{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Final Project \n",
"\n",
"## \"Forecasting the winner of tennis matches in the Men’s ATP World Tour\"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Problem Statement"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The goal of the project is to predict the probability that the higher-ranked player will win a tennis match. We will call that a `win`. This can be stated more formally as:\n",
"\n",
"For two players ${\\cal P}_1$ and ${\\cal P}_2$ where ${{\\rm Rank}_1} > {{\\rm Rank}_2}$ we calculate the probability that ${\\cal P}_1$ will win the match, or that a `win` will happen.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Dataset"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Results for the men's ATP tour date back to January 2000 from the dateset http://www.tennis-data.co.uk/data.php (obtained from Kaggle). The original dataset is shown below."
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>ATP</th>\n",
" <th>Location</th>\n",
" <th>Tournament</th>\n",
" <th>Date</th>\n",
" <th>Series</th>\n",
" <th>Court</th>\n",
" <th>Surface</th>\n",
" <th>Round</th>\n",
" <th>Best of</th>\n",
" <th>Winner</th>\n",
" <th>...</th>\n",
" <th>UBW</th>\n",
" <th>UBL</th>\n",
" <th>LBW</th>\n",
" <th>LBL</th>\n",
" <th>SJW</th>\n",
" <th>SJL</th>\n",
" <th>MaxW</th>\n",
" <th>MaxL</th>\n",
" <th>AvgW</th>\n",
" <th>AvgL</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1</td>\n",
" <td>Adelaide</td>\n",
" <td>Australian Hardcourt Championships</td>\n",
" <td>3/01/2000</td>\n",
" <td>International</td>\n",
" <td>Outdoor</td>\n",
" <td>Hard</td>\n",
" <td>1st Round</td>\n",
" <td>3</td>\n",
" <td>Dosedel S.</td>\n",
" <td>...</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1</td>\n",
" <td>Adelaide</td>\n",
" <td>Australian Hardcourt Championships</td>\n",
" <td>3/01/2000</td>\n",
" <td>International</td>\n",
" <td>Outdoor</td>\n",
" <td>Hard</td>\n",
" <td>1st Round</td>\n",
" <td>3</td>\n",
" <td>Enqvist T.</td>\n",
" <td>...</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1</td>\n",
" <td>Adelaide</td>\n",
" <td>Australian Hardcourt Championships</td>\n",
" <td>3/01/2000</td>\n",
" <td>International</td>\n",
" <td>Outdoor</td>\n",
" <td>Hard</td>\n",
" <td>1st Round</td>\n",
" <td>3</td>\n",
" <td>Escude N.</td>\n",
" <td>...</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>1</td>\n",
" <td>Adelaide</td>\n",
" <td>Australian Hardcourt Championships</td>\n",
" <td>3/01/2000</td>\n",
" <td>International</td>\n",
" <td>Outdoor</td>\n",
" <td>Hard</td>\n",
" <td>1st Round</td>\n",
" <td>3</td>\n",
" <td>Federer R.</td>\n",
" <td>...</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>1</td>\n",
" <td>Adelaide</td>\n",
" <td>Australian Hardcourt Championships</td>\n",
" <td>3/01/2000</td>\n",
" <td>International</td>\n",
" <td>Outdoor</td>\n",
" <td>Hard</td>\n",
" <td>1st Round</td>\n",
" <td>3</td>\n",
" <td>Fromberg R.</td>\n",
" <td>...</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>5 rows × 54 columns</p>\n",
"</div>"
],
"text/plain": [
" ATP Location Tournament Date \\\n",
"0 1 Adelaide Australian Hardcourt Championships 3/01/2000 \n",
"1 1 Adelaide Australian Hardcourt Championships 3/01/2000 \n",
"2 1 Adelaide Australian Hardcourt Championships 3/01/2000 \n",
"3 1 Adelaide Australian Hardcourt Championships 3/01/2000 \n",
"4 1 Adelaide Australian Hardcourt Championships 3/01/2000 \n",
"\n",
" Series Court Surface Round Best of Winner ... UBW \\\n",
"0 International Outdoor Hard 1st Round 3 Dosedel S. ... NaN \n",
"1 International Outdoor Hard 1st Round 3 Enqvist T. ... NaN \n",
"2 International Outdoor Hard 1st Round 3 Escude N. ... NaN \n",
"3 International Outdoor Hard 1st Round 3 Federer R. ... NaN \n",
"4 International Outdoor Hard 1st Round 3 Fromberg R. ... NaN \n",
"\n",
" UBL LBW LBL SJW SJL MaxW MaxL AvgW AvgL \n",
"0 NaN NaN NaN NaN NaN NaN NaN NaN NaN \n",
"1 NaN NaN NaN NaN NaN NaN NaN NaN NaN \n",
"2 NaN NaN NaN NaN NaN NaN NaN NaN NaN \n",
"3 NaN NaN NaN NaN NaN NaN NaN NaN NaN \n",
"4 NaN NaN NaN NaN NaN NaN NaN NaN NaN \n",
"\n",
"[5 rows x 54 columns]"
]
},
"execution_count": 69,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import pandas as pd\n",
"df_atp = pd.read_csv('Data.csv')\n",
"df_atp.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Features "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The features for each match that were used in the project follow:\n",
"- `Date`: date of the match \n",
"- `Series`: name of ATP tennis series (we kept the four main current categories namely Grand Slams, Masters 1000, ATP250, ATP500)\n",
"- `Surface`: type of surface (clay, hard or grass)\n",
"- `Round`: round of match (from first round to the final)\n",
"- `Best of`: maximum number of sets playable in match (Best of 3 or Best of 5)\n",
"- `WRank`: ATP Entry ranking of the match winner as of the start of the tournament\n",
"- `LRank`: ATP Entry ranking of the match loser as of the start of the tournament"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The output variable is binary. The better player has higher rank by definition. We define the `win` variable by:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"${\\rm{win}} = \\left\\{ {\\begin{array}{*{20}{c}}\n",
"1&{{\\rm{higher\\,\\,ranked\\,\\,player\\,\\, wins}}}\\\\\n",
"0&{{\\rm{higher\\,\\,ranked\\,\\,player\\,\\, loses}}}\n",
"\\end{array}} \\right.$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Importing basic modules"
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import numpy as np\n",
"import statsmodels.api as sm\n",
"import matplotlib.pyplot as plt\n",
"from sklearn import metrics\n",
"import seaborn as sns\n",
"sns.set_style(\"darkgrid\")\n",
"import pylab as pl\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Pre-Processing of dataset"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"After loading the dataset we proceed as following:\n",
"- Keep only completed matches i.e. eliminate matches with injury withdrawals and walkovers.\n",
"- For convenience we rename `Best of` to `Best_of`\n",
"- Choose the features listed above\n",
"- Drop `NaN` entries\n",
"- Consider the two final years only (to avoid comparing different categories of tournaments which existed in the past). We note that this choice is somewhat arbitrary and can be changed if needed.\n",
"- Choose only higher ranked players for better accuracy (as suggested by Corral and Prieto-Rodriguez (2010) and confirmed here)"
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {
"collapsed": false
},
"outputs": [
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" <thead>\n",
" <tr style=\"text-align: right;\">\n",
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" <th>Date</th>\n",
" <th>Series</th>\n",
" <th>Surface</th>\n",
" <th>Round</th>\n",
" <th>Best_of</th>\n",
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" <th>39530</th>\n",
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" <td>18</td>\n",
" <td>111</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
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"text/plain": [
" Date Series Surface Round Best_of WRank LRank\n",
"39530 2014-12-02 ATP250 Clay 1st Round 3 92 42\n",
"39531 2014-12-02 ATP250 Clay 1st Round 3 45 78\n",
"39532 2014-12-02 ATP250 Clay 1st Round 3 53 230\n",
"39533 2014-12-02 ATP250 Clay 1st Round 3 84 165\n",
"39534 2014-12-02 ATP250 Clay 1st Round 3 18 111"
]
},
"execution_count": 71,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df_atp['Date'] = pd.to_datetime(df_atp['Date']) \n",
"# Restricing dates\n",
"df_atp = df_atp.loc[(df_atp['Date'] > '2014-11-09') & (df_atp['Date'] <= '2016-11-09')]\n",
"# Keeping only completed matches\n",
"df_atp = df_atp[df_atp['Comment'] == 'Completed'].drop(\"Comment\",axis = 1)\n",
"# Rename Best of to Best_of\n",
"df_atp.rename(columns = {'Best of':'Best_of'},inplace=True)\n",
"# Choosing features\n",
"cols_to_keep = ['Date','Series','Surface', 'Round','Best_of', 'WRank','LRank']\n",
"# Dropping NaN\n",
"df_atp = df_atp[cols_to_keep].dropna()\n",
"# Dropping errors in the dataset and unimportant entries (e.g. there are very few entries for Masters Cup)\n",
"df_atp = df_atp[(df_atp['LRank'] != 'NR') & (df_atp['WRank'] != 'NR') & (df_atp['Series'] != 'Masters Cup')]\n",
"df_atp.head()"
]
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {
"collapsed": false
},
"outputs": [
{
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" <th>Date</th>\n",
" <th>Series</th>\n",
" <th>Surface</th>\n",
" <th>Round</th>\n",
" <th>Best_of</th>\n",
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" <th>39530</th>\n",
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" <th>39534</th>\n",
" <td>2014-12-02</td>\n",
" <td>ATP250</td>\n",
" <td>Clay</td>\n",
" <td>1st Round</td>\n",
" <td>3</td>\n",
" <td>18</td>\n",
" <td>111</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date Series Surface Round Best_of WRank LRank\n",
"39530 2014-12-02 ATP250 Clay 1st Round 3 92 42\n",
"39531 2014-12-02 ATP250 Clay 1st Round 3 45 78\n",
"39532 2014-12-02 ATP250 Clay 1st Round 3 53 230\n",
"39533 2014-12-02 ATP250 Clay 1st Round 3 84 165\n",
"39534 2014-12-02 ATP250 Clay 1st Round 3 18 111"
]
},
"execution_count": 72,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Transform strings into numerical values\n",
"df_atp[['Best_of','WRank','LRank']] = df_atp[['Best_of','WRank','LRank']].astype(int)\n",
"df_atp.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now create an extra columns for the variable `win` described above using an auxiliary function `win(x)`"
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>Series</th>\n",
" <th>Surface</th>\n",
" <th>Round</th>\n",
" <th>Best_of</th>\n",
" <th>WRank</th>\n",
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" <th>39534</th>\n",
" <td>2014-12-02</td>\n",
" <td>ATP250</td>\n",
" <td>Clay</td>\n",
" <td>1st Round</td>\n",
" <td>3</td>\n",
" <td>18</td>\n",
" <td>111</td>\n",
" <td>1</td>\n",
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" </tbody>\n",
"</table>\n",
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"text/plain": [
" Date Series Surface Round Best_of WRank LRank win\n",
"39530 2014-12-02 ATP250 Clay 1st Round 3 92 42 0\n",
"39531 2014-12-02 ATP250 Clay 1st Round 3 45 78 1\n",
"39532 2014-12-02 ATP250 Clay 1st Round 3 53 230 1\n",
"39533 2014-12-02 ATP250 Clay 1st Round 3 84 165 1\n",
"39534 2014-12-02 ATP250 Clay 1st Round 3 18 111 1"
]
},
"execution_count": 73,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def win(x):\n",
" if x > 0:\n",
" return 0\n",
" elif x <= 0:\n",
" return 1 \n",
" \n",
"df_atp['win'] = (df_atp['WRank'] - df_atp['LRank']).apply(win)\n",
"df_atp.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Following Corral and Prieto-Rodriguez (2010) we restrict the analysis to higher ranked players (the analysis including all players has indeed less predictive power as we tested)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>Series</th>\n",
" <th>Surface</th>\n",
" <th>Round</th>\n",
" <th>Best_of</th>\n",
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" <td>2014-12-02</td>\n",
" <td>ATP250</td>\n",
" <td>Clay</td>\n",
" <td>2nd Round</td>\n",
" <td>3</td>\n",
" <td>17</td>\n",
" <td>108</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>39537</th>\n",
" <td>2014-12-02</td>\n",
" <td>ATP250</td>\n",
" <td>Clay</td>\n",
" <td>2nd Round</td>\n",
" <td>3</td>\n",
" <td>14</td>\n",
" <td>58</td>\n",
" <td>1</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date Series Surface Round Best_of WRank LRank win\n",
"39530 2014-12-02 ATP250 Clay 1st Round 3 92 42 0\n",
"39531 2014-12-02 ATP250 Clay 1st Round 3 45 78 1\n",
"39534 2014-12-02 ATP250 Clay 1st Round 3 18 111 1\n",
"39536 2014-12-02 ATP250 Clay 2nd Round 3 17 108 1\n",
"39537 2014-12-02 ATP250 Clay 2nd Round 3 14 58 1"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"newdf = df_atp.copy()\n",
"newdf2 = newdf[(newdf['WRank'] <= 150) & (newdf['LRank'] <= 150)]\n",
"newdf2.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Best_of = 5\n",
"We now restrict our analysis to matches of Best_of = 5. Since only Grand Slams have 5 sets we can drop the new `Series` column. The case of Best_of = 3 will be considered afterwards."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>Surface</th>\n",
" <th>Round</th>\n",
" <th>WRank</th>\n",
" <th>LRank</th>\n",
" <th>win</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>41911</th>\n",
" <td>2015-01-19</td>\n",
" <td>Hard</td>\n",
" <td>1st Round</td>\n",
" <td>85</td>\n",
" <td>84</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>41912</th>\n",
" <td>2015-01-19</td>\n",
" <td>Hard</td>\n",
" <td>1st Round</td>\n",
" <td>11</td>\n",
" <td>90</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>41913</th>\n",
" <td>2015-01-19</td>\n",
" <td>Hard</td>\n",
" <td>1st Round</td>\n",
" <td>15</td>\n",
" <td>59</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>41914</th>\n",
" <td>2015-01-19</td>\n",
" <td>Hard</td>\n",
" <td>1st Round</td>\n",
" <td>31</td>\n",
" <td>91</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>41915</th>\n",
" <td>2015-01-19</td>\n",
" <td>Hard</td>\n",
" <td>1st Round</td>\n",
" <td>99</td>\n",
" <td>98</td>\n",
" <td>0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date Surface Round WRank LRank win\n",
"41911 2015-01-19 Hard 1st Round 85 84 0\n",
"41912 2015-01-19 Hard 1st Round 11 90 1\n",
"41913 2015-01-19 Hard 1st Round 15 59 1\n",
"41914 2015-01-19 Hard 1st Round 31 91 1\n",
"41915 2015-01-19 Hard 1st Round 99 98 0"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df3 = newdf2.copy()\n",
"df3 = df3[df3['Best_of'] == 5]\n",
"# Drop Best_of and Series columns\n",
"df3.drop(\"Series\",axis = 1,inplace=True)\n",
"df3.drop(\"Best_of\",axis = 1,inplace=True)\n",
"df3.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we notice that our dataset is uneven in terms of frequency of `wins`:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"618\n",
"816\n"
]
},
{
"data": {
"text/plain": [
"0.7573529411764706"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"print(df3['win'].sum(axis=0))\n",
"print(len(df3.index))\n",
"df3['win'].sum(axis=0)/float(len(df3.index))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To correct this problem, and create a balanced dataset, we use a stratified sampling procedure. "
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"y_0 = df3[df3.win == 0] \n",
"y_1 = df3[df3.win == 1] \n",
"n = min([len(y_0), len(y_1)]) \n",
"y_0 = y_0.sample(n = n, random_state = 0) \n",
"y_1 = y_1.sample(n = n, random_state = 0)\n",
"df_strat = pd.concat([y_0, y_1]) \n",
"X_strat = df_strat[['Date', 'Surface', 'Round','WRank', 'LRank']]\n",
"y_strat = df_strat.win"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>Surface</th>\n",
" <th>Round</th>\n",
" <th>WRank</th>\n",
" <th>LRank</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>41984</th>\n",
" <td>2015-01-21</td>\n",
" <td>Hard</td>\n",
" <td>2nd Round</td>\n",
" <td>46</td>\n",
" <td>31</td>\n",
" </tr>\n",
" <tr>\n",
" <th>46044</th>\n",
" <td>2016-08-07</td>\n",
" <td>Grass</td>\n",
" <td>Semifinals</td>\n",
" <td>7</td>\n",
" <td>3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>43308</th>\n",
" <td>2015-06-29</td>\n",
" <td>Grass</td>\n",
" <td>1st Round</td>\n",
" <td>148</td>\n",
" <td>93</td>\n",
" </tr>\n",
" <tr>\n",
" <th>46497</th>\n",
" <td>2016-08-29</td>\n",
" <td>Hard</td>\n",
" <td>1st Round</td>\n",
" <td>120</td>\n",
" <td>54</td>\n",
" </tr>\n",
" <tr>\n",
" <th>43345</th>\n",
" <td>2015-06-30</td>\n",
" <td>Grass</td>\n",
" <td>1st Round</td>\n",
" <td>37</td>\n",
" <td>32</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date Surface Round WRank LRank\n",
"41984 2015-01-21 Hard 2nd Round 46 31\n",
"46044 2016-08-07 Grass Semifinals 7 3\n",
"43308 2015-06-29 Grass 1st Round 148 93\n",
"46497 2016-08-29 Hard 1st Round 120 54\n",
"43345 2015-06-30 Grass 1st Round 37 32"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X_strat.head()"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"41984 0\n",
"46044 0\n",
"43308 0\n",
"46497 0\n",
"43345 0\n",
"Name: win, dtype: int64"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y_strat.head()"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>Surface</th>\n",
" <th>Round</th>\n",
" <th>WRank</th>\n",
" <th>LRank</th>\n",
" <th>win</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>41984</th>\n",
" <td>2015-01-21</td>\n",
" <td>Hard</td>\n",
" <td>2nd Round</td>\n",
" <td>46</td>\n",
" <td>31</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>46044</th>\n",
" <td>2016-08-07</td>\n",
" <td>Grass</td>\n",
" <td>Semifinals</td>\n",
" <td>7</td>\n",
" <td>3</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>43308</th>\n",
" <td>2015-06-29</td>\n",
" <td>Grass</td>\n",
" <td>1st Round</td>\n",
" <td>148</td>\n",
" <td>93</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>46497</th>\n",
" <td>2016-08-29</td>\n",
" <td>Hard</td>\n",
" <td>1st Round</td>\n",
" <td>120</td>\n",
" <td>54</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>43345</th>\n",
" <td>2015-06-30</td>\n",
" <td>Grass</td>\n",
" <td>1st Round</td>\n",
" <td>37</td>\n",
" <td>32</td>\n",
" <td>0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date Surface Round WRank LRank win\n",
"41984 2015-01-21 Hard 2nd Round 46 31 0\n",
"46044 2016-08-07 Grass Semifinals 7 3 0\n",
"43308 2015-06-29 Grass 1st Round 148 93 0\n",
"46497 2016-08-29 Hard 1st Round 120 54 0\n",
"43345 2015-06-30 Grass 1st Round 37 32 0"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X_strat_1=X_strat.copy()\n",
"X_strat_1['win']=y_strat\n",
"X_strat_1.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now define the variables ${\\cal P}_1$ and ${\\cal P}_2$ where ${{\\rm Rank}_1} > {{\\rm Rank}_2}$"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>Surface</th>\n",
" <th>Round</th>\n",
" <th>WRank</th>\n",
" <th>LRank</th>\n",
" <th>win</th>\n",
" <th>P1</th>\n",
" <th>P2</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>41984</th>\n",
" <td>2015-01-21</td>\n",
" <td>Hard</td>\n",
" <td>2nd Round</td>\n",
" <td>46</td>\n",
" <td>31</td>\n",
" <td>0</td>\n",
" <td>46</td>\n",
" <td>31</td>\n",
" </tr>\n",
" <tr>\n",
" <th>46044</th>\n",
" <td>2016-08-07</td>\n",
" <td>Grass</td>\n",
" <td>Semifinals</td>\n",
" <td>7</td>\n",
" <td>3</td>\n",
" <td>0</td>\n",
" <td>7</td>\n",
" <td>3</td>\n",
" </tr>\n",
" <tr>\n",
" <th>43308</th>\n",
" <td>2015-06-29</td>\n",
" <td>Grass</td>\n",
" <td>1st Round</td>\n",
" <td>148</td>\n",
" <td>93</td>\n",
" <td>0</td>\n",
" <td>148</td>\n",
" <td>93</td>\n",
" </tr>\n",
" <tr>\n",
" <th>46497</th>\n",
" <td>2016-08-29</td>\n",
" <td>Hard</td>\n",
" <td>1st Round</td>\n",
" <td>120</td>\n",
" <td>54</td>\n",
" <td>0</td>\n",
" <td>120</td>\n",
" <td>54</td>\n",
" </tr>\n",
" <tr>\n",
" <th>43345</th>\n",
" <td>2015-06-30</td>\n",
" <td>Grass</td>\n",
" <td>1st Round</td>\n",
" <td>37</td>\n",
" <td>32</td>\n",
" <td>0</td>\n",
" <td>37</td>\n",
" <td>32</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date Surface Round WRank LRank win P1 P2\n",
"41984 2015-01-21 Hard 2nd Round 46 31 0 46 31\n",
"46044 2016-08-07 Grass Semifinals 7 3 0 7 3\n",
"43308 2015-06-29 Grass 1st Round 148 93 0 148 93\n",
"46497 2016-08-29 Hard 1st Round 120 54 0 120 54\n",
"43345 2015-06-30 Grass 1st Round 37 32 0 37 32"
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df = X_strat_1.copy()\n",
"df[\"P1\"] = df[[\"WRank\", \"LRank\"]].max(axis=1)\n",
"df[\"P2\"] = df[[\"WRank\", \"LRank\"]].min(axis=1)\n",
"df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exploratory Analysis for Best_of = 5"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We first look at percentage of wins for each surface. We find that when the `Surface` is Clay there is a higher likelihood of upsets (opposite of wins) i.e. the percentage of wins is lower. The difference is not too large tough."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th>Surface</th>\n",
" <th>Clay</th>\n",
" <th>Grass</th>\n",
" <th>Hard</th>\n",
" </tr>\n",
" <tr>\n",
" <th>win</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>0.557692</td>\n",
" <td>0.474747</td>\n",
" <td>0.481865</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.442308</td>\n",
" <td>0.525253</td>\n",
" <td>0.518135</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
"Surface Clay Grass Hard\n",
"win \n",
"0 0.557692 0.474747 0.481865\n",
"1 0.442308 0.525253 0.518135"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"win_by_Surface = pd.crosstab(df.win, df.Surface).apply( lambda x: x/x.sum(), axis = 0 )\n",
"win_by_Surface"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x11994f610>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"win_by_Surface = pd.DataFrame( win_by_Surface.unstack() ).reset_index()\n",
"win_by_Surface.columns = [\"Surface\", \"win\", \"total\" ]\n",
"fig2 = sns.barplot(win_by_Surface.Surface, win_by_Surface.total, hue = win_by_Surface.win )\n",
"fig2.figure.set_size_inches(8,5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What about the dependence on rounds? The relation is not very clear but we can clearly see that upsets are unlikely to happen on the semifinals."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th>Round</th>\n",
" <th>1st Round</th>\n",
" <th>2nd Round</th>\n",
" <th>3rd Round</th>\n",
" <th>4th Round</th>\n",
" <th>Quarterfinals</th>\n",
" <th>Semifinals</th>\n",
" <th>The Final</th>\n",
" </tr>\n",
" <tr>\n",
" <th>win</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>0</th>\n",
" <td>0.521505</td>\n",
" <td>0.542056</td>\n",
" <td>0.469388</td>\n",
" <td>0.354839</td>\n",
" <td>0.666667</td>\n",
" <td>0.111111</td>\n",
" <td>0.4</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.478495</td>\n",
" <td>0.457944</td>\n",
" <td>0.530612</td>\n",
" <td>0.645161</td>\n",
" <td>0.333333</td>\n",
" <td>0.888889</td>\n",
" <td>0.6</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
"Round 1st Round 2nd Round 3rd Round 4th Round Quarterfinals Semifinals \\\n",
"win \n",
"0 0.521505 0.542056 0.469388 0.354839 0.666667 0.111111 \n",
"1 0.478495 0.457944 0.530612 0.645161 0.333333 0.888889 \n",
"\n",
"Round The Final \n",
"win \n",
"0 0.4 \n",
"1 0.6 "
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"win_by_round = pd.crosstab(df.win, df.Round).apply( lambda x: x/x.sum(), axis = 0 )\n",
"win_by_round"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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EcTOfGcAuwNmZeWn5pfBvFM/rJsbgJj6Z+eWIaGy0LKTYW2g8B3cDc4G/By4F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\nlNQAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1199af4d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"win_by_round = pd.DataFrame(win_by_round.unstack() ).reset_index()\n",
"win_by_round.columns = [\"Round\", \"win\", \"total\" ]\n",
"fig2 = sns.barplot(win_by_round.Round, win_by_round.total, hue = win_by_round.win )\n",
"fig2.figure.set_size_inches(8,5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's check these results before stratification"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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kSZpkjT6FvqTsQiRJUuMafQp9EfAeoIviKfTpwIGZeVB5pUmSpNFMa/C6lcAVFIH/GeAO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\nYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11c3f1e90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"win_by_Surface_before_strat = pd.crosstab(df3.win, df3.Surface).apply( lambda x: x/x.sum(), axis = 0 )\n",
"win_by_Surface_before_strat = pd.DataFrame( win_by_Surface_before_strat.unstack() ).reset_index()\n",
"win_by_Surface_before_strat.columns = [\"Surface\", \"win\", \"total\" ]\n",
"fig2 = sns.barplot(win_by_Surface_before_strat.Surface, win_by_Surface_before_strat.total, hue = win_by_Surface_before_strat.win )\n",
"fig2.figure.set_size_inches(8,5)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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Nr4mISZm5LiLmUn5ffhhwRCeFmDVrS6ZMmdxhkUfX0qXTurau2bOnMWfO9K6trxPdqv9Y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\nELF6AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11c044690>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"win_by_round_before_strat = pd.crosstab(df3.win, df3.Round).apply( lambda x: x/x.sum(), axis = 0 )\n",
"win_by_round_before_strat = pd.DataFrame(win_by_round_before_strat.unstack() ).reset_index()\n",
"win_by_round_before_strat.columns = [\"Round\", \"win\", \"total\" ]\n",
"fig2 = sns.barplot(win_by_round_before_strat.Round, win_by_round_before_strat.total, hue = win_by_round_before_strat.win )\n",
"fig2.figure.set_size_inches(8,5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Dummy variables\n",
"------"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To keep the dataframe cleaner we transform the `Round` entries into numbers. We then transform rounds into dummy variables"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>Surface</th>\n",
" <th>Round</th>\n",
" <th>WRank</th>\n",
" <th>LRank</th>\n",
" <th>win</th>\n",
" <th>P1</th>\n",
" <th>P2</th>\n",
" <th>Round_2</th>\n",
" <th>Round_3</th>\n",
" <th>Round_4</th>\n",
" <th>Round_5</th>\n",
" <th>Round_6</th>\n",
" <th>Round_7</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>41984</th>\n",
" <td>2015-01-21</td>\n",
" <td>Hard</td>\n",
" <td>2</td>\n",
" <td>46</td>\n",
" <td>31</td>\n",
" <td>0</td>\n",
" <td>46</td>\n",
" <td>31</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>46044</th>\n",
" <td>2016-08-07</td>\n",
" <td>Grass</td>\n",
" <td>6</td>\n",
" <td>7</td>\n",
" <td>3</td>\n",
" <td>0</td>\n",
" <td>7</td>\n",
" <td>3</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>43308</th>\n",
" <td>2015-06-29</td>\n",
" <td>Grass</td>\n",
" <td>1</td>\n",
" <td>148</td>\n",
" <td>93</td>\n",
" <td>0</td>\n",
" <td>148</td>\n",
" <td>93</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>46497</th>\n",
" <td>2016-08-29</td>\n",
" <td>Hard</td>\n",
" <td>1</td>\n",
" <td>120</td>\n",
" <td>54</td>\n",
" <td>0</td>\n",
" <td>120</td>\n",
" <td>54</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>43345</th>\n",
" <td>2015-06-30</td>\n",
" <td>Grass</td>\n",
" <td>1</td>\n",
" <td>37</td>\n",
" <td>32</td>\n",
" <td>0</td>\n",
" <td>37</td>\n",
" <td>32</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date Surface Round WRank LRank win P1 P2 Round_2 Round_3 \\\n",
"41984 2015-01-21 Hard 2 46 31 0 46 31 1 0 \n",
"46044 2016-08-07 Grass 6 7 3 0 7 3 0 0 \n",
"43308 2015-06-29 Grass 1 148 93 0 148 93 0 0 \n",
"46497 2016-08-29 Hard 1 120 54 0 120 54 0 0 \n",
"43345 2015-06-30 Grass 1 37 32 0 37 32 0 0 \n",
"\n",
" Round_4 Round_5 Round_6 Round_7 \n",
"41984 0 0 0 0 \n",
"46044 0 0 1 0 \n",
"43308 0 0 0 0 \n",
"46497 0 0 0 0 \n",
"43345 0 0 0 0 "
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df1 = df.copy()\n",
"def round_number(x):\n",
" if x == '1st Round':\n",
" return 1\n",
" elif x == '2nd Round':\n",
" return 2\n",
" elif x == '3rd Round':\n",
" return 3\n",
" elif x == '4th Round':\n",
" return 4\n",
" elif x == 'Quarterfinals':\n",
" return 5\n",
" elif x == 'Semifinals':\n",
" return 6\n",
" elif x == 'The Final':\n",
" return 7\n",
" \n",
"df1['Round'] = df1['Round'].apply(round_number)\n",
"\n",
"dummy_ranks = pd.get_dummies(df1['Round'], prefix='Round')\n",
"\n",
"df1 = df1.join(dummy_ranks.ix[:, 'Round_2':])\n",
"df1[['Round_2', 'Round_3',\n",
" 'Round_4', 'Round_5', 'Round_6', 'Round_7']] = df1[['Round_2', 'Round_3','Round_4', 'Round_5', 'Round_6', 'Round_7']].astype('int_')\n",
"df1.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We repeat this for the `Surface` variable"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Surface_Clay</th>\n",
" <th>Surface_Grass</th>\n",
" <th>Surface_Hard</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>41984</th>\n",
" <td>0.0</td>\n",
" <td>0.0</td>\n",
" <td>1.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>46044</th>\n",
" <td>0.0</td>\n",
" <td>1.0</td>\n",
" <td>0.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>43308</th>\n",
" <td>0.0</td>\n",
" <td>1.0</td>\n",
" <td>0.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>46497</th>\n",
" <td>0.0</td>\n",
" <td>0.0</td>\n",
" <td>1.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>43345</th>\n",
" <td>0.0</td>\n",
" <td>1.0</td>\n",
" <td>0.0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Surface_Clay Surface_Grass Surface_Hard\n",
"41984 0.0 0.0 1.0\n",
"46044 0.0 1.0 0.0\n",
"43308 0.0 1.0 0.0\n",
"46497 0.0 0.0 1.0\n",
"43345 0.0 1.0 0.0"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dummy_ranks = pd.get_dummies(df1['Surface'], prefix='Surface')\n",
"dummy_ranks.head()"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>WRank</th>\n",
" <th>LRank</th>\n",
" <th>win</th>\n",
" <th>P1</th>\n",
" <th>P2</th>\n",
" <th>Round_2</th>\n",
" <th>Round_3</th>\n",
" <th>Round_4</th>\n",
" <th>Round_5</th>\n",
" <th>Round_6</th>\n",
" <th>Round_7</th>\n",
" <th>Surface_Grass</th>\n",
" <th>Surface_Hard</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>41984</th>\n",
" <td>2015-01-21</td>\n",
" <td>46</td>\n",
" <td>31</td>\n",
" <td>0</td>\n",
" <td>46</td>\n",
" <td>31</td>\n",
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" <tr>\n",
" <th>46044</th>\n",
" <td>2016-08-07</td>\n",
" <td>7</td>\n",
" <td>3</td>\n",
" <td>0</td>\n",
" <td>7</td>\n",
" <td>3</td>\n",
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" <td>1</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>43308</th>\n",
" <td>2015-06-29</td>\n",
" <td>148</td>\n",
" <td>93</td>\n",
" <td>0</td>\n",
" <td>148</td>\n",
" <td>93</td>\n",
" <td>0</td>\n",
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" <td>0</td>\n",
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" <td>1</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>46497</th>\n",
" <td>2016-08-29</td>\n",
" <td>120</td>\n",
" <td>54</td>\n",
" <td>0</td>\n",
" <td>120</td>\n",
" <td>54</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>43345</th>\n",
" <td>2015-06-30</td>\n",
" <td>37</td>\n",
" <td>32</td>\n",
" <td>0</td>\n",
" <td>37</td>\n",
" <td>32</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
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" <td>0</td>\n",
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" <td>1</td>\n",
" <td>0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date WRank LRank win P1 P2 Round_2 Round_3 Round_4 \\\n",
"41984 2015-01-21 46 31 0 46 31 1 0 0 \n",
"46044 2016-08-07 7 3 0 7 3 0 0 0 \n",
"43308 2015-06-29 148 93 0 148 93 0 0 0 \n",
"46497 2016-08-29 120 54 0 120 54 0 0 0 \n",
"43345 2015-06-30 37 32 0 37 32 0 0 0 \n",
"\n",
" Round_5 Round_6 Round_7 Surface_Grass Surface_Hard \n",
"41984 0 0 0 0 1 \n",
"46044 0 1 0 1 0 \n",
"43308 0 0 0 1 0 \n",
"46497 0 0 0 0 1 \n",
"43345 0 0 0 1 0 "
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df_2 = df1.join(dummy_ranks.ix[:, 'Surface_Grass':])\n",
"df_2.drop(\"Surface\",axis = 1,inplace=True)\n",
"df_2[['Surface_Grass','Surface_Hard']] = df_2[['Surface_Grass','Surface_Hard']].astype('int_')\n",
"df_2.drop(\"Round\",axis = 1,inplace=True)\n",
"df_2.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now take the logarithms of ${\\cal P}_1$ and ${\\cal P}_2$, then create a variable `D` "
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>WRank</th>\n",
" <th>LRank</th>\n",
" <th>win</th>\n",
" <th>P1</th>\n",
" <th>P2</th>\n",
" <th>Round_2</th>\n",
" <th>Round_3</th>\n",
" <th>Round_4</th>\n",
" <th>Round_5</th>\n",
" <th>Round_6</th>\n",
" <th>Round_7</th>\n",
" <th>Surface_Grass</th>\n",
" <th>Surface_Hard</th>\n",
" <th>D</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>41984</th>\n",
" <td>2015-01-21</td>\n",
" <td>46</td>\n",
" <td>31</td>\n",
" <td>0</td>\n",
" <td>5.523562</td>\n",
" <td>4.954196</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0.569366</td>\n",
" </tr>\n",
" <tr>\n",
" <th>46044</th>\n",
" <td>2016-08-07</td>\n",
" <td>7</td>\n",
" <td>3</td>\n",
" <td>0</td>\n",
" <td>2.807355</td>\n",
" <td>1.584963</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>1.222392</td>\n",
" </tr>\n",
" <tr>\n",
" <th>43308</th>\n",
" <td>2015-06-29</td>\n",
" <td>148</td>\n",
" <td>93</td>\n",
" <td>0</td>\n",
" <td>7.209453</td>\n",
" <td>6.539159</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0.670295</td>\n",
" </tr>\n",
" <tr>\n",
" <th>46497</th>\n",
" <td>2016-08-29</td>\n",
" <td>120</td>\n",
" <td>54</td>\n",
" <td>0</td>\n",
" <td>6.906891</td>\n",
" <td>5.754888</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>1.152003</td>\n",
" </tr>\n",
" <tr>\n",
" <th>43345</th>\n",
" <td>2015-06-30</td>\n",
" <td>37</td>\n",
" <td>32</td>\n",
" <td>0</td>\n",
" <td>5.209453</td>\n",
" <td>5.000000</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0.209453</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date WRank LRank win P1 P2 Round_2 Round_3 \\\n",
"41984 2015-01-21 46 31 0 5.523562 4.954196 1 0 \n",
"46044 2016-08-07 7 3 0 2.807355 1.584963 0 0 \n",
"43308 2015-06-29 148 93 0 7.209453 6.539159 0 0 \n",
"46497 2016-08-29 120 54 0 6.906891 5.754888 0 0 \n",
"43345 2015-06-30 37 32 0 5.209453 5.000000 0 0 \n",
"\n",
" Round_4 Round_5 Round_6 Round_7 Surface_Grass Surface_Hard \\\n",
"41984 0 0 0 0 0 1 \n",
"46044 0 0 1 0 1 0 \n",
"43308 0 0 0 0 1 0 \n",
"46497 0 0 0 0 0 1 \n",
"43345 0 0 0 0 1 0 \n",
"\n",
" D \n",
"41984 0.569366 \n",
"46044 1.222392 \n",
"43308 0.670295 \n",
"46497 1.152003 \n",
"43345 0.209453 "
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df4 = df_2.copy()\n",
"df4['P1'] = np.log2(df4['P1'].astype('float64')) \n",
"df4['P2'] = np.log2(df4['P2'].astype('float64')) \n",
"df4['D'] = df4['P1'] - df4['P2']\n",
"df4['D'] = np.absolute(df4['D'])\n",
"df4.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model 1: Logistic Regression"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now use a logistic regression to study our data."
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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kCsEYU038L/rHgK9bazsTj68Htp3r+6y1DvDVMx7e1+v59cC8pJKKZLgt757gRFMniy8d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\nrkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11cca9210>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"# Logit Function\n",
"def logit(x):\n",
" return np.exp(x) / (1 + np.exp(x)) \n",
" \n",
"x = np.linspace(-6,6,50, dtype=float)\n",
"\n",
"y = logit(x)\n",
"\n",
"plt.plot(x, y)\n",
"plt.ylabel(\"Probability\")\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 251,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"['Date',\n",
" 'WRank',\n",
" 'LRank',\n",
" 'win',\n",
" 'P1',\n",
" 'P2',\n",
" 'Round_2',\n",
" 'Round_3',\n",
" 'Round_4',\n",
" 'Round_5',\n",
" 'Round_6',\n",
" 'Round_7',\n",
" 'Surface_Grass',\n",
" 'Surface_Hard',\n",
" 'D']"
]
},
"execution_count": 251,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df4.columns.tolist()"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"feature_cols = ['Round_2',\n",
" 'Round_3',\n",
" 'Round_4',\n",
" 'Round_5',\n",
" 'Round_6',\n",
" 'Round_7',\n",
" 'Surface_Grass',\n",
" 'Surface_Hard',\n",
" 'D']"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Round_2</th>\n",
" <th>Round_3</th>\n",
" <th>Round_4</th>\n",
" <th>Round_5</th>\n",
" <th>Round_6</th>\n",
" <th>Round_7</th>\n",
" <th>Surface_Grass</th>\n",
" <th>Surface_Hard</th>\n",
" <th>D</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>41984</th>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0.569366</td>\n",
" </tr>\n",
" <tr>\n",
" <th>46044</th>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>1.222392</td>\n",
" </tr>\n",
" <tr>\n",
" <th>43308</th>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0.670295</td>\n",
" </tr>\n",
" <tr>\n",
" <th>46497</th>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>1.152003</td>\n",
" </tr>\n",
" <tr>\n",
" <th>43345</th>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0.209453</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Round_2 Round_3 Round_4 Round_5 Round_6 Round_7 Surface_Grass \\\n",
"41984 1 0 0 0 0 0 0 \n",
"46044 0 0 0 0 1 0 1 \n",
"43308 0 0 0 0 0 0 1 \n",
"46497 0 0 0 0 0 0 0 \n",
"43345 0 0 0 0 0 0 1 \n",
"\n",
" Surface_Hard D \n",
"41984 1 0.569366 \n",
"46044 0 1.222392 \n",
"43308 0 0.670295 \n",
"46497 1 1.152003 \n",
"43345 0 0.209453 "
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dfnew = df4.copy()\n",
"dfnew[feature_cols].head()"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"X = dfnew[feature_cols]\n",
"y = dfnew.win\n",
"#pd.value_counts(dfnew['Best_of_5'].values, sort=False)"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
" intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,\n",
" penalty='l2', random_state=None, solver='liblinear', tol=0.0001,\n",
" verbose=0, warm_start=False)"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn.cross_validation import train_test_split\n",
"X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)\n",
"from sklearn.linear_model import LogisticRegression\n",
"logreg = LogisticRegression()\n",
"logreg.fit(X_train, y_train)"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.707070707071\n"
]
}
],
"source": [
"y_pred_class = logreg.predict(X_test)\n",
"from sklearn import metrics\n",
"print(metrics.accuracy_score(y_test, y_pred_class))"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"True: [1 1 1 0 0 1 1 0 1 1 1 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 1 0\n",
" 1 1 0]\n",
"Pred: [0 0 1 0 0 1 1 0 1 1 0 1 1 0 0 0 0 1 1 1 0 0 1 0 1 0 1 0 0 0 0 0 1 0 1 0 0\n",
" 0 0 0]\n"
]
}
],
"source": [
"from __future__ import print_function\n",
"print('True:', y_test.values[0:40])\n",
"print('Pred:', y_pred_class[0:40])"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.75469387755102035"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y_pred_prob = logreg.predict_proba(X_test)[:, 1]\n",
"auc_score = metrics.roc_auc_score(y_test, y_pred_prob)\n",
"auc_score"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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2ZuTI+6yHUoxEq2KaqKpXA3eKyD4lBlXtGNPITMIrqdXOrDEy+XTqdBoffDCXpk2b+R1K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\nyBKEMcaYiCxBGGOMiej/ATHhpv9vrztLAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11d06f750>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"y_pred_prob = logreg.predict_proba(X_test)[:, 1]\n",
"auc_score = metrics.roc_auc_score(y_test, y_pred_prob)\n",
"auc_score\n",
"fpr, tpr, thresholds = metrics.roc_curve(y_test, y_pred_prob)\n",
"fig = plt.plot(fpr, tpr,label='ROC curve (area = %0.2f)' % auc_score )\n",
"plt.plot([0, 1], [0, 1], 'k--')\n",
"plt.xlim([0.0, 1.0])\n",
"plt.ylim([0.0, 1.0])\n",
"plt.title('ROC curve for win classifier')\n",
"plt.xlabel('False Positive Rate (1 - Specificity)')\n",
"plt.ylabel('True Positive Rate (Sensitivity)')\n",
"plt.legend(loc=\"lower right\")\n",
"plt.grid(True)"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Optimization terminated successfully.\n",
" Current function value: 0.584223\n",
" Iterations 6\n"
]
},
{
"data": {
"text/html": [
"<table class=\"simpletable\">\n",
"<caption>Logit Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>win</td> <th> No. Observations: </th> <td> 396</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>Logit</td> <th> Df Residuals: </th> <td> 386</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>MLE</td> <th> Df Model: </th> <td> 9</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Thu, 10 Nov 2016</td> <th> Pseudo R-squ.: </th> <td>0.1571</td> \n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>11:45:45</td> <th> Log-Likelihood: </th> <td> -231.35</td> \n",
"</tr>\n",
"<tr>\n",
" <th>converged:</th> <td>True</td> <th> LL-Null: </th> <td> -274.49</td> \n",
"</tr>\n",
"<tr>\n",
" <th> </th> <td> </td> <th> LLR p-value: </th> <td>9.105e-15</td>\n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <td></td> <th>coef</th> <th>std err</th> <th>z</th> <th>P>|z|</th> <th>[95.0% Conf. Int.]</th> \n",
"</tr>\n",
"<tr>\n",
" <th>const</th> <td> -1.4661</td> <td> 0.292</td> <td> -5.014</td> <td> 0.000</td> <td> -2.039 -0.893</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Round_2</th> <td> -0.3527</td> <td> 0.270</td> <td> -1.306</td> <td> 0.192</td> <td> -0.882 0.177</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Round_3</th> <td> -0.2240</td> <td> 0.364</td> <td> -0.615</td> <td> 0.538</td> <td> -0.937 0.489</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Round_4</th> <td> 0.1382</td> <td> 0.449</td> <td> 0.308</td> <td> 0.758</td> <td> -0.742 1.018</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Round_5</th> <td> -1.2500</td> <td> 0.841</td> <td> -1.486</td> <td> 0.137</td> <td> -2.899 0.399</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Round_6</th> <td> 2.0958</td> <td> 1.103</td> <td> 1.900</td> <td> 0.057</td> <td> -0.066 4.257</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Round_7</th> <td> 0.4501</td> <td> 0.959</td> <td> 0.470</td> <td> 0.639</td> <td> -1.429 2.329</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Surface_Grass</th> <td> 0.5040</td> <td> 0.316</td> <td> 1.597</td> <td> 0.110</td> <td> -0.115 1.123</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Surface_Hard</th> <td> 0.3538</td> <td> 0.276</td> <td> 1.280</td> <td> 0.200</td> <td> -0.188 0.895</td>\n",
"</tr>\n",
"<tr>\n",
" <th>D</th> <td> 0.7876</td> <td> 0.108</td> <td> 7.313</td> <td> 0.000</td> <td> 0.576 0.999</td>\n",
"</tr>\n",
"</table>"
],
"text/plain": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" Logit Regression Results \n",
"==============================================================================\n",
"Dep. Variable: win No. Observations: 396\n",
"Model: Logit Df Residuals: 386\n",
"Method: MLE Df Model: 9\n",
"Date: Thu, 10 Nov 2016 Pseudo R-squ.: 0.1571\n",
"Time: 11:45:45 Log-Likelihood: -231.35\n",
"converged: True LL-Null: -274.49\n",
" LLR p-value: 9.105e-15\n",
"=================================================================================\n",
" coef std err z P>|z| [95.0% Conf. Int.]\n",
"---------------------------------------------------------------------------------\n",
"const -1.4661 0.292 -5.014 0.000 -2.039 -0.893\n",
"Round_2 -0.3527 0.270 -1.306 0.192 -0.882 0.177\n",
"Round_3 -0.2240 0.364 -0.615 0.538 -0.937 0.489\n",
"Round_4 0.1382 0.449 0.308 0.758 -0.742 1.018\n",
"Round_5 -1.2500 0.841 -1.486 0.137 -2.899 0.399\n",
"Round_6 2.0958 1.103 1.900 0.057 -0.066 4.257\n",
"Round_7 0.4501 0.959 0.470 0.639 -1.429 2.329\n",
"Surface_Grass 0.5040 0.316 1.597 0.110 -0.115 1.123\n",
"Surface_Hard 0.3538 0.276 1.280 0.200 -0.188 0.895\n",
"D 0.7876 0.108 7.313 0.000 0.576 0.999\n",
"=================================================================================\n",
"\"\"\""
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import statsmodels.api as sm\n",
"\n",
"X = dfnew[feature_cols]\n",
"X = sm.add_constant(X)\n",
"y = dfnew['win']\n",
"\n",
"lm = sm.Logit(y, X)\n",
"result = lm.fit()\n",
"\n",
"result.summary()"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.72848476454293631"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn.cross_validation import cross_val_score\n",
"cross_val_score(logreg, X, y, cv=10, scoring='roc_auc').mean()"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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Hysou1IrgVijOGMIdwA8B3P1lM/sxcCdwVD4DE5Fk1C0Z3Y1Qtmx7qqvvpjYJhPIQtTWC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\n/w8/nHNwVbkULgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11cc4a210>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"logreg.fit(dfnew[[\"D\"]],dfnew[\"win\"])\n",
"pred_probs = logreg.predict_proba(dfnew[[\"D\"]])\n",
"plt.scatter(dfnew[\"D\"], pred_probs[:,1])\n",
"plt.title('Win Probability for 5 sets matches')\n",
"plt.xlabel('D')\n",
"plt.ylabel('Win Probability for 5 sets matches')\n",
"plt.legend(loc=\"lower right\")\n",
"plt.grid(True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Decision Trees and Random Forests\n",
"-------"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now build a decision tree model to predict the upsets likelihood of a given match"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"DecisionTreeClassifier(class_weight=None, criterion='gini', max_depth=None,\n",
" max_features=None, max_leaf_nodes=None, min_samples_leaf=1,\n",
" min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
" presort=False, random_state=None, splitter='best')"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn.tree import DecisionTreeClassifier\n",
"\n",
"model = DecisionTreeClassifier()\n",
"\n",
"X = dfnew[feature_cols].dropna()\n",
"y = dfnew['win']\n",
"\n",
"\n",
"model.fit(X, y)"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"AUC [ 0.5875 0.5875 0.5625 0.6025641 0.50756082], Average AUC 0.569524983563\n"
]
}
],
"source": [
"from sklearn.cross_validation import cross_val_score\n",
"\n",
"scores = cross_val_score(model, X, y, scoring='roc_auc', cv=5)\n",
"print('AUC {}, Average AUC {}'.format(scores, scores.mean()))"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CV AUC [ 0.66625 0.720625 0.6090625 0.74621959 0.55555556], Average AUC 0.659542529586\n"
]
}
],
"source": [
"model = DecisionTreeClassifier(\n",
" max_depth = 4,\n",
" min_samples_leaf = 6)\n",
"\n",
"model.fit(X, y)\n",
"scores = cross_val_score(model, X, y, scoring='roc_auc', cv=5)\n",
"print('CV AUC {}, Average AUC {}'.format(scores, scores.mean()))"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"RandomForestClassifier(bootstrap=True, class_weight=None, criterion='gini',\n",
" max_depth=None, max_features='auto', max_leaf_nodes=None,\n",
" min_samples_leaf=1, min_samples_split=2,\n",
" min_weight_fraction_leaf=0.0, n_estimators=200, n_jobs=1,\n",
" oob_score=False, random_state=None, verbose=0,\n",
" warm_start=False)"
]
},
"execution_count": 45,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn.ensemble import RandomForestClassifier\n",
"from sklearn.cross_validation import cross_val_score\n",
"\n",
"X = dfnew[feature_cols].dropna()\n",
"y = dfnew['win']\n",
"\n",
"model = RandomForestClassifier(n_estimators = 200)\n",
" \n",
"model.fit(X, y)\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Features</th>\n",
" <th>Importance Score</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>D</td>\n",
" <td>0.850724</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>Surface_Hard</td>\n",
" <td>0.025179</td>\n",
" </tr>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>Round_2</td>\n",
" <td>0.025132</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>Surface_Grass</td>\n",
" <td>0.022049</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>Round_3</td>\n",
" <td>0.017896</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>Round_4</td>\n",
" <td>0.016429</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>Round_6</td>\n",
" <td>0.016345</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>Round_7</td>\n",
" <td>0.013936</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>Round_5</td>\n",
" <td>0.012309</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Features Importance Score\n",
"8 D 0.850724\n",
"7 Surface_Hard 0.025179\n",
"0 Round_2 0.025132\n",
"6 Surface_Grass 0.022049\n",
"1 Round_3 0.017896\n",
"2 Round_4 0.016429\n",
"4 Round_6 0.016345\n",
"5 Round_7 0.013936\n",
"3 Round_5 0.012309"
]
},
"execution_count": 46,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"features = X.columns\n",
"feature_importances = model.feature_importances_\n",
"\n",
"features_df = pd.DataFrame({'Features': features, 'Importance Score': feature_importances})\n",
"features_df.sort_values('Importance Score', inplace=True, ascending=False)\n",
"\n",
"features_df"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/marcotavora/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:2: FutureWarning: sort is deprecated, use sort_values(inplace=True) for INPLACE sorting\n",
" from ipykernel import kernelapp as app\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x1198f9d50>"
]
},
"execution_count": 47,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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vK0nSlEor5p6xhYg4BDgKeDQiPgicSlWoWzLz8oi4ErguM7dGxBrg3Mx8a0Q8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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11c00add0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"feature_importances = pd.Series(model.feature_importances_, index=X.columns)\n",
"feature_importances.sort()\n",
"feature_importances.plot(kind=\"barh\", figsize=(7,6))"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"AUC [ 0.72956841 0.66758494 0.64152893], Average AUC 0.679560759106\n",
"n trees: 1, CV AUC [ 0.65151515 0.66666667 0.5632461 ], Average AUC 0.627142638506\n",
"n trees: 11, CV AUC [ 0.74437557 0.64543159 0.62775482], Average AUC 0.672520661157\n",
"n trees: 21, CV AUC [ 0.71613866 0.65381084 0.63636364], Average AUC 0.668771043771\n",
"n trees: 31, CV AUC [ 0.72623967 0.67229109 0.64577594], Average AUC 0.681435567799\n",
"n trees: 41, CV AUC [ 0.73783287 0.65048209 0.64015152], Average AUC 0.676155494337\n",
"n trees: 51, CV AUC [ 0.72463269 0.65438476 0.64290634], Average AUC 0.673974594429\n",
"n trees: 61, CV AUC [ 0.71705693 0.66069789 0.65587695], Average AUC 0.677877257423\n",
"n trees: 71, CV AUC [ 0.73519284 0.66609275 0.64623508], Average AUC 0.682506887052\n",
"n trees: 81, CV AUC [ 0.72945363 0.65943526 0.62775482], Average AUC 0.672214569942\n",
"n trees: 91, CV AUC [ 0.74368687 0.67171717 0.63429752], Average AUC 0.683233853688\n"
]
}
],
"source": [
"from sklearn.cross_validation import cross_val_score\n",
"\n",
"scores = cross_val_score(model, X, y, scoring='roc_auc')\n",
"print('AUC {}, Average AUC {}'.format(scores, scores.mean()))\n",
"\n",
"for n_trees in range(1, 100, 10):\n",
" model = RandomForestClassifier(n_estimators = n_trees)\n",
" scores = cross_val_score(model, X, y, scoring='roc_auc')\n",
" print('n trees: {}, CV AUC {}, Average AUC {}'.format(n_trees, scores, scores.mean()))"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"## Best_of = 3\n",
"We now restrict our analysis to matches of Best_of = 3. "
]
},
{
"cell_type": "code",
"execution_count": 189,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>Series</th>\n",
" <th>Surface</th>\n",
" <th>Round</th>\n",
" <th>Best_of</th>\n",
" <th>WRank</th>\n",
" <th>LRank</th>\n",
" <th>win</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>39530</th>\n",
" <td>2014-12-02</td>\n",
" <td>ATP250</td>\n",
" <td>Clay</td>\n",
" <td>1st Round</td>\n",
" <td>3</td>\n",
" <td>92</td>\n",
" <td>42</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>39531</th>\n",
" <td>2014-12-02</td>\n",
" <td>ATP250</td>\n",
" <td>Clay</td>\n",
" <td>1st Round</td>\n",
" <td>3</td>\n",
" <td>45</td>\n",
" <td>78</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>39532</th>\n",
" <td>2014-12-02</td>\n",
" <td>ATP250</td>\n",
" <td>Clay</td>\n",
" <td>1st Round</td>\n",
" <td>3</td>\n",
" <td>53</td>\n",
" <td>230</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>39533</th>\n",
" <td>2014-12-02</td>\n",
" <td>ATP250</td>\n",
" <td>Clay</td>\n",
" <td>1st Round</td>\n",
" <td>3</td>\n",
" <td>84</td>\n",
" <td>165</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>39534</th>\n",
" <td>2014-12-02</td>\n",
" <td>ATP250</td>\n",
" <td>Clay</td>\n",
" <td>1st Round</td>\n",
" <td>3</td>\n",
" <td>18</td>\n",
" <td>111</td>\n",
" <td>1</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date Series Surface Round Best_of WRank LRank win\n",
"39530 2014-12-02 ATP250 Clay 1st Round 3 92 42 0\n",
"39531 2014-12-02 ATP250 Clay 1st Round 3 45 78 1\n",
"39532 2014-12-02 ATP250 Clay 1st Round 3 53 230 1\n",
"39533 2014-12-02 ATP250 Clay 1st Round 3 84 165 1\n",
"39534 2014-12-02 ATP250 Clay 1st Round 3 18 111 1"
]
},
"execution_count": 189,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import pandas as pd\n",
"df_atp = pd.read_csv('Data.csv')\n",
"df_atp['Date'] = pd.to_datetime(df_atp['Date']) \n",
"# Restricing dates\n",
"df_atp = df_atp.loc[(df_atp['Date'] > '2014-11-09') & (df_atp['Date'] <= '2016-11-09')]\n",
"# Keeping only completed matches\n",
"df_atp = df_atp[df_atp['Comment'] == 'Completed'].drop(\"Comment\",axis = 1)\n",
"# Rename Best of to Best_of\n",
"df_atp.rename(columns = {'Best of':'Best_of'},inplace=True)\n",
"# Choosing features\n",
"cols_to_keep = ['Date','Series','Surface', 'Round','Best_of', 'WRank','LRank']\n",
"# Dropping NaN\n",
"df_atp = df_atp[cols_to_keep].dropna()\n",
"# Dropping errors in the dataset and unimportant entries (e.g. there are very few entries for Masters Cup)\n",
"df_atp = df_atp[(df_atp['LRank'] != 'NR') & (df_atp['WRank'] != 'NR') & (df_atp['Series'] != 'Masters Cup')]\n",
"df_atp[['Best_of','WRank','LRank']] = df_atp[['Best_of','WRank','LRank']].astype(int)\n",
"def win(x):\n",
" if x > 0:\n",
" return 0\n",
" elif x <= 0:\n",
" return 1 \n",
" \n",
"df_atp['win'] = (df_atp['WRank'] - df_atp['LRank']).apply(win)\n",
"df_atp.head()"
]
},
{
"cell_type": "code",
"execution_count": 190,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>Series</th>\n",
" <th>Surface</th>\n",
" <th>Round</th>\n",
" <th>Best_of</th>\n",
" <th>WRank</th>\n",
" <th>LRank</th>\n",
" <th>win</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>39530</th>\n",
" <td>2014-12-02</td>\n",
" <td>ATP250</td>\n",
" <td>Clay</td>\n",
" <td>1st Round</td>\n",
" <td>3</td>\n",
" <td>92</td>\n",
" <td>42</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>39531</th>\n",
" <td>2014-12-02</td>\n",
" <td>ATP250</td>\n",
" <td>Clay</td>\n",
" <td>1st Round</td>\n",
" <td>3</td>\n",
" <td>45</td>\n",
" <td>78</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>39537</th>\n",
" <td>2014-12-02</td>\n",
" <td>ATP250</td>\n",
" <td>Clay</td>\n",
" <td>2nd Round</td>\n",
" <td>3</td>\n",
" <td>14</td>\n",
" <td>58</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>39560</th>\n",
" <td>2014-12-02</td>\n",
" <td>ATP250</td>\n",
" <td>Hard</td>\n",
" <td>1st Round</td>\n",
" <td>3</td>\n",
" <td>96</td>\n",
" <td>56</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>39563</th>\n",
" <td>2014-12-02</td>\n",
" <td>ATP250</td>\n",
" <td>Hard</td>\n",
" <td>2nd Round</td>\n",
" <td>3</td>\n",
" <td>85</td>\n",
" <td>81</td>\n",
" <td>0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date Series Surface Round Best_of WRank LRank win\n",
"39530 2014-12-02 ATP250 Clay 1st Round 3 92 42 0\n",
"39531 2014-12-02 ATP250 Clay 1st Round 3 45 78 1\n",
"39537 2014-12-02 ATP250 Clay 2nd Round 3 14 58 1\n",
"39560 2014-12-02 ATP250 Hard 1st Round 3 96 56 0\n",
"39563 2014-12-02 ATP250 Hard 2nd Round 3 85 81 0"
]
},
"execution_count": 190,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"newdf = df_atp.copy()\n",
"newdf2 = newdf[(newdf['WRank'] <= 100) & (newdf['LRank'] <= 100)]\n",
"newdf2.head()"
]
},
{
"cell_type": "code",
"execution_count": 191,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>Surface</th>\n",
" <th>Round</th>\n",
" <th>WRank</th>\n",
" <th>LRank</th>\n",
" <th>win</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>39530</th>\n",
" <td>2014-12-02</td>\n",
" <td>Clay</td>\n",
" <td>1st Round</td>\n",
" <td>92</td>\n",
" <td>42</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>39531</th>\n",
" <td>2014-12-02</td>\n",
" <td>Clay</td>\n",
" <td>1st Round</td>\n",
" <td>45</td>\n",
" <td>78</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>39537</th>\n",
" <td>2014-12-02</td>\n",
" <td>Clay</td>\n",
" <td>2nd Round</td>\n",
" <td>14</td>\n",
" <td>58</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>39560</th>\n",
" <td>2014-12-02</td>\n",
" <td>Hard</td>\n",
" <td>1st Round</td>\n",
" <td>96</td>\n",
" <td>56</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>39563</th>\n",
" <td>2014-12-02</td>\n",
" <td>Hard</td>\n",
" <td>2nd Round</td>\n",
" <td>85</td>\n",
" <td>81</td>\n",
" <td>0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date Surface Round WRank LRank win\n",
"39530 2014-12-02 Clay 1st Round 92 42 0\n",
"39531 2014-12-02 Clay 1st Round 45 78 1\n",
"39537 2014-12-02 Clay 2nd Round 14 58 1\n",
"39560 2014-12-02 Hard 1st Round 96 56 0\n",
"39563 2014-12-02 Hard 2nd Round 85 81 0"
]
},
"execution_count": 191,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df3 = newdf2.copy()\n",
"df3 = df3[df3['Best_of'] == 3]\n",
"# Drop Best_of and Series columns\n",
"df3.drop(\"Series\",axis = 1,inplace=True)\n",
"df3.drop(\"Best_of\",axis = 1,inplace=True)\n",
"df3.head()"
]
},
{
"cell_type": "code",
"execution_count": 192,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"y_0 = df3[df3.win == 0] \n",
"y_1 = df3[df3.win == 1] \n",
"n = min([len(y_0), len(y_1)]) \n",
"y_0 = y_0.sample(n = n, random_state = 0) \n",
"y_1 = y_1.sample(n = n, random_state = 0)\n",
"df_strat = pd.concat([y_0, y_1]) \n",
"X_strat = df_strat[['Date', 'Surface', 'Round','WRank', 'LRank']]\n",
"y_strat = df_strat.win"
]
},
{
"cell_type": "code",
"execution_count": 193,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>Surface</th>\n",
" <th>Round</th>\n",
" <th>WRank</th>\n",
" <th>LRank</th>\n",
" <th>win</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>43714</th>\n",
" <td>2015-12-08</td>\n",
" <td>Hard</td>\n",
" <td>2nd Round</td>\n",
" <td>49</td>\n",
" <td>34</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>42431</th>\n",
" <td>2015-03-15</td>\n",
" <td>Hard</td>\n",
" <td>2nd Round</td>\n",
" <td>41</td>\n",
" <td>32</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>45333</th>\n",
" <td>2016-04-20</td>\n",
" <td>Clay</td>\n",
" <td>2nd Round</td>\n",
" <td>51</td>\n",
" <td>35</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>42802</th>\n",
" <td>2015-01-05</td>\n",
" <td>Clay</td>\n",
" <td>Quarterfinals</td>\n",
" <td>63</td>\n",
" <td>50</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>45438</th>\n",
" <td>2016-01-05</td>\n",
" <td>Clay</td>\n",
" <td>The Final</td>\n",
" <td>87</td>\n",
" <td>29</td>\n",
" <td>0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date Surface Round WRank LRank win\n",
"43714 2015-12-08 Hard 2nd Round 49 34 0\n",
"42431 2015-03-15 Hard 2nd Round 41 32 0\n",
"45333 2016-04-20 Clay 2nd Round 51 35 0\n",
"42802 2015-01-05 Clay Quarterfinals 63 50 0\n",
"45438 2016-01-05 Clay The Final 87 29 0"
]
},
"execution_count": 193,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X_strat_1=X_strat.copy()\n",
"X_strat_1['win']=y_strat\n",
"X_strat_1.head()"
]
},
{
"cell_type": "code",
"execution_count": 194,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>Surface</th>\n",
" <th>Round</th>\n",
" <th>WRank</th>\n",
" <th>LRank</th>\n",
" <th>win</th>\n",
" <th>P1</th>\n",
" <th>P2</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>43714</th>\n",
" <td>2015-12-08</td>\n",
" <td>Hard</td>\n",
" <td>2nd Round</td>\n",
" <td>49</td>\n",
" <td>34</td>\n",
" <td>0</td>\n",
" <td>49</td>\n",
" <td>34</td>\n",
" </tr>\n",
" <tr>\n",
" <th>42431</th>\n",
" <td>2015-03-15</td>\n",
" <td>Hard</td>\n",
" <td>2nd Round</td>\n",
" <td>41</td>\n",
" <td>32</td>\n",
" <td>0</td>\n",
" <td>41</td>\n",
" <td>32</td>\n",
" </tr>\n",
" <tr>\n",
" <th>45333</th>\n",
" <td>2016-04-20</td>\n",
" <td>Clay</td>\n",
" <td>2nd Round</td>\n",
" <td>51</td>\n",
" <td>35</td>\n",
" <td>0</td>\n",
" <td>51</td>\n",
" <td>35</td>\n",
" </tr>\n",
" <tr>\n",
" <th>42802</th>\n",
" <td>2015-01-05</td>\n",
" <td>Clay</td>\n",
" <td>Quarterfinals</td>\n",
" <td>63</td>\n",
" <td>50</td>\n",
" <td>0</td>\n",
" <td>63</td>\n",
" <td>50</td>\n",
" </tr>\n",
" <tr>\n",
" <th>45438</th>\n",
" <td>2016-01-05</td>\n",
" <td>Clay</td>\n",
" <td>The Final</td>\n",
" <td>87</td>\n",
" <td>29</td>\n",
" <td>0</td>\n",
" <td>87</td>\n",
" <td>29</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date Surface Round WRank LRank win P1 P2\n",
"43714 2015-12-08 Hard 2nd Round 49 34 0 49 34\n",
"42431 2015-03-15 Hard 2nd Round 41 32 0 41 32\n",
"45333 2016-04-20 Clay 2nd Round 51 35 0 51 35\n",
"42802 2015-01-05 Clay Quarterfinals 63 50 0 63 50\n",
"45438 2016-01-05 Clay The Final 87 29 0 87 29"
]
},
"execution_count": 194,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df = X_strat_1.copy()\n",
"df[\"P1\"] = df[[\"WRank\", \"LRank\"]].max(axis=1)\n",
"df[\"P2\"] = df[[\"WRank\", \"LRank\"]].min(axis=1)\n",
"df.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exploratory Analysis for Best_of = 3"
]
},
{
"cell_type": "code",
"execution_count": 195,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x11d0cded0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#Without stratification\n",
"win_by_Surface = pd.crosstab(df3.win, df3.Surface).apply( lambda x: x/x.sum(), axis = 0 )\n",
"win_by_Surface\n",
"win_by_Surface = pd.DataFrame( win_by_Surface.unstack() ).reset_index()\n",
"win_by_Surface.columns = [\"Surface\", \"win\", \"total\" ]\n",
"fig2 = sns.barplot(win_by_Surface.Surface, win_by_Surface.total, hue = win_by_Surface.win )\n",
"fig2.figure.set_size_inches(8,5)"
]
},
{
"cell_type": "code",
"execution_count": 196,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
"<matplotlib.figure.Figure at 0x11c52ed10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"#without stratification\n",
"win_by_round = pd.crosstab(df.win, df.Round).apply( lambda x: x/x.sum(), axis = 0 )\n",
"win_by_round\n",
"win_by_round = pd.DataFrame(win_by_round.unstack() ).reset_index()\n",
"win_by_round.columns = [\"Round\", \"win\", \"total\" ]\n",
"fig2 = sns.barplot(win_by_round.Round, win_by_round.total, hue = win_by_round.win )\n",
"fig2.figure.set_size_inches(8,5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Dummy variables\n",
"------"
]
},
{
"cell_type": "code",
"execution_count": 197,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>Surface</th>\n",
" <th>Round</th>\n",
" <th>WRank</th>\n",
" <th>LRank</th>\n",
" <th>win</th>\n",
" <th>P1</th>\n",
" <th>P2</th>\n",
" <th>Round_2</th>\n",
" <th>Round_3</th>\n",
" <th>Round_4</th>\n",
" <th>Round_5</th>\n",
" <th>Round_6</th>\n",
" <th>Round_7</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>43714</th>\n",
" <td>2015-12-08</td>\n",
" <td>Hard</td>\n",
" <td>2</td>\n",
" <td>49</td>\n",
" <td>34</td>\n",
" <td>0</td>\n",
" <td>49</td>\n",
" <td>34</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>42431</th>\n",
" <td>2015-03-15</td>\n",
" <td>Hard</td>\n",
" <td>2</td>\n",
" <td>41</td>\n",
" <td>32</td>\n",
" <td>0</td>\n",
" <td>41</td>\n",
" <td>32</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>45333</th>\n",
" <td>2016-04-20</td>\n",
" <td>Clay</td>\n",
" <td>2</td>\n",
" <td>51</td>\n",
" <td>35</td>\n",
" <td>0</td>\n",
" <td>51</td>\n",
" <td>35</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>42802</th>\n",
" <td>2015-01-05</td>\n",
" <td>Clay</td>\n",
" <td>5</td>\n",
" <td>63</td>\n",
" <td>50</td>\n",
" <td>0</td>\n",
" <td>63</td>\n",
" <td>50</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>45438</th>\n",
" <td>2016-01-05</td>\n",
" <td>Clay</td>\n",
" <td>7</td>\n",
" <td>87</td>\n",
" <td>29</td>\n",
" <td>0</td>\n",
" <td>87</td>\n",
" <td>29</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date Surface Round WRank LRank win P1 P2 Round_2 Round_3 \\\n",
"43714 2015-12-08 Hard 2 49 34 0 49 34 1 0 \n",
"42431 2015-03-15 Hard 2 41 32 0 41 32 1 0 \n",
"45333 2016-04-20 Clay 2 51 35 0 51 35 1 0 \n",
"42802 2015-01-05 Clay 5 63 50 0 63 50 0 0 \n",
"45438 2016-01-05 Clay 7 87 29 0 87 29 0 0 \n",
"\n",
" Round_4 Round_5 Round_6 Round_7 \n",
"43714 0 0 0 0 \n",
"42431 0 0 0 0 \n",
"45333 0 0 0 0 \n",
"42802 0 1 0 0 \n",
"45438 0 0 0 1 "
]
},
"execution_count": 197,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df1 = df.copy()\n",
"def round_number(x):\n",
" if x == '1st Round':\n",
" return 1\n",
" elif x == '2nd Round':\n",
" return 2\n",
" elif x == '3rd Round':\n",
" return 3\n",
" elif x == '4th Round':\n",
" return 4\n",
" elif x == 'Quarterfinals':\n",
" return 5\n",
" elif x == 'Semifinals':\n",
" return 6\n",
" elif x == 'The Final':\n",
" return 7\n",
" \n",
"df1['Round'] = df1['Round'].apply(round_number)\n",
"\n",
"dummy_ranks = pd.get_dummies(df1['Round'], prefix='Round')\n",
"\n",
"df1 = df1.join(dummy_ranks.ix[:, 'Round_2':])\n",
"df1[['Round_2', 'Round_3',\n",
" 'Round_4', 'Round_5', 'Round_6', 'Round_7']] = df1[['Round_2', 'Round_3','Round_4', 'Round_5', 'Round_6', 'Round_7']].astype('int_')\n",
"df1.head()"
]
},
{
"cell_type": "code",
"execution_count": 198,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>WRank</th>\n",
" <th>LRank</th>\n",
" <th>win</th>\n",
" <th>P1</th>\n",
" <th>P2</th>\n",
" <th>Round_2</th>\n",
" <th>Round_3</th>\n",
" <th>Round_4</th>\n",
" <th>Round_5</th>\n",
" <th>Round_6</th>\n",
" <th>Round_7</th>\n",
" <th>Surface_Grass</th>\n",
" <th>Surface_Hard</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>43714</th>\n",
" <td>2015-12-08</td>\n",
" <td>49</td>\n",
" <td>34</td>\n",
" <td>0</td>\n",
" <td>49</td>\n",
" <td>34</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>42431</th>\n",
" <td>2015-03-15</td>\n",
" <td>41</td>\n",
" <td>32</td>\n",
" <td>0</td>\n",
" <td>41</td>\n",
" <td>32</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <th>45333</th>\n",
" <td>2016-04-20</td>\n",
" <td>51</td>\n",
" <td>35</td>\n",
" <td>0</td>\n",
" <td>51</td>\n",
" <td>35</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>42802</th>\n",
" <td>2015-01-05</td>\n",
" <td>63</td>\n",
" <td>50</td>\n",
" <td>0</td>\n",
" <td>63</td>\n",
" <td>50</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>45438</th>\n",
" <td>2016-01-05</td>\n",
" <td>87</td>\n",
" <td>29</td>\n",
" <td>0</td>\n",
" <td>87</td>\n",
" <td>29</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date WRank LRank win P1 P2 Round_2 Round_3 Round_4 \\\n",
"43714 2015-12-08 49 34 0 49 34 1 0 0 \n",
"42431 2015-03-15 41 32 0 41 32 1 0 0 \n",
"45333 2016-04-20 51 35 0 51 35 1 0 0 \n",
"42802 2015-01-05 63 50 0 63 50 0 0 0 \n",
"45438 2016-01-05 87 29 0 87 29 0 0 0 \n",
"\n",
" Round_5 Round_6 Round_7 Surface_Grass Surface_Hard \n",
"43714 0 0 0 0 1 \n",
"42431 0 0 0 0 1 \n",
"45333 0 0 0 0 0 \n",
"42802 1 0 0 0 0 \n",
"45438 0 0 1 0 0 "
]
},
"execution_count": 198,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dummy_ranks = pd.get_dummies(df1['Surface'], prefix='Surface')\n",
"df_2 = df1.join(dummy_ranks.ix[:, 'Surface_Grass':])\n",
"df_2.drop(\"Surface\",axis = 1,inplace=True)\n",
"df_2[['Surface_Grass','Surface_Hard']] = df_2[['Surface_Grass','Surface_Hard']].astype('int_')\n",
"df_2.drop(\"Round\",axis = 1,inplace=True)\n",
"df_2.head()"
]
},
{
"cell_type": "code",
"execution_count": 199,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Date</th>\n",
" <th>WRank</th>\n",
" <th>LRank</th>\n",
" <th>win</th>\n",
" <th>P1</th>\n",
" <th>P2</th>\n",
" <th>Round_2</th>\n",
" <th>Round_3</th>\n",
" <th>Round_4</th>\n",
" <th>Round_5</th>\n",
" <th>Round_6</th>\n",
" <th>Round_7</th>\n",
" <th>Surface_Grass</th>\n",
" <th>Surface_Hard</th>\n",
" <th>D</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>43714</th>\n",
" <td>2015-12-08</td>\n",
" <td>49</td>\n",
" <td>34</td>\n",
" <td>0</td>\n",
" <td>5.614710</td>\n",
" <td>5.087463</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0.527247</td>\n",
" </tr>\n",
" <tr>\n",
" <th>42431</th>\n",
" <td>2015-03-15</td>\n",
" <td>41</td>\n",
" <td>32</td>\n",
" <td>0</td>\n",
" <td>5.357552</td>\n",
" <td>5.000000</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0.357552</td>\n",
" </tr>\n",
" <tr>\n",
" <th>45333</th>\n",
" <td>2016-04-20</td>\n",
" <td>51</td>\n",
" <td>35</td>\n",
" <td>0</td>\n",
" <td>5.672425</td>\n",
" <td>5.129283</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0.543142</td>\n",
" </tr>\n",
" <tr>\n",
" <th>42802</th>\n",
" <td>2015-01-05</td>\n",
" <td>63</td>\n",
" <td>50</td>\n",
" <td>0</td>\n",
" <td>5.977280</td>\n",
" <td>5.643856</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0.333424</td>\n",
" </tr>\n",
" <tr>\n",
" <th>45438</th>\n",
" <td>2016-01-05</td>\n",
" <td>87</td>\n",
" <td>29</td>\n",
" <td>0</td>\n",
" <td>6.442943</td>\n",
" <td>4.857981</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1</td>\n",
" <td>0</td>\n",
" <td>0</td>\n",
" <td>1.584963</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Date WRank LRank win P1 P2 Round_2 Round_3 \\\n",
"43714 2015-12-08 49 34 0 5.614710 5.087463 1 0 \n",
"42431 2015-03-15 41 32 0 5.357552 5.000000 1 0 \n",
"45333 2016-04-20 51 35 0 5.672425 5.129283 1 0 \n",
"42802 2015-01-05 63 50 0 5.977280 5.643856 0 0 \n",
"45438 2016-01-05 87 29 0 6.442943 4.857981 0 0 \n",
"\n",
" Round_4 Round_5 Round_6 Round_7 Surface_Grass Surface_Hard \\\n",
"43714 0 0 0 0 0 1 \n",
"42431 0 0 0 0 0 1 \n",
"45333 0 0 0 0 0 0 \n",
"42802 0 1 0 0 0 0 \n",
"45438 0 0 0 1 0 0 \n",
"\n",
" D \n",
"43714 0.527247 \n",
"42431 0.357552 \n",
"45333 0.543142 \n",
"42802 0.333424 \n",
"45438 1.584963 "
]
},
"execution_count": 199,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df4 = df_2.copy()\n",
"df4['P1'] = np.log2(df4['P1'].astype('float64')) \n",
"df4['P2'] = np.log2(df4['P2'].astype('float64')) \n",
"df4['D'] = df4['P1'] - df4['P2']\n",
"df4['D'] = np.absolute(df4['D'])\n",
"df4.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model 1: Logistic Regression"
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"['Date',\n",
" 'WRank',\n",
" 'LRank',\n",
" 'win',\n",
" 'P1',\n",
" 'P2',\n",
" 'Round_2',\n",
" 'Round_3',\n",
" 'Round_4',\n",
" 'Round_5',\n",
" 'Round_6',\n",
" 'Round_7',\n",
" 'Surface_Grass',\n",
" 'Surface_Hard',\n",
" 'D']"
]
},
"execution_count": 61,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df4.columns.tolist()"
]
},
{
"cell_type": "code",
"execution_count": 266,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"#feature_cols = ['P1','P2','Round_2','Round_3','Round_4','Round_5','Round_6','Round_7','Surface_Grass','Surface_Hard','D']\n",
"feature_cols = ['D','Surface_Hard','Surface_Grass','Round_6','Round_5','Round_3']"
]
},
{
"cell_type": "code",
"execution_count": 267,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.591885441527\n",
"0.620670798396\n"
]
}
],
"source": [
"dfnew = df4.copy()\n",
"X = dfnew[feature_cols]\n",
"y = dfnew.win\n",
"from sklearn.cross_validation import train_test_split\n",
"X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=0)\n",
"from sklearn.linear_model import LogisticRegression\n",
"logreg = LogisticRegression()\n",
"logreg.fit(X_train, y_train)\n",
"y_pred_class = logreg.predict(X_test)\n",
"from sklearn import metrics\n",
"print(metrics.accuracy_score(y_test, y_pred_class))\n",
"y_pred_prob = logreg.predict_proba(X_test)[:, 1]\n",
"auc_score = metrics.roc_auc_score(y_test, y_pred_prob)\n",
"print(auc_score)"
]
},
{
"cell_type": "code",
"execution_count": 268,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
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64jwM6N6k3GMr2kJp48YNNGpUtkmAKqMSE0RBchCRBcDrwARV3VjcPgGcDSSqal8R6QM8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\nAUIIIUQpChBCCCFK+Q+Lt8ikHd6LvAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11d737d10>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"y_pred_prob = logreg.predict_proba(X_test)[:, 1]\n",
"auc_score = metrics.roc_auc_score(y_test, y_pred_prob)\n",
"auc_score\n",
"fpr, tpr, thresholds = metrics.roc_curve(y_test, y_pred_prob)\n",
"fig = plt.plot(fpr, tpr,label='ROC curve (area = %0.2f)' % auc_score )\n",
"plt.plot([0, 1], [0, 1], 'k--')\n",
"plt.xlim([0.0, 1.0])\n",
"plt.ylim([0.0, 1.0])\n",
"plt.title('ROC curve for win classifier')\n",
"plt.xlabel('False Positive Rate (1 - Specificity)')\n",
"plt.ylabel('True Positive Rate (Sensitivity)')\n",
"plt.legend(loc=\"lower right\")\n",
"plt.grid(True)"
]
},
{
"cell_type": "code",
"execution_count": 269,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"0.64683339949421492"
]
},
"execution_count": 269,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn.cross_validation import cross_val_score\n",
"cross_val_score(logreg, X, y, cv=10, scoring='roc_auc').mean()"
]
},
{
"cell_type": "code",
"execution_count": 271,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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klpb9gVsJhemWMWbMEVmMUiT7lBCkTpsyZTqDBr0CfA04CPiUUJX9MUJiaAgs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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11d5f40d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"logreg.fit(dfnew[[\"D\"]],dfnew[\"win\"])\n",
"pred_probs = logreg.predict_proba(dfnew[[\"D\"]])\n",
"plt.scatter(dfnew[\"D\"], pred_probs[:,1])\n",
"plt.title('Win Probability for 3 sets matches')\n",
"plt.xlabel('D')\n",
"plt.ylabel('Win Probability for 3 sets matches')\n",
"plt.legend(loc=\"lower right\")\n",
"plt.grid(True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Decision Trees and Random Forests"
]
},
{
"cell_type": "code",
"execution_count": 272,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"DecisionTreeClassifier(class_weight=None, criterion='gini', max_depth=None,\n",
" max_features=None, max_leaf_nodes=None, min_samples_leaf=1,\n",
" min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
" presort=False, random_state=None, splitter='best')"
]
},
"execution_count": 272,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn.tree import DecisionTreeClassifier\n",
"\n",
"model = DecisionTreeClassifier()\n",
"\n",
"X = dfnew[feature_cols].dropna()\n",
"y = dfnew['win']\n",
"\n",
"\n",
"model.fit(X, y)"
]
},
{
"cell_type": "code",
"execution_count": 273,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"AUC [ 0.55257937 0.57486536 0.53993056 0.5170318 0.49804582], Average AUC 0.536490582524\n"
]
}
],
"source": [
"from sklearn.cross_validation import cross_val_score\n",
"\n",
"scores = cross_val_score(model, X, y, scoring='roc_auc', cv=5)\n",
"print('AUC {}, Average AUC {}'.format(scores, scores.mean()))"
]
},
{
"cell_type": "code",
"execution_count": 274,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"CV AUC [ 0.61034935 0.67795139 0.61050879 0.6052207 0.55577468], Average AUC 0.611960979666\n"
]
}
],
"source": [
"model = DecisionTreeClassifier(\n",
" max_depth = 4,\n",
" min_samples_leaf = 6)\n",
"\n",
"model.fit(X, y)\n",
"scores = cross_val_score(model, X, y, scoring='roc_auc', cv=5)\n",
"print('CV AUC {}, Average AUC {}'.format(scores, scores.mean()))"
]
},
{
"cell_type": "code",
"execution_count": 275,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"RandomForestClassifier(bootstrap=True, class_weight=None, criterion='gini',\n",
" max_depth=None, max_features='auto', max_leaf_nodes=None,\n",
" min_samples_leaf=1, min_samples_split=2,\n",
" min_weight_fraction_leaf=0.0, n_estimators=200, n_jobs=1,\n",
" oob_score=False, random_state=None, verbose=0,\n",
" warm_start=False)"
]
},
"execution_count": 275,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn.ensemble import RandomForestClassifier\n",
"from sklearn.cross_validation import cross_val_score\n",
"\n",
"X = dfnew[feature_cols].dropna()\n",
"y = dfnew['win']\n",
"\n",
"model = RandomForestClassifier(n_estimators = 200)\n",
" \n",
"model.fit(X, y)\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 276,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Features</th>\n",
" <th>Importance Score</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>D</td>\n",
" <td>0.958857</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>Surface_Hard</td>\n",
" <td>0.010787</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>Surface_Grass</td>\n",
" <td>0.008321</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>Round_3</td>\n",
" <td>0.007937</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>Round_5</td>\n",
" <td>0.007525</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>Round_6</td>\n",
" <td>0.006573</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Features Importance Score\n",
"0 D 0.958857\n",
"1 Surface_Hard 0.010787\n",
"2 Surface_Grass 0.008321\n",
"5 Round_3 0.007937\n",
"4 Round_5 0.007525\n",
"3 Round_6 0.006573"
]
},
"execution_count": 276,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"features = X.columns\n",
"feature_importances = model.feature_importances_\n",
"\n",
"features_df = pd.DataFrame({'Features': features, 'Importance Score': feature_importances})\n",
"features_df.sort_values('Importance Score', inplace=True, ascending=False)\n",
"\n",
"features_df"
]
},
{
"cell_type": "code",
"execution_count": 277,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/marcotavora/anaconda/lib/python2.7/site-packages/ipykernel/__main__.py:2: FutureWarning: sort is deprecated, use sort_values(inplace=True) for INPLACE sorting\n",
" from ipykernel import kernelapp as app\n"
]
},
{
"data": {
"text/plain": [
"<matplotlib.axes._subplots.AxesSubplot at 0x1211caf10>"
]
},
"execution_count": 277,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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"text/plain": [
"<matplotlib.figure.Figure at 0x11ebd11d0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"feature_importances = pd.Series(model.feature_importances_, index=X.columns)\n",
"feature_importances.sort()\n",
"feature_importances.plot(kind=\"barh\", figsize=(7,6))"
]
},
{
"cell_type": "code",
"execution_count": 278,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"AUC [ 0.56410714 0.55746329 0.54182243], Average AUC 0.554464288773\n",
"n trees: 1, CV AUC [ 0.54352679 0.52182012 0.52169808], Average AUC 0.529014994355\n",
"n trees: 11, CV AUC [ 0.57148597 0.5538084 0.55104636], Average AUC 0.558780245814\n",
"n trees: 21, CV AUC [ 0.55047194 0.54987731 0.53842448], Average AUC 0.546257911153\n",
"n trees: 31, CV AUC [ 0.57475765 0.55339731 0.54241338], Average AUC 0.556856114695\n",
"n trees: 41, CV AUC [ 0.55816327 0.5527357 0.54013952], Average AUC 0.550346161769\n",
"n trees: 51, CV AUC [ 0.5441199 0.55787438 0.53792988], Average AUC 0.546641388544\n",
"n trees: 61, CV AUC [ 0.56126913 0.55277424 0.54369805], Average AUC 0.552580476248\n",
"n trees: 71, CV AUC [ 0.56765306 0.55975643 0.53744813], Average AUC 0.554952539745\n",
"n trees: 81, CV AUC [ 0.56794643 0.55797716 0.54158477], Average AUC 0.555836118697\n",
"n trees: 91, CV AUC [ 0.5585523 0.55412315 0.53579733], Average AUC 0.549490924948\n"
]
}
],
"source": [
"from sklearn.cross_validation import cross_val_score\n",
"\n",
"scores = cross_val_score(model, X, y, scoring='roc_auc')\n",
"print('AUC {}, Average AUC {}'.format(scores, scores.mean()))\n",
"\n",
"for n_trees in range(1, 100, 10):\n",
" model = RandomForestClassifier(n_estimators = n_trees)\n",
" scores = cross_val_score(model, X, y, scoring='roc_auc')\n",
" print('n trees: {}, CV AUC {}, Average AUC {}'.format(n_trees, scores, scores.mean()))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
"display_name": "Python [Root]",
"language": "python",
"name": "Python [Root]"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.12"
}
},
"nbformat": 4,
"nbformat_minor": 0
}