Xy/b82rVrj9hAJrFw4SIUK1NUrRY8fXbytWJFfpKvxkb7tFgxHjzISvvtF8WBAed7eSuKwrZt16GkE3jDzo85yoXl0UiWBzh23CzaovtMJsO//uvnAYgsFnN6OhOwS1v6+sQmXxPu8Zim+b8Mw/gk8CTwkGmaX8n1wqZpZoD3X/Xpo5d9/evA16cQqzRLZOu6lEwGqzh3SOaE4JkeFFVl587dokOZ0KWC80HSAXeu0F3N0x/B4/GweHFjXq6XbUyqR3qgCLv9g90AE6C/v4+aGueHXG/dup3HH/82vv7TJCpm1vi2UJJVJcTaujl7tr0om60+9dSTtLWdZKTOIBUU0xDY0jUsXaO/X2yd6KQvfaZpfhi7LcSbDcOQFe/SjOn6aFG95c7lfQm0SAxvzxAbWjdSWenurunz5s0HQIsNTvJIl0hn8AyMsGzZirzVOK5YkW25UbyHxtOjydfAgJiDA62tG/F4vfj6zgi5fy4S1XYN0bFjRyd5pPskk0m+8MXPgqISWbxNaCxpv0fY8yxrotOOGS4V5WSrohOGYSiAZZqmTMSkacm+4ChWRlZ9uVTgtP0ivnfvzYIjmdylJqPFse3oGRxByVisXNmUt2tWVlZSU1NLV7jrdQdZikXGl02+xIwQ9vl8rF/Xyr59L6DGI2R8zs2YzFVitOjeNI9wyy23C45map544rt0XLzA8Px1Qmq9Lpfxexjo68eyLBRBf1fGTb5M05QbQlJBXNp2dG9TwznNsgi2dePxeLjhBndvOcJl43ViRZJ89UUAWLnSyOt1V61aQ8/TP0eLDzkyJy/fsslXOCxuBXPjxi3s2/cCvoGzrjz1mKwMYakKR48eER3KlITDYR577FNYgL/nFL7eNmJ1BkONO654XOVrj1/RNiZVUkv/mruueEx2gkD29SNwuhvf6BSOXOfapv0eMpkMkUiE0lIx7SZkgiU5zuezj/oqabnt6EaevmE84Sg7duwkFHLfu/+rVVVVoygqWiIiOpSceHvtOJua8tvgcc0au/eTx6UF45PJ+Oy1gHBY3InNDRs2AeAdPC8shglpKsnKECdPHieRSIiOJmdf/vIXsCwLS/dhuWBVNvtcGxwUs8oKuXW4l6S88vn89i/kypcrBdvsuZE333yb4Ehyo+s6lZWVdI0Miw4lJ54+u9g+e0IxX9autRvOesMXiNXlb0vTKdkXxKEhccnXsmXLKSkpJeXW5At769HbG+HkyeOsXu3+ZqtnzrTx+OPfJu0vp2vTgxOOEupvvnfS62UnCHj72qg+9J9EG2sZ2Db+IZNrzbUte/k0AIODgyxcOPn/QyHIlS/JcX6/nXypmaTgSKTXSWcInu6hvLyCLVvEFsVORVVVFVoyKjqMyaUzePpHWL58Zd4bCjc1Gfj8fnwD5/J6XadkvNnkS9z2saqqrFmzFj0WRk24M5nPFt0fOeL+1piWZfHoo/9AJpNhcNkNjs5wnIgbVlknKrh/ZKJvNE3zT/IfjjQX+P32OAklLZMvt/Ff6EeNJ7nprluKatpAZWU1yonjKOkEluYVHc64PP3DKJaV9y1HsFcA17W08uKLz7m2YHwi1mjyFYmIrd1bAaZvLgAAIABJREFUvXotL7zwHJ6hLuLV+V2dzIdEjZ18HT3q/uTr6ad/zssv7yNWuZh4VaPocMZk6wsHB8WdeJxo5UsZ/dgG/BqQARLAXYD71zol1woEsslX8dQszBXBU/aW46233ik4kqmpqLD7e6kuX/3K1nsVaqDv5s1240pff3tBrl9IlqZiKQrDw2JXnLKJsSfSJTSO8aRL/WS8OocPu7sveSwW49Of/kdQVMLLdrnqBK4btrgn6nD/cdM0P449w3GHaZp/Zprm/wN2A8U9Ul0SKhgMAqCkZPLlJmo0QeB8PytWrGT58uJq1Jkdf6QmY4IjmZi3117VKVTytWXLdsCeUVh0FAXLqzEiuHZv2bLRhrXDLp0Xqigkakrp7OwQ3qV9It/4xlfo7u4ksmAD6WCl6HCucGnlS9zJ2lxqvmq5cgifB3B310XJ1UpK7GVzVa58uUqwrRssi9tuu2vyB7tM9ri425MvT28EfyDAwoWFef+6cOEi5s9fgH+gvSgPtGQ8GpFhsadWq6trCIZCV7Q8cJv46MDmw4cPCY7k2jo6LvKNb3yVjDdEZPFm0eG8zqWaL3cnX58F9hmG8VeGYfw1sA/4u8KGJc1mJSV2LYqaiguORBpjWQRPdqLrOjfe6P7GqlcrLbX7Wikufk4pyRSecBSjadVlw+XzfA9F4frrb0BJJ/H1ny3IPQrJ0jWiUbFbx4qisGjhYvRY2G5Y60LZuq/Dh18VHMm1feYz/0QymWBw6fWurMF0Q83XpBW1pmn+lWEYTwJ7sFfA3mya5oFCBybNXmVl7n+hnGu8PUN4wlF27rmRsjKx3aen41JC796VL0+B672ydu7cw7e+9XUqjv6AjCcw9vmZNrUco2p0b35HQWLP6BrR8LDQzuNgT00wzSOoyREy3pCwOMaTrCnFUhQOHXJf3deBAy/zy18+RaJsHrFad7Y8yXh1LEXsacdcW00Y2FuN/wysL1w40lyQfXF3e3H0XBI82QnA7bffLTiS6ck2g3XzIY5ssf2qVa/vO5RPq1evoa6uvignSFgeDSuTIZkUexK6trYOAC3uzsa9lq6RrAxiHjtKPO6eN7GZTIZ//udHAQgv2+mqIvsrKAqWT+x8x0lXvgzD+H/AQmAT8BfAuwzDWD86cFuSpiy7ReTvbaPu+S+gJkcm+Q6pkJRkmuCZXurq6sc6fBebUMhenXDzVra3xy62L3TypSgKN954C1//+r8xtPS6CVcfptLU0gmWZq8HxONxvF5x21WVlXaBuJpw779NidoyvH0XMc0jrFvXKjocAH7+8yc5ftwkWttEsrRBdDgTSnt1BsPubDWRdRvwDiBmmmYYuAW4o6BRSbOaruvccsvtzG+oZ2F1GfMbGtiz58aC1cFIEwuc6UFJpbn99rtQ1eLsu3xp5culveMsC29vhOqamrFVlULKTicIdBbXDEBLt59/sZjYVfGx1XkXb2PH6+w3sa+9dlBwJLZ0OsUXv/QvoKgMLdkuOpxJZfweIkNDpNNiVohz6aKYGf1vtvLQd9nnJGlaPvKR/ys6BGlU8GQniqJw663F+54q275EdWn7Em04jhZNsGZzsyP3W7KkkdWr13LkyCHU2BAZv5jhwVOVXfkSve2YrSF0czucRK27kq8nn/wJF86fY7ihmXTA/XWjab8Hy7IIh8NUVjrfwCGX5OubwDeAKsMwfhd7FeyrBY1KkiRH6IMj+HqG2LhpC/X17t4mmEggMNo7LuPOF0tvt73l6OQsvjvvvIcjRw4R7DhEpLGwKxE1Pz2EpY5f39O7dw2p8uCE1yjb30bgTA+A8DqmsSkcLh6Blgl4SZX6ee21V0mn00J3DjKZDF/72pdBUYkscl9riWvJ+O0Tj/39fUKSr0n3GEzT/AvgX4BvYTdX/SPTNP+80IFJklR42UL7O+64R3AkMxMMjr5Yptz5Yunttk9VrV3b4tg9d+++kWAoRKjzEGTSjt13ZuwELiX4zzFbb+b2QwvxunKi0RFOnTox+YML6IUXfsXZs+2M1DYVzSprxm//Gff39wu5f67D2yLASeAL2OOGJEkqdukMobZuysrK2bHjetHRzIim6Xi8XhIuPe3o6w7j8XpZudK5o/eBQIDbb7uTb3/7W/h7ThCrMwp2r56b1k66sjWZ8MaloCiUHj5PMik26cnONVUy7q6wideVETrZycGDr7ByZeH+fCfzve99G4DhBe4o/M9FenTlS9SUgElXvgzD+F/AnwEfAkLAPxuG8XuFDkySpMLyn+9DjSW55ZbbhJ4sy5dgIIjqwoJ7JZ7CMzDCmtVr8Xg8jt77vvt+DUVRCJ1/xbUNQy+X3boUvfJ16eCJu39midGi+4MHXxEWQ1dXJy+99CKJ0gZSJbXC4piqTMD+uzgwIGblK5ejTQ9jn3gcNk2zD9gCvLuQQUmSVHihk/bg4GIcJ3QtwWDQlX2+fN32CBMR7QDmz1/AddftxBvpwjt4wfH7T9loX6iM4BUnVR2tn7LcvfKVLvGTCvk4ePCAsJ/Zk0/+BMuyGKlfLeT+05Ue3Xbs7XXpyheQNk3z8n/RYkCxFBBIknQN6kgc/8V+DGM1S5cuEx1OXgQCQVfOC/V12vVeonoxvelNbwUgdO4lIfefiksrX2K3HUV215+qeH05kcgQbW2nhNz/6aefAkUlVrNCyP2nKxOwky9R24651Hz9fHSmY8gwjPuB9wE/LWxYkiQVUvBUF1hwxx3F2dH+WkKhkN3ny7Km3Fm79LWzhMyLAEQbawm3Lrni69U/O4w+eKnhZrIyRN/uK9/pl+1vI9B+6R9yS1XouncTvo4BPF4va9Y4d9LxcmvXttDcvI7XXjuIHul2+daQ/edmCd4iLaLci0RdGaFTXRw48DLLlzubAA0M9GOaR4mXL8Ty+B2990ylA2JrvnJJvv438F7gAPAQ8N/AY4UMSpKkArIsQqe68Hp97Nlzk+ho8ubyEUOW7hMcjU2NJvAMjNC8YRNer7iY3va2h/j93/89StpfZGDNncLimNRo0iM6+RrjkjAmEq+3e2odOLCfN7zhTY7eO1tr5ol0UfvCF8d9XP/ae0mFJm7n8LoZotcQrV9DZMnWKcd5TapKxuehp6c7P9ebolwGa2ewi+w/B7QCJ03TdPf5W0mSxuXtCqMPxdh1821jY3lmg8tHDKWnmHwNNS8isnrBuF/v3Tv5SKDwxqX2ib3LBNrsf9g3btwypXjybfPmrTQZqzhmHiUy3EsqVC00nslYgmutstuOShFkX+kSP6kSPwcOvOJ4vy/TtCcoWGqujRPcJRX00uu2lS/DMFYAXwf+CPgJ8AugDtAMw3iraZrPOBOiJEmT8XYPUfefL+f0WDVunyS77TYXr4BMw6Wu5O6Z7+i/aJ+k2rw5T+/Wp0lRFB56x7v4gz/4P5S0v8DAardPMxC77zd22tEtK3CTiNeXMXyyi1OnTjjaciJbZ9a9+e0zXm12coZoVibgJdbfz/DwsONvRCcquP8H4K+xtxnfDpQAK4Gbgb8sfGiSJE1GVTU2b95KeaiEKkvP6aPCG2DTpi2uGcabL9mB7a4Zrm1Z+C8OUFFZybJly0VHw9atOzCMVQR6TqBHxGy15Ep0wbumja5LuPy0Y1Z26/GVV3J7A5Yv58+fI+MJuGabf6rSgeyJxx7H7z3RWuEC0zS/DmAYxi3Av49uNx4zDMP9g5skaQ5QFIVPfOKTosNwhbFhyEl3DEP29EVQY0m27d7hioHliqLwzne+h9///d+j9Mzz9K914WGL0YUm0clXsXS4z7q87utNb3qLY/ft7esl7S2OjvbXkg7af849Pd0sXrxkkkfn10TJlwJgGIYC7AUevez3s6dQRJKkWaG8PJt8RQVHYvOf6wNg27YdgiO5ZPPmrWMnHz3hiyTL5okO6Sp29iU6WfX77ZN7/p4TeAfPj30+Vmcw1Hjln2fla4+jj/SN/T5VUkv/mit7572umFzV6N78jrzFmwn6SJX6OXjwAOl06tLKXQGl0ynisRiZ8pqC36tQssmXiJWviZ7hBw3D+D/AI0AceMYwDC/wMeA5J4KTJEnKVUVFJQBqcmSSRzrDf74fXdfZtElsvdflFEXhN37jNwEoPf0r19U0KaPxiF75Cgbt9QXFZT+ficTr7TmPx46ZjtwvOwLKcsGq7nS5ddvxt4FPAA3A/aZpZgzD+DtgNeDcuqYkSVIOKiuzyZf4lS8tEsPbP8yGLdsIBmc28zDfmpvXsX37dTz33LP4+s8Qr2oUHdIlGTvZyc5WFMXn8+Hxehn2VtC74dcnfGx/872TXs+JYvJ4fTmhE50cOPAyq1cXvqfc2PzLIqmLu5aMG5Mv0zQHgd+66nO/Nc7DJUmShKqqstsnaIlhwZFc2nK87robBEdybe9613t5/vlfUXr6WeKVS1zTVVRxSfIFUFlZRaw/IjqMnF0qut/PW97y9oLfT9M0e5h9yn1TJXKVDtoHBXp63LXtKEmSVDTKysrRdQ9qXPwLZqC9F0VRuP56dyZfy5at4KabbsUz3Eug25ltqlxcSr6cHUB+LTXVNajJ4aI58ZgJeEmWB3jttYOOjGdSFIXKikq0hDu2+acj49OxVEVIl3uZfEmSNCsoikJNTY3wlS81msDXHaa5eR2VlRN39Rbp4Yffg657KD39HGRcMq43bSc6Ho/45GvevHkoloUWHxIdSs7i9eXE4/Gx5qeF1tAwDy0RgSI5Ffo6ikLG76XHZQX3ABiG8ZtOBCJJkjRT9fUNdvIlMJnIznfctWuPsBhyUV/fwH33vQEtPkTo4kHR4QCgZNyTfC1YsAgAfWSgoPfRonHqv7tv7KPslTOve0z1zw5f8Ziqn78+uSrb30bgjJ1EZMf+FNqSJY0A6MN9Ez/QxdIBD329PY6PtMpl5esDBY9CkiQpD+rrGwCErlYEzvSgKAo7d+4RFkOu3va2dxAMhSg5u88VkwGUlJ18+Xzim3Y2Ni4DQB92flVkuizNfkk/cMCZZqsrVjQB4B3qdOR+hZAOeEmlUgwNOftvRi5VjWcNw3gSeB4YO0ZkmuafFCwqSZKkaWhosPtWabFB0oEKx++vjsTtLceW9dTUuL//UVlZOW/59Qf5/Oc/Q+jcfiKNYnuSKWn3JF8rV9qJhSfSVdD7pAM+Ou/fPOFjpjJbtO6J/Rw6/Joj/b5aWtYD4B08z8j8loLeq1AyfnuVtb+/j7KyMsfum8vK13PAz4EYduPV7IckSZKrLFiwEAA9WtitovFktxx3775RyP2n44EH3kRlVTUlFw6gCq6XyyZf2SanItXXN1BRUYk33OG6fmgTSdSVEYtGOXHieMHvtXDhImpr6/ANtBfNwYSrpS9Lvpw0afJlmubHsWc8fgf4U+CvRz8nSZLkKpeSr0Eh9w+e6UFRVdfXe13O7/fz0DvehZJOUtL+otBYlGQaVVXxeLxC4wD7AEdLy3q0RAQtJub5NB3xOnv15rXXCl/HpygK27dfj5qK4x04V/D7FULGbz/XBgedfcOWS8H9jcAB4HtAHXDGMIxbCx2YJEnSVC1cuBgAfaTf8XtrkRjeniE2tG509SnHa7n99ruYP38BoY5DaIISVwA1lcYfCAjvcJ+1YcMmAHz97YIjyV2iNpt8verI/fbssVd5A93HHLlfvmV89tbswIDLki/sLvc7gQHTNDuAXcBfTfZNhmGohmE8ZhjGrwzDeMowjBVXff0fDMN4afRrT8lh3ZIkzVQoFKK6uuaKWXtOyZ40K6Ytxyxd13nnO98DVoaS9heExaGk0oSC7hkdvGXLNgB8fW2CI8ldOuQjHfTy2qGDjpzga25eR319A4Ge4644tDFV2ZqvcNjZNx25JF/qaNIFgGmah3O89v2A3zTNHcBHgU9e9fWNwG2mae4Z/SiedV1JklyrsXEpWiLi+AtB4EwPmq6zc+duR++bL3v23Ejj0mUEu0w0AckrgJrMEAq5J/lqaJjH8uUr8Q2cK57EQlGI15Qy0N/PxYsXCn47VVW54457UNIpAp3O9BfLp4zXXvkKh8OO3jeXoxDnDMO4G7AMw6jAnvmYyxrsTuAHAKZpPmcYxthxDsMwVGAl8BnDMOqBfzFN8/MTXayyMoiuazncVpKkuWzt2tW89NKL6MO9JMvnO3JPfXAEb/8w1+/axfLlCxy5ZyF84Hd+mw9/+MOUtr/IwKrbnL25ZaEkUpSXl1FbW+rsvSdw++238uijj+LvPUW0frXocHKSqC0j2N7LuXMnWb9+VcHv99BDb+WrX/0SZaeeJnT+Uo+xWJ3B0FUnaCtfe/yKlelUSS39a+664jGlp57G33Pi0idUje7N77jiMdmt4MDpbnwXx98y7N27hlT5+PNVMz575SuZjDr6vMsl+fpN4O+BRcAp4KfA+3L4vjLg8tWstGEYummaKSAEfAr4G0ADfmYYxj7TNMetEOzvL94RBpIkOaehwW6O6RnucSz5ym457tixi+7u4umIfrXm5s0sW7aCU6eOM7Rkm6PtOpRUGsWy8PuDrvoZbtu2i0cffZRA59HiSb5q7CTihRdeYuvWXQ7c0cNtt93FE098BzWdJKOJb5Kbq4zXXtTp7e3P+/NuomRu0uTLNM0u4K3TuG8YuPzO6mjiBTAC/L1pmiMAo33E1gPuaLMsSVLRWrFiJQCeSLdj9wy09+LxeNixY6dj9ywEVVV58MGH+NM/fYSSs/sYbLrZuXsn7KkEJSUljt0zF/PmzaelZT2vvnrA7h/nd395crIyhKUomOZRx+75lrc8yPe//wRx3Uv3preDeu2dqv7meye91tCynQwtm/jvUrxyMSUXDhJtrGVg24oJHzsRS9ewgEjE2ZmwuZx2vMswjOcNwzhpGMap7EcO134GuHP0GtuBy49eNAFPG4ahGYbhwd6i3D+N+CVJkq6wePESPF6vY8mXPjCCZ3CErVu3u6peabp27tzNokWLCXaZqA5OClDjSQBKS92X3Nxxx90ABDsOCY4kR5pKsjLIiRPHSCaTjtyyrq6ee+55AC0WJnjRmZOWeaEo4NEYGXF2dy2Xgvu/B/4EuAnYe9nHZL4DxAzDeBb4W+CDhmF8yDCMe0176udXuNTA9V9N0yySZ7UkSW6maTorlq9EH+l1ZOBvoN3ecty1q/hOOV6Lqqq8+c1vAytD6PwB5+4bt/+sysvdl3zt2rWXktJSgh2Hi2aIdLKqhFQqxZkzzp3UfPDBhwiGQpS1v4CSjE7+DS6R0TWiUWeTr1xqvgZN0/yvqV7YNM0M8P6rPn30sq//JfCXU72uJEnSZJqaDI4cOYQn0kOyrKGg98puOW7ffl1B7+OkG2+8hc9//jNYHYeILN6KpRe+6akas1do3Jh8+Xw+7rzjHr75za8S6DpGtGHycT+iJapKCNHJ8ePHxmYwFlp5eQXvfOjdfPrTn6Ks7VkGm25y5L4zZekq8bizp1nHXfkyDGOXYRi7gEOjPbluzH5u9POSJEmuZBh2YbSnwAN/9cFLW47B4PgnqoqN1+vlvvt+DSWdcKx9gBpLAFBR4c4Gtffd9wZUVbVP8xXBuKFklb0FfvJk4ccMXe7ee99gtyzpPIxn8Lyj954uS1OJxZxdqZto2/Hjox+LgBbgDy/73B8XPDJJkqRpWr3aXpnwDnVM8siZ8Z+1ZzkWa2+vidx11z3ouofQxVcdSTa00ZWvysrKgt9rOurq6tmz5yY8I734+s+IDmdSyfIglgInT56Y/MF5pOs6H/zdj6AoChXHn4S0+7dpLU11rDYua9xtR9M0c6nrkiRJcp0FCxZRWlZGOlzY5CtwthdN09i2bfZsOWZVVFSye/cefvrTH+MdvECiorD9y7SovfJVXV1T0PvMxJvf/DaefPLHlJzdR7yqUXQ4E9M1UqUBTrWdxLIsR0c2rVmzlgceeCPf/va3KD3zK4aW3eDYvafDUl2UfGWNtoG4nAVEgSPAn5um6fwQNUmSpAkoisLaNc0899yzqPEIGV/+2xdow3G8fcO0btpCaal7moLm05133stPf/pjAp2HC558qWPJV3VB7zMTy5evYOvW7bzwwnN4B8+TKHd3Q91URZCR9l66u7uoq6t39N7vetf7eP755zh//hXiVY0kKhY5ev8pUe3ENJPJoKq5nEPMwy1zeMwR7P5bvzv68SIwAFwA/qVwoUmSJE3f2rUtAHgLtPrlP2d36b7+ene/q5+Jlpb1NMybT6D3BEo6UdB7aSMJSktL8Xp9Bb3PTD344DsBKGl/UXAkk0uOdnZvb3d+m9Tv9/PRj/4BqqpSeewnrj79aI0uCqbTacfumUvytd00zd81TfPg6MdHAcM0zb8FlhY4PkmSpGnJJl+e8MWCXN9/3k6+tm+/viDXdwNFUbj5pltR0il8vQVsWWBZ6CNxamudXZ2ZjjVrmtmwYRO+gbN4CrytPVOpsgAA7e2nhdx/1ao1PPTQb6DGI1Qc/6mLDyrY2ZcTg8izckm+PIZhrM3+ZvTXmmEYAaDw548lSZKmwTBWoesevOH8DxdWkil8nYOsWNFEbW1d3q/vJnv32l3uAz2FOzWnJFIoqQx1dcXxs3z72x8GoKT9ebGBTCKbfJ07d1ZYDG95y4OsX78Bf28bwQsuHWIzVg7nruTrfwLfNwzjRcMw9gNPAB/APvH4rwWMTZIkadq8Xh9NTQbeSDdKKr9bZr6LgygZi23bdkz+4CK3ePESFi9egq//LEq6MEXJ+rDdY6mhYV5Brp9v69a12glFf7urV7/ckHxpmsZHP/oIZeUVlLc9XfD2L9MyuuKljjMSqRAmTb5M03wKWIY9TPth7C3HZ4CPmqb5FwWNTpIkaQZaWtYDFp48t5zwX7C3HOdC8gVw3XU7UTIpvAPnCnJ9LRIDiif5AnjooXcDUNL+guBIxmfpGumAl/MXCvPnlquamhp+/2OPoGBReeT7KMmY0HiupowlX84U28PETVb/ePS/XwA+g73a9bvAPxuG8XnTNN26eStJkgRkky/wDuZx69Gy8F8YoKysnKamVfm7rotlW2kUqr+VPlR8ydel1a8z7l79KvHT3d1NKiW239amTVt4+9sfRosPUWH+yF31X2kLTdPckXwBL43+9yns+YtXf0iSJLlac3MLiqLgzWOnbX1gBC2aYMuWrWiac9sUIq1atQZ/IIBvoDDbV/royteCBS5uR3AN73jHuwB3r36lS3xYmQzd3V2iQ+HBB9/Jpk1b8PefoeTsPtHhjFEyGXQ9l2mL+TNRk9UnRv/7JefCkSRJyp9QqIRly1Zwou0UZNKQh5oO/wW7teHmzdtmfK1ioes661rW88ILz6Emhsl4Q/m9/pDdhmDevPl5vW6hrV+/gZaW9bz66gE8Q50kS913WjMVslt3dHV1Cv/5aprGxz72CO9//7vhzPMkShtIVIpPuJVUBq/P2RYnE207ZgzDSF/jI2MYhnPNMCRJkmagpWU9Siadt7ovX8cAYG+jzCXNzesA8A7mv3WHHo5RX9+Az+EXwHxw++pXOngp+XKD8vIK/vAP/xRN06g0f4gaj4gOCSWdwe/zO3rPiVa+xhIzwzBeNk1zgzMhSZIk5U9Lyzq++91/xzt4geQMO5IrqTS+rjArVqykstKdA6ALZc2aZgA8kU5itSuu+FrNTw9hjXYJjzbWEm5dcsXXq392GH1wZOz3ycoQfbvt4edKIoUWTbC4+crvKRatrRtZu7aFQ4deRY90kyqpFR3SFdJBuyNUb2+P4EguWbNmLe9//+/w6KN/R+XRH9Db8kBeVqWnS02lCQQCzt4zx8e5qDJOkiQpd2NF93no9+XtCqNkLDZunFurXgArVxoAeIbyWzvkGU3KFi8uzuRLUZRLXe9dVMeUlQnYyVdPT7fgSK50331vYPfuG/GGL1J65jlxgVgWSjJNKJT/EWQTybXCzLmJnJIkSXlUWVnFggULOXfhHDX7/u2Kr6lTHHkyV7ccAYLBIPPnL+BcV499Uu2yQc09N60lNTrK5lp6964Z92vZFbHGxmX5C9ZhmzdvZcWKJk6cOMbQSD/pYKXokMakR5Ovvr4+wZFcSVEUPvjBj3D8xDEunNtPonwh8SrnE3AlnUHJWIRC+a1jnIxc+ZIkada7++77qCwvp8ZrXfFR6p3aVoevYxCP1zs2umiuWbp0OWoqhpocmfzBOfIMZJOv4p1WpygKb33r2wEoOb9fcDRXyvg8WMDAQL/oUF4nFArxh3/wcXRdp+LYj1ETw47HoCTsFhylpWWO3nfclS/DMNq4lHQtMAzj1OivFcAyTbN436ZIkjSnvPGNb+GNb3zL6z7/q189wyOPfDSna6ixBN7+YZo3bCrKwvB8WLx4Cc88A/pIP4k8nXj09A+jqGpRr3wBXH/9LubPX8D5DpOhJdtzPhGqRePUf3fi7crevWsmXFkEKNvfRqC995pfs3weBgcHcorHaStWNPHe9/4Wn/70P1B+7Cf0r733ilXVQtNi9tSGsjJnk6+JVr72AHtHP5ou+3X285IkSXOGr2MQYE7We2UtXGi3BdCieXohtyy8/SMsWrgIv9/Z02b5pmkab3zjW1AyaUIum2GY9ukMDg6KDmNcDzzwRrZs2Ya/v53gxVcdvbcat5Ovigpnt4onOu1YmFbGkiRJRShb77VhwybBkYgzf759WlSP5eeFXIvEUJIpli9fmZfriXbrrXfwxS9+jszF1xhatBk0z6Tfkw746Lx/84zvHd64lPDGa2/d1vzwIEN9YSzLQnFwVSlXiqLw4Q9/lPe85yGs088Sr1xCOlDuyL3VqJ18OX162ble+pIkSUXM1zFIKFTCihWzI1GYjuz4Hy0Wzsv1vL12j6emJiMv1xPN5/Nxzz33o6ZiBLpM0eGMsbw6mUyGaHRqB0ycVF1dwwc+8EGUdJLy4086Nn5IiyZG71/tyP2yZPIlSZI0CW0ohj4cp7V145wZKXQtlZVVaJqGlqduc8kzAAAaIElEQVTGmJ4++zrZNhazwd1334+mafbWo0vmF2Y89nN2ZMT5gvap2Lv3ZrZvvw7f4DkCXUcdueel5KvGkftlyeRLkiRpEr5Oe8uxtXWj4EjE0jSN6uoatER+ki9vTwRFVWfNyhdATU0NN9ywB89IL5489JbLB2ss+crfKdVCUBSFD3zgQ/h8PsrankFJxgp+T204DkBdnbOjoWTyJUmSNIlssf1crvfKqq6uQU2MzHxVJ2Ph7Y/QuKSRQGDik3zF5p577gcg5HDx+Hgyup18xWKFT2Zmqq6unre//WHUZJSSsy8W/H7acByv10dZmTM1Zlky+ZIkSZqIZeHvHKSqurpou7DnU1VVNYqVQUnN7IXcMzCMksqwatX4DViLVUvLehYvXoK/5yRqQnydlaXbL/WxmPhYcvGGN7yJ+oZ5lFw4iJanwx3j8UTizJs3z/GDCLl2uJckSZq1Sl89S8nRcbaILFBjSTbu3OzKk2JOq6y0j+RriZltYXm7hwBmZcNaRVG46657+fSnP0XJ2ReIVywWGo+l2clXIpEQGkeuvF4f737Xe/nEJ/6EkjMvMGjcUpD7qPEkSjLFvHnzC3L9icjkS5KkOWvlyiaamlYRiQxN+Di9VufOO+9xKCp3yx7Jn+popqt5u+0Tk9mB3bPNTTfdymc/+xihCwfF9/1S7eQrmUyKjWMK9uy5ia997cucPmMSWby1IK0ntCF79XbBgkV5v/ZkZPIlSdKcVVNTy6OPflZ0GEWlvLwCAH2kDyWTmd5FLAtfd5jyioqxxq2zTXl5BX/+53/FiRPHxn3M1772ZfrThV+NslR7xTaVShX8XvmiqipvfetDfOITHyd0/mXCK/Zc83GB0934LtoHYqKNtYRbrywNqP7Z4bH5oQDJyhB9u1cD4AnbbyBEPAdl8iVJkiTlLLvtWH7y59O+hjYcRxtJ0LJxx6zeyt2wYdOEhzQef/w79IcdGHg9+jPOZNKFv1ce7d69h8/9y2NYnUcYWrIdy5PfKQjZpExELadMviRJkqScbd68jQceeBORyBBHjhzi3LmzU76Gt8vecmxpWZfv8KRrGc1vLZf0HcuVpuncd+8DfO5zjxHoOsrIgtbXPSbaWMvAthXjXqN37/gHOrJD3ZcsaZxxrFMlTztKkiRJOQsGg/zWb/1PPvKR/zvt1hu+TvsE27p1G/IZmjSJYku+AG677U40TSPYeSTv1/YMjlBZWTW2le4kmXxJkiRJjvJ12aOali1bLjqUuWE051LV4pvOUFFRybZtO/AM96AP9+btuko8iTYcF/YclMmXJEmS5BgtEkOPxGlt3YCqypcgR4yueBXrz3vv3psB8PecyNs1Pf32qKUVK5ryds2pKM4/CUmSJKkoZbcc16+f26OanJQ9lerxFGeZ99atO9B1D/7eU3m7plfwXFGZfEmSJEmOyY5qmutzMp2kpO2VL4/HKziS6QkGg6xf34pnuAc1X0Pde+3rGMaqvFxvqmTyJUmSJDnDsvB1DlJRWUlj41LR0cwZSspuMeH357dVg5M2bdoKgG/wXF6u5+uNUF5eQX19Q16uN1Uy+ZIkSZIcoYejaNEEG1o3zer+Xm5zKfkKCI5k+lpb7ZOx3sHzM76WOhJHG46zevVaYc9DmXxJkiRJjsh2It+4cbPgSOYWNWEnXyUlJYIjmb5ly5bjDwTwDF6c8bXcMFdUJl+SJEmSI3wdMvkSQU3YY4WKOfnSNB2jaRWeaD9KamYjmXyjc0Wbm8UlXwU7+mAYhgr8E7AeiAPvMU3zxDUe81/A90zTfKxQsUiSJEmCZTL4u8IsWLCQurp60dHMKWo8iabrBIMh0aHMSFOTwYEDL6MPd8/oOt6uMB6Ph6YmMcX2UNiVr/sBv2maO4CPAp+8xmP+DKgqYAySJEmSC3h7IijJNBs3bhEdypyjxlOUl5UXfZ3dsmX2GCHPcM+0r6HEU3j7h1m1ag1er7jTn4VMvnYCPwAwTfM54Ip1ZsMw3ghkgO8XMAZJkiTJBeSWoyCWhRZNUF1dIzqSGVu61O5GHzr3MqVtz03rGr4uu9XJdEdj5UshO66VAYOX/T5tGIZummbKMIxm4G3AG4FHcrlYZWUQXS++0QiSJEmzld/vyfmxvo4BVFXlpptuoKystIBRFQ9VLfxKlJJIoaQzzJ/fQG1tcf/cy8vXsmjxYs62twND07pGtsnv7t3XC/15FDL5CgOX/5+ppmmmRn/9ELAAeBJoBBKGYZw2TfMH412sv3+kUHFKkiRJ0xCLJXN6nJJM4e2J0GSsJh5X6O6e3gvnbJPJFH7QtT4cB6CionpW/Nw/99kvk8lkOHu2nfe9751T/n7fxQF8Ph/z5i0t+M9jouSukMnXM8A9wDcNw9gOvJr9gmmaH8n+2jCMPwY6Jkq8JEmSpOLl6wyjWJbcchRAi9jJV339PMGR5IeqqqiqiqZNfSdMHYnjCUdZt2U7Hk/uq7aFUMjk6zvALYZhPAsowLsMw/gQcMI0zccLeF9JkiTJRXydst5rPFo0Tv139439PtpYS7h1yRWPqf7ZYfTBS7s/ycoQfbtXX/GYsv1tBNp7x35vqQpd925CH4oCsGDBwkKEX1T8o33mNm/eKjiSAiZfpmlmgPdf9emj13jcHxcqBkmSJEk8X8cgXq+P1avXig5lztHDMvnK8l3oB2DTJvEnbotzxLkkSZJUFNRYAs/ACM0btwg92u9W6YCPzvsnXhHs3btm0uuENy4lvPH18zI9gyNoui6Tr4yFv2OQ2rp6Fi9eMvnjC0x2uJckSZIKxteRPdq/UXAkc1DGwjMYZfGixej63F5r8fYOoSZSbN2yzRX9zmTyJUmSJBVM9mj/+vUbBEcy9+hDUZRUmhUrmkSHIlx2y3Hr1u2CI7HJ5EuSJEkqGG9XGH8gQFOTITqUOcfTFwGQyRfgv9CPpuu0toptrpolky9JkiSpINRoAk84SkvzOjRtbm97ieDtsftYrV49ec3YbKZGE3j7hlm/rpVgMCg6HEAmX5IkSVKB+LrCAKxbJ7ccRfB2D+HxeFi+fKXoUITyu2zLEWTyJUmSJBWId3SO3rp16wVHMvcoCXcMkHYD/3k7+dq2bYfgSC6RyZckSZJUEL6uMF6vj5UrZb2X03xjiW+r4EgES2fwdwwwb958FixYJDqaMTL5kiRJkvJOSaTwDIywatVq4aNc5qJsi4+5PlXA2x1GSabZtu06V7SYyJLJlyRJkpR32WLvtWtbBEcyN/kv9OMPBOb8VAE3bjmCTL4kSZKkAriUfDULjmTu0cJR9KEYmzZumfOrjv4L/fh8PtfVHcrkS5IkScq7bPK1atXcbnMgQuB8H+C+1R6naZEYnnCUDRs24fX6RIdzBZl8SZIkSfllWXj7IsybN5/y8grR0cw5/rN9KIrKjh3Xiw5FKN/FAQA2b94mOJLXk8mXJEmSlFdaJIYaT2EYq0WHMueoI3F83WGam1uoqKgUHY5Q2f5eW7bI5EuSJEma5by99libpqZVgiOZewJnewHYtWuv4EgEy2Twdw4yb9585s9fIDqa15HJlyRJkpRXnv5hADnPUYDA6R4UReWGG3aLDkUob08EJZl25ZYjyORLkiRJyrNs8rV8+QrBkcwt2lAMX88QGzZspLq6RnQ4Qvk67HqvTZvc2edMJl+SJElSXnn7h6mvb6CkpFR0KHNKsK0LgJtuulVwJOL5OgZRVJX16905V1QmX5IkSVLeqNEEaizJsmVy1ctRlkWwrRufzzfntxyVVBpv7xArVzS59g2ATL4kSZKkvPEMjACwdOkywZHMLd6uMHokxq5dewkEgqLDEcrbPYSSsWhtdeeqF8jkS5IkScojfdBOvpYsWSo4krkldKITgNtvv0twJOJ5i2CouEy+JEmSpLzRw1EAlixpFBvIHKLEkwTO9rJgwUJaWtw1RkcEX1cYRVFcPVdUJl+SJElS3njCIyiKwsKFi0SHMmcE27pR0hnuvPMeFEURHY5YmQze3ghLly5zbb0XyORLkiRJyiM9HKO2tg6fz12z9GYtyyJ0vANN17nlljtERyOcp38YJZ1x9aoXyORLkiRJyhMlmUaLJliwYKHoUOYMb1cYTzjKrhv2UFk5t8cJgd1cFdw/0F0mX5IkSVJeaJEYgEy+HBQ63gHA3XffJzgSd/D2DgEy+ZIkSZLmCH00+Zo3b77gSOYGNZogcLaXJUuWykL7UZ7eCIFA0PU1hzL5kiRJkvIiu/LV0DBPcCRzQ+hEJ0rG4t57H5CF9tjNVT3hKCtWrERV3Z3euDs6SZIkqWjoI3EA6usbBEcyB2QsQic68AcC3HzzbaKjcQV9tMHv8uUrBUcyOZl8SZIkSXmhDdvJV11dveBIZj//uT60kQS33Hw7weDc7mifVUwD3WXyJUmSJOWFNpJA13UqKuSpu0ILHb8IwL33PiA4EvfwDBbPaCuZfEmSJEl5oY0kqK6ukfVHBaaHR/B3DLJuXSuNjXKMU1Z2tNXixUsERzI5mXxJkiRJM5exUGMJampqRUcy64WO23Mc77nnfsGRuIsnHKW2rr4oBovL5EuSJEmaMTWeRLGgqqpKdCizWypN8FQXFZWVXH/9LtHRuIaSTKONJFi0cLHoUHIiky9JkiRpxtRYEoCKCpl8FVKwvRc1keKO2+/G4/GIDsc1iq3Br0y+JEmSpBnTYglArnwVWvB4B4qicOed94gOxVX0ITv5mj+/OBr8yuRLkiRJmrFLK1/ypGOh6AMj+HqG2LRpi2xkexV9ONvgVyZfkiRJ0hyhxlMAlJeXC45k9gqdtAvt5arX62V7zDU0FEeDX5l8SZIkSTOmxu2Vr7IymXwVRDpDsK2b8vIKtm+/XnQ0rpNNvmpr6wRHkhuZfEmSJEkzpibsla/S0lLBkcxO/gv9qPEkN998qyy0vwZtJP7/27v3IDvru47j73M2e9/QpE1CQoVSAv3ScItcxgQEApJ2WqStgzrSwggolqHt1F7UlrEKnSrOqPRm6W1ISUFntNoywFipLSSKoi0MSFH50tu0HXrJlZBwy+7m+MfzHBJDgV12z3nOs3m//sl5nnNy9pMzyeazv+f3/H709/fXpvzP69QbR0QTuA44AXga+O3M/PY+z78NuBhoAR/MzNs6lUWS1Fnty47z5x9UcZK5aeS7mwBYu/Z1FSfpTX1PjrNo0eLaLPDbyZGvNwFDmbkaeB/wl+0nImIRcAVwKvBLwCcjoh6fmCTpWZrjkwCMjTnyNduaT40z9Mh2jjjiyFrsW9h15QK/L33py6pOMmWdLF+/CPwTQGb+B3By+4nM3AKckJnjwFLg0cxsdTCLJKmDmrsn6OvrY2hoqOooc87QD7bQaLU455zXVB2lJzV312+B345ddgQOAnbsczwZEfMycwIgMyci4u3A1cDHXujNFi4cYd68vs4klSRN29DQ3rlHjd0TjI2NsWSJlx2nqtmc2gWfke9vodFocP75b2TxYkcWAXbtGn3mcfPJ4maPpUuX1Obz6WT5egzY91NototXW2b+VUR8BvhyRJyVmXc+15tt3/5Eh2JKkl6Mp8q1vQCaE5OMvGSUzZt3VpioXvbseeELPs0nnmZw02Mce9wJNJsjfr6lbdsef+Zx+07bwcHe+vv3fEWwk+Xr34DzgL+LiFXAN9tPREQA1wDnA+MUE/L3dDCLJKmDmuOTjIyMvvALNS3DP9wKwJlnnl1xkt7VV8M15jpZvr4ErI2IfwcawCUR8W7g25l5S0T8F3A3xd2OX87MjR3MIknqlBYwPsnIyEjVSeacdvlyE+3n1qjhGnMdK1+ZuQe4fL/TD+3z/NUU870kSTXWmJikAQwPD1cdZU5pPj3O4KbHWLHiGBYtWlR1nJ61d425+sw3dJFVSdKMNCaKZSYc+Zpdg49shxasXn161VF6Wrt8jY2NVZxk6ixfkqQZaZbla2jIka/ZNPTINgBWrz614iS9rbm7fmvMWb4kSTPSmCjul7J8zaI9LYZ+soMlBx/MYYcdXnWantYYL0a+Rkfrc8OH5UuSNCONZ0a+BitOMncMbN1Jc/cEp5y8qjZb5lSlvbvC6KiXHSVJBwhHvmbf4I8fBeCkk06pOEnva45P0tfXx8DAQNVRpszyJUmakb0jX24tNFsGf7qDRrPJypUnVh2l5zXGJxkeHqnVCKHlS5I0I+2Rr8FBy9esmJhkYMtOjlx+FPPn12cSeVUaNVxjzvIlSZqR5mS7fDnnazYMbN1FY0+L449fWXWUWmhOWL4kSQeY/m27AC87zpbBTY8BcOyxx1ecpB4aE5O1m29o+ZIkvSjtvRzbZWHBgoVVxpkzBrYUm0Mfc8xxFSfpfUM/3EpjT6t2I1+d3NtRkjSHXXDBhSxffiSTk5PMn3+QZWE2tFoMbNnJsmWHsHChZfa5LF68hEMPewWbN2+iMTxQu7tCLV+SpBdldHSMs846p+oYc0rfzqdo7p7g1a8+puooPW14eJh1199UdYwXzcuOkiT1iIGtxfy5iKMrTqJOsnxJktQj2jcvHHVUVJxEnWT5kiSpR/RvfxyA5cuPqjiJOsk5X5IkVaTvyac5+OZ79h4/sZtly15eu7v3ND2WL0mSKnD66WeyceOd///kKJx77nnVBFLXNFqtVtUZpmTz5p31CCpJkg54ixfPf87NJp3zJUmS1EWWL0mSpC6yfEmSJHWR5UuSJKmLLF+SJEldZPmSJEnqIsuXJElSF1m+JEmSusjyJUmS1EWWL0mSpC6yfEmSJHWR5UuSJKmLLF+SJEldZPmSJEnqIsuXJElSFzVarVbVGSRJkg4YjnxJkiR1keVLkiSpiyxfkiRJXWT5kiRJ6iLLlyRJUhdZviRJkrrI8iVJktRF86oOUGcR0Q+sAw4HBoEPZeYtlYaqkYjoAz4LBDAJXJKZ36k2Vf1ExBLgXmBtZj5UdZ46iYj7gB3l4fcy85Iq89RJRLwfeAMwAFyXmddXHKk2IuJi4OLycAhYCSzNzEerylQn5f+96yn+750ELqvb9z7L18xcCGzNzIsi4mXAfYDla+rOA8jM0yJiDXAt8MZKE9VM+U3o08CTVWepm4gYAsjMNRVHqZ3y3+upwGnACPDeSgPVTGbeANwAEBGfANZZvKbl9cC8zDw1ItYCfwKcX3GmafGy48x8AfjAPscTVQWpo8y8Gfid8vAVwE8rjFNXfwF8CvhR1UFq6ARgJCK+EhF3RMSqqgPVyGuBbwJfAm4Fbqs2Tj1FxMnAMZn5maqz1MzDwLyIaAIHAeMV55k2y9cMZOauzNwZEfOBvwf+sOpMdZOZExGxHvg4xWeoKSovXWzOzNurzlJTT1CU19cClwN/HRFeDZiaRcDJwK+x97NrVBuplq4Erq46RA3torjk+BDF1JWPVZrmRbB8zVBEHArcCdyYmX9TdZ46yszfBF4FfDYiRqvOUyOXAmsjYgPFnJHPR8TSaiPVysPATZnZysyHga3Asooz1cVW4PbM3J2ZCTwFLK44U61ExALg6My8s+osNfQuir9/r6IYwV7fnkZQF/6UNwMRcTDwFeDtmfm1qvPUTURcBPxcZl5DMQqxh2LypKYgM89oPy4L2OWZ+ZPqEtXOpcBxwBURcQjF5YsfVxupNu4C3hkR11IU1lGKQqapOwP4atUhamo7ey81bgP6gb7q4kyf5WtmrgQWAh+IiPbcr9dlppOfp+aLwOci4l8o/vH8bmY+VXEmHTiuB26IiLuAFnBpZjpvcwoy87aIOAP4OsUVlLdlpj84TU8A3606RE19GFgXEf9KcbftlZn5eMWZpqXRarWqziBJknTAcM6XJElSF1m+JEmSusjyJUmS1EWWL0mSpC6yfEmSJHWRS01IqlxEHA5syMzD9zvfysxGRLwBODkz/+h53mMDcFVmbpiFPAuATwDHl6ceAd6Rmd+ahfe+CiAzr5rpe0mqJ8uXpJ6XmbfQ3U3rrwEezMy3AETEBcDfAid2MYOkOcryJannlftYrsnMiyNiDcVeoBPA3cCKzFxTvvS3ylXXFwDvzMxby50oPg0cSrGLwvsz86vlCNQq4DDg45n5yX2+5FJgU0Q0M3MPRfHaVWbpA/4cWEOxqvYNmfnh8rn3Ab9enr8d+IPMbEXE71FsIr+FYnXur8/uJySpTixfknrFIRFx//O9ICL6gRuBczPzgYj46H4v2ZGZJ0bELwN/DNwKfBRYl5m3RMQy4K6IWFm+figzV/yML/Uh4GaKrYfuAP4ZuKl87jKA8usMArdHxD0UW+ycBJxCsWL+jcBbIuIhiq2Mfr48fzeWL+mAZvmS1Ct+lJkr9z0REftvwXEcsCkzHyiP11GUq7aby1//G1hUPj4HODoiPlge9wPLy8f/+bOCZOa9EfFK4LTy978HeGtErC6PV0bE2eXLx8pcRwC/ANxbnh8GfkAxivaPmdkeOfsCNduHTtLssnxJqpNJnv8u7fbejC2gUT7uA87OzG0A5ejXJuBNwLP2YY2IBnAd8K7M3AhsLIvbtyhGr/qA38/ML5avX0RxSfIa4COZeW15fkGZ5637ZGlntHxJBzCXmpBUJ/8LLIyI48rjN1MUredzB3AFQESsAB4ERp7rxZnZAlYA742I9vfIV1L8sPqd8v0ui4j+iBgD7qKYO3YHcFFEjEXEPIpRuF8FvgacFxEviYgh4Fem+WeWNMdYviTVRmbuBi4EPh8R91JMon/W6NV+3gGsiogHKCbOX5iZO1/g9/wGcCzwvYj4H2A98OZy9OxTFKNg9wH3AJ/LzA2ZeSvwDxSXMh8E7gfWZ+b9wEeAbwAbge9P848taY5ptFov9EOjJPWGciTqz4CrM/PxiHg38PLMfE/F0SRpyhz5klQb5bIP24BvlHdGngH8abWpJGl6HPmSJEnqIke+JEmSusjyJUmS1EWWL0mSpC6yfEmSJHWR5UuSJKmL/g8b6nw4yVilLAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10b072a58>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(10, 7))\n",
"ax = violinplot_kenpom(data, ax, 'win_prob_hi', 'Higher Seed KenPom Win Prob.')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A few things are immediately clear from this plot:\n",
"\n",
"- Overall, the win probabilities slope down and to the right, since win probability drops for lower seeds.\n",
"- The green distributions (where an upset actually occurred) are lower than the blue distributions (where no upset occurred).\n",
"- There is substantial overlap between the green and blue distributions, so KenPom doesn't do a perfect job of identifying upsets. Far from it. But, if you focus on the dashed lines in the distributions (which represent the 25%, 50% and 75% quantiles of the distriubutions), you'll see that there is a noticeable distinction between the upset and non-upset distributions.\n",
"\n",
"### Visualizing the Efficiency Margin Differences\n",
"\n",
"The KenPom win probability is a function of the difference between the teams' efficiency margins. We can also look at those efficiency margins directly. The story isn't really that different, as we'll soon see. But, since the efficiency margins are relatively easy to understand, it may help your intuition to look at the data from this perspective."
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a1a5aaac8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(10, 7))\n",
"palette_colors = sns.color_palette()\n",
"data[data['upset'] == 0].plot(\n",
" kind='scatter',\n",
" x='adj_em_lo',\n",
" y='adj_em_hi',\n",
" label='No Upset',\n",
" color=palette_colors[1],\n",
" ax=ax,\n",
")\n",
"data[data['upset'] == 1].plot(\n",
" kind='scatter',\n",
" x='adj_em_lo',\n",
" y='adj_em_hi',\n",
" label='Upset',\n",
" marker='x',\n",
" color=palette_colors[2],\n",
" ax=ax,\n",
")\n",
"ax.set_xlabel('Lower Seed KenPom Adj EM')\n",
"ax.set_ylabel('Higher Seed KenPom Adj EM')\n",
"ax.set_title('First Round NCAA Tournament Upsets and KenPom Adj EMs')\n",
"ax.text(x=-4, y=11, s='Excludes 1 and 16 seeds')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The upsets (marked with 'x' for each data point) are clearly skewed to the lower right relative to the non-upset dots. Upsets have tended to occurr more often when the lower seeded team has a relatively high KenPom _AdjEM_, or where the higher seeded team has a relativley low KenPom _AdjEM_. Of course, this is just another way of saying that the higher seeded team has a lower KenPom win probability.\n",
"\n",
"#### Visualizing the Distribution by Seed\n",
"\n",
"The overall picture makes it clear that KenPom data should be somewhat useful in predicting first round upsets. However, it's important to look at the results in more detail by seed.\n",
"\n",
"Let's decompose the scatter plot above into 6 plots, one for each seed 3 through 8. We will skip the second seed games since there are so few upsets.\n",
"\n",
"First, we need a function to isolate the data we need for each sub-plot."
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {},
"outputs": [],
"source": [
"def select(data, upset=None, seed_hi=None):\n",
" \"\"\"Extract data based upon higher seed and upset dummy variable.\"\"\"\n",
" if upset and seed_hi:\n",
" return data[(data['upset'] == upset) & (data['seed_hi'] == seed_hi)]\n",
" elif upset:\n",
" return data[data['upset'] == upset]\n",
" elif seed_hi:\n",
" return data[data['seed_hi'] == seed_hi]\n",
" else:\n",
" raise ValueError('invalid parameters')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This function converts a seed into a `tuple` telling us which sub-plot goes with which seed."
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [],
"source": [
"def ax_map(seed):\n",
" \"\"\"Map higher seed to a sub-plot.\"\"\"\n",
" return (seed-3)%3, (seed-3)//3"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This function will plot the scatter plot for one particular seed game."
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {},
"outputs": [],
"source": [
"def subplot_kenpom(data, ax, seed_hi, x, y):\n",
" \"\"\"Scatter sub-plot for a particular seed.\"\"\"\n",
" palette_colors = sns.color_palette()\n",
" df0 = select(data, upset=0, seed_hi=seed_hi)\n",
" df1 = select(data, upset=1, seed_hi=seed_hi)\n",
" ax.plot(df0[x], df0[y], '.', ms=8.0, color=palette_colors[1])\n",
" ax.plot(df1[x], df1[y], 'x', ms=8.0, mew=2, color=palette_colors[2])\n",
" ax.set_title(f'{seed_hi}-{17-seed_hi} Games')\n",
" return ax"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, we can put everything together in one function which will generate the 6 sub-plots."
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {},
"outputs": [],
"source": [
"def scatterplot_kenpom(data, x='adj_em_lo', y='adj_em_hi'):\n",
" \"\"\"Create matrix of scatter sub-plots by seed.\"\"\"\n",
" fig, axarr = plt.subplots(nrows=3, ncols=2, figsize=(12, 12), sharex='col', sharey='row')\n",
" for seed_hi in range(3, 9):\n",
" ax = axarr[ax_map(seed_hi)]\n",
" subplot_kenpom(data, ax, seed_hi, x, y)\n",
" axarr[0, 0].legend(['No Upset', 'Upset'], loc='upper right')\n",
" axarr[2, 0].set_xlabel(x)\n",
" axarr[2, 1].set_xlabel(x)\n",
" axarr[0, 0].set_ylabel(y)\n",
" axarr[1, 0].set_ylabel(y)\n",
" axarr[2, 0].set_ylabel(y)\n",
" plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a1a5cbbe0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"scatterplot_kenpom(data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"These plots show that there is a lot of noise under the surface, and that we should be cautious about relying on KenPom data in picking upsets. Although the overall patterns make sense, the historical predictive accuracy by seed is mixed. And of course, the data set is relatively small.\n",
"\n",
"### Logistic Regression Plots\n",
"\n",
"Let's look at the distribution by seed in another way. We can use the [logistic regression](https://en.wikipedia.org/wiki/Logistic_regression) plotting functionality in the [`seaborn`](https://seaborn.pydata.org/) package to visualize the estimated upset probability as a function of the KenPom efficiency margin difference, by seed.\n",
"\n",
"We won't try to explain the math behind logistic regression here. That will need to wait for future posts. The main idea is it tries to predict the value of binary variables (taking the value 0 or 1) based on the values of other variables. In our case, the binary variable is whether the upset occurred or not. The predictive variable (we hope) is the KenPom efficiency margin difference between the teams.\n",
"\n",
"Using `seaborn`, we can create the plots and simultaneously have the package estimate the logistic regressions for us.\n",
"\n",
"The idea is similar to the 6 scatter sub-plots we did above, except in this case we want 6 logistic regression plots."
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {},
"outputs": [],
"source": [
"def subplot_kenpom_logistic(data, ax, seed_hi, x):\n",
" \"\"\"Logistic regression sub-plot for a particular seed.\"\"\"\n",
" palette_colors = sns.color_palette()\n",
" ax = sns.regplot(\n",
" data=data[data['seed_hi'] == seed_hi],\n",
" x=x,\n",
" y='upset',\n",
" logistic=True,\n",
" n_boot=500,\n",
" y_jitter=0.03,\n",
" ax=ax,\n",
" )\n",
" ax.set_title(f'{seed_hi}-{17-seed_hi} Games')\n",
" return ax"
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {},
"outputs": [],
"source": [
"def regplot_kenpom(data, x='kenpom_em_diff'):\n",
" \"\"\"Create matrix of logistic regression sub-plots by seed.\"\"\"\n",
" fig, axarr = plt.subplots(nrows=3, ncols=2, figsize=(12, 12), sharex='col', sharey='row')\n",
" for seed_hi in range(3, 9):\n",
" ax = axarr[ax_map(seed_hi)]\n",
" subplot_kenpom_logistic(data, ax, seed_hi, x)\n",
" axarr[2, 0].set_xlabel(x)\n",
" axarr[2, 1].set_xlabel(x)\n",
" plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1a1a953e48>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"with warnings.catch_warnings():\n",
" warnings.simplefilter(\"ignore\")\n",
" regplot_kenpom(data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In these plots, the upsets are the dots with the value 'upset' equal to 1, while the 0 values are the non-upsets. The curved lines (with the surrounding shading) are the estimated probabilities of an upset, given the value of the KenPom efficiency margin difference immediately below the curve.\n",
"\n",
"For example, for the 4-13 game, if the KenPom efficiency margin difference is 5, the estimated upset probability is about 60%. On the other hand, if the KenPom efficiency margin difference is 10, the estimated upset probability is only about 20% for the 4-13 game.\n",
"\n",
"You can see that the model doesn't ever predict a high upset probability for the 3-14 games. The message is similar to the scatter plots we saw above. The model is more confident predicting upsets in the 4-13 games than in the 5-12 games (since the probabilty curve gets to higher values). Don't be too confident in this result, however. The data set is quite small and this could be the result of noise, or the KenPom data caveats we've discussed previously.\n",
"\n",
"In any case, if you are inclined to pick upsets, this analysis shows you how to make the best possible use of the available KenPom data in making your picks.\n",
"\n",
"Good luck with your brackets!"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python [conda env:sports_py36]",
"language": "python",
"name": "conda-env-sports_py36-py"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.4"
}
},
"nbformat": 4,
"nbformat_minor": 2
}