{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predicting Fantasy Football Points\n",
    "\n",
    "If you read my last [post](http://nbviewer.ipython.org/github/tfolkman/learningwithdata/blob/master/Biggest_Misses.ipynb) you will know that I recently started fantasy football and my team isn't doing so great. Currently 0 and 4. Ha!\n",
    "\n",
    "What seemed strange to me, though, is that my team kept underperforming relative to the ESPN projections. The consistent underperformance lead me to try and develop my own prediction model to see if I couldn't maybe do a better job.\n",
    "\n",
    "Skip the next few blocks of code to see more discussion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import sqlalchemy\n",
    "from sqlalchemy.orm import create_session\n",
    "from sklearn import preprocessing\n",
    "from collections import namedtuple\n",
    "from sklearn.ensemble import RandomForestRegressor\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set(style='ticks', palette='Set2')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "engine = sqlalchemy.create_engine('postgresql://localhost/fantasyfootball')    \n",
    "session = create_session(bind=engine)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class Prediction:\n",
    "\n",
    "    \n",
    "    def __init__(self, test_proj_week, position='ALL'):\n",
    "        self.train_proj_week = test_proj_week - 1\n",
    "        self.test_proj_week = test_proj_week\n",
    "        self.position = position\n",
    "\n",
    "\n",
    "    def make_prediction(self):\n",
    "        encoders = self.create_position_factors()\n",
    "        \n",
    "        self.train_data = self.week_df(self.train_proj_week, encoders.position,\n",
    "                             encoders.team, self.position)\n",
    "        test_data = self.week_df(self.test_proj_week, encoders.position, encoders.team, self.position)\n",
    "        \n",
    "        clf = RandomForestRegressor(n_estimators=5000, max_depth=5)\n",
    "        clf.fit(self.train_data.X, self.train_data.y)\n",
    "        model_predicted_points = clf.predict(test_data.X)\n",
    "        \n",
    "        results = self.rmean_sq(test_data.y.values, model_predicted_points)\n",
    "        espn = self.rmean_sq(test_data.y.values, test_data.espn_proj.values)\n",
    "        \n",
    "        # Put some variables in self for easier access\n",
    "        self.my_prediction = model_predicted_points\n",
    "        self.model = clf\n",
    "        self.results = results\n",
    "        self.espn_results = espn\n",
    "        self.actual = test_data.y.values\n",
    "        self.espn_prediction = test_data.espn_proj.values\n",
    "        \n",
    "        self.get_combined_df(test_data)\n",
    "      \n",
    "    \n",
    "    def get_combined_df(self, data):\n",
    "        df=pd.concat([data.X, data.index, data.espn_proj, data.y], axis=1)\n",
    "        df['name'] = df['index'].str.split(\"_\").str.get(0)\n",
    "        df['team'] = df['index'].str.split(\"_\").str.get(1)\n",
    "        df['position'] = df['index'].str.split(\"_\").str.get(2)\n",
    "        df['my_prediction'] = self.my_prediction\n",
    "        self.combined_test_df = df\n",
    "        \n",
    "    \n",
    "    def report(self):\n",
    "        print(\"Prediction for Week {0} for {1} position(s)\".format(self.test_proj_week, self.position))\n",
    "        print(\"My RMSE: {}\".format(self.results.rmse))\n",
    "        print(\"ESPN RMSE: {}\".format(self.espn_results.rmse))\n",
    "        self.plot_feature_importance()\n",
    "        plt.title(\"Feature Importance\", fontsize=20)\n",
    "        plt.show()\n",
    "        self.plot_dist_comp()\n",
    "        plt.title(\"Distribution of RMSE\", fontsize=20)\n",
    "        plt.show()\n",
    "        self.scatter_plot(self.actual, self.my_prediction)\n",
    "        plt.title(\"My Predictions\", fontsize=20)\n",
    "        plt.show()\n",
    "        self.scatter_plot(self.actual, self.espn_prediction)\n",
    "        plt.title(\"ESPN Predictions\", fontsize=20)\n",
    "        plt.show()\n",
    "        \n",
    "    \n",
    "    def plot_feature_importance(self):\n",
    "        plt.figure(figsize=(8,5))\n",
    "        df = pd.DataFrame()\n",
    "        df['fi'] = self.model.feature_importances_\n",
    "        df['name'] = self.train_data.X.columns\n",
    "        df = df.sort('fi')\n",
    "        sns.barplot(x=df.name, y=df.fi)\n",
    "        plt.xticks(rotation='vertical')\n",
    "        sns.despine()\n",
    "        \n",
    "    \n",
    "    def plot_dist_comp(self):\n",
    "        plt.figure(figsize=(8,5))\n",
    "        sns.distplot(self.results.array, label=\"Me\")\n",
    "        sns.distplot(self.espn_results.array, label=\"ESPN\")\n",
    "        plt.legend()\n",
    "        sns.despine()\n",
    "        \n",
    "    \n",
    "    def scatter_plot(self, x, y):\n",
    "        plt.figure(figsize=(8,5))\n",
    "        max_v = 40\n",
    "        x_45 = np.arange(0, max_v)\n",
    "        plt.scatter(x, y)\n",
    "        plt.plot(x_45, x_45)\n",
    "        plt.xlabel(\"Actual\")\n",
    "        plt.ylabel(\"Predicted\")\n",
    "        plt.ylim([0, max_v])\n",
    "        plt.xlim([0, max_v])\n",
    "    \n",
    "    \n",
    "    def week_df(self, proj_week, position_encoder, team_encoder, position = 'ALL'):\n",
    "        \n",
    "        # Get actual data for all previous weeks\n",
    "        actual_data = pd.read_sql_query(\"\"\"select name, team, position, opponent, week,\n",
    "                                    at_home, total_points, won_game, opponent_score, team_score\n",
    "                                    from scoring_leaders_weekly\"\"\", engine)\n",
    "        \n",
    "        # Calculate how team's perform on average against positions for fantasy points\n",
    "        team_data = pd.DataFrame(actual_data.groupby(['opponent', 'position']).total_points.mean())\n",
    "        team_data.reset_index(level=0, inplace=True)\n",
    "        team_data.reset_index(level=0, inplace=True)\n",
    "        team_data.rename(columns={'total_points': 'opponent_points'}, inplace=True)\n",
    "        actual_data = actual_data.merge(team_data, on=['opponent', 'position'], how='left')\n",
    "        team_data.rename(columns={'opponent_points': 'next_opponent_points', 'opponent': 'next_opponent'}, inplace=True)\n",
    "        \n",
    "        actual_data['index'] = actual_data.name + \"_\" + actual_data.team + \"_\" + actual_data.position\n",
    "        actual_data.week = actual_data.week.astype(int)\n",
    "        actual_data = actual_data[actual_data.week < proj_week]\n",
    "\n",
    "        # Calculate the average values for previous week metrics\n",
    "        wgt_df = actual_data[['opponent_points', 'index', 'at_home', 'total_points',\n",
    "                              'won_game', 'opponent_score', 'team_score']]\n",
    "        group_wgt_df = wgt_df.groupby('index')\n",
    "        player_df = group_wgt_df.mean()\n",
    "        player_df.reset_index(level=0, inplace=True)\n",
    "        \n",
    "        # Get the opponent data for the next week as well as espn projection\n",
    "        predicted_data = pd.read_sql_query(\"\"\"select name, team, position, opponent as next_opponent,\n",
    "                                            at_home as next_at_home, total_points as predicted_points\n",
    "                                            from next_week_projections\n",
    "                                            where week = '{0}'\"\"\".format(proj_week), engine)\n",
    "        predicted_data['index'] = predicted_data.name + \"_\" + predicted_data.team + \"_\" + predicted_data.position\n",
    "        predicted_data.drop(['name', 'team'], axis=1, inplace=True)\n",
    "\n",
    "        # Start combining everything - messy - sorry...\n",
    "        X = player_df.merge(predicted_data, on='index', how='left')\n",
    "        X = X.dropna()\n",
    "\n",
    "        # Get the actual result as our target\n",
    "        actual_result = pd.read_sql_query(\"\"\"select name, team, position, total_points as actual_points\n",
    "                                            from scoring_leaders_weekly\n",
    "                                            where week = '{0}'\"\"\".format(proj_week), engine)\n",
    "        actual_result['index'] = actual_result.name + \"_\" + actual_result.team + \"_\" + actual_result.position\n",
    "        actual_result.drop(['name', 'team', 'position'], axis=1, inplace=True)\n",
    "\n",
    "        X = X.merge(actual_result, on='index', how='left')\n",
    "        X = X.merge(team_data, on=['position', 'next_opponent'], how='left')\n",
    "        X = X.dropna()\n",
    "        if position != 'ALL':\n",
    "            X = X[X.position == position]\n",
    "        y = X.actual_points\n",
    "\n",
    "        X['team'] = X['index'].str.split(\"_\").str.get(1)\n",
    "\n",
    "        # Sklearn won't create factors for you, so encode the categories to integers\n",
    "        X['team_factor'] = team_encoder.transform(X.team)\n",
    "        if position == 'ALL':\n",
    "            X['position_factor'] = position_encoder.transform(X.position)\n",
    "        X['next_opponent_factor'] = team_encoder.transform(X.next_opponent)\n",
    "\n",
    "        espn = X['predicted_points']\n",
    "        index = X['index']\n",
    "        X.drop(['predicted_points', 'actual_points', 'team', 'position', 'next_opponent', 'index'], axis=1, inplace=True)\n",
    "        \n",
    "        # Return named tuple of all the data I need\n",
    "        week_tuple = namedtuple('Week', ['X', 'y', 'espn_proj', 'index'])\n",
    "        return week_tuple(X, y, espn, index)\n",
    "    \n",
    "    \n",
    "    def create_position_factors(self):\n",
    "        # Convert positions into integer categories\n",
    "        position_encoder = preprocessing.LabelEncoder()\n",
    "        positions = np.ravel(pd.read_sql_query(\"\"\"select distinct position from scoring_leaders_weekly;\"\"\", engine).values)\n",
    "        position_encoder.fit(positions)\n",
    "\n",
    "        # Convert team names into integer categories\n",
    "        team_encoder = preprocessing.LabelEncoder()\n",
    "        teams = np.ravel(pd.read_sql_query(\"\"\"select distinct team from scoring_leaders_weekly;\"\"\", engine).values)\n",
    "        team_encoder.fit(teams)\n",
    "        encoders = namedtuple('encoders', ['team', 'position'])\n",
    "        return encoders(team_encoder, position_encoder)\n",
    "    \n",
    "    \n",
    "    def rmean_sq(self, y_true, y_pred):\n",
    "        rmse = namedtuple('rmse', ['rmse', 'array'])\n",
    "        sq_error = []\n",
    "        assert len(y_true) == len(y_pred)\n",
    "        for i in range(len(y_true)):\n",
    "            sq_error.append((y_true[i] - y_pred[i])**2)\n",
    "        return rmse(np.sqrt(np.mean(sq_error)), np.sqrt(sq_error))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Put my model to the test\n",
    "\n",
    "If you look through the class above, you will see that I am using a random forest regressor as my model of choice with 5,000 trees and a max depth of 5. I did some cross validation testing with a few other models and hyper parameter selection and this seemed to work the best.\n",
    "\n",
    "I use a handful of variables including things like a player's average fantasy points, the average number of game's a player has won, and a player's position (more on variables in a bit). I tried modeling each position individually, but a global model provided a better root mean squared error in the end.\n",
    "\n",
    "So - lets try it out. What I will be doing is predicting fantasy points for players in week 3 of the season. To do this, I will use week 2 as my training set. Thus, I use week 1 data to train my model to predict week 2 outcomes. I then take this trained model and use it with week 1 and 2 data to predict week 3 fantasy points for players. Here we go..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Prediction for Week 3 for ALL position(s)\n",
      "My RMSE: 6.56041003517\n",
      "ESPN RMSE: 6.76700270293\n"
     ]
    },
    {
     "data": {
      "image/png": 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ZWUW0ckMXW8AkjQDWJW2O80yxja1ViKRlgTWBxyMi376oHUzSjhHxt9xx9ETS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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c830650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Ky8u5+uqrufHGG3Fdl6VLl3LNNddkrXxnQg9AERGRWWWezxPP6vPERUREplUgEBh3TrcM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\nq+5+XQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ccc7fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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lOmWki4RPunHwBW/ZslG7zygk9zReveti07ne8eoiPty2hcp+A5k0+CxOOKB/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\nEYmg/w+7iC/GJsx00AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d5fb650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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oakp9TPLhbyR2klFVNZyqquGMGDG7wzaLSPoiewWfD6LezTR69Jl897t37y6q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\nO+3pA95jrrdsTy2trQz8wkC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3h8ndAewCdtGv350ph8nV19dz2GG/Ys6c65gz5zoOO+xX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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f1b38d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "week_3_proj_all = Prediction(3)\n",
    "week_3_proj_all.make_prediction()\n",
    "week_3_proj_all.report()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Analysis\n",
    "\n",
    "## RMSE \n",
    "\n",
    "First, you will notice that I achieved a better RMSE than ESPN! Yay! The next thing you should notice is that I barely did better. But RMSE is just a single number, so lets dive a bit deeper.\n",
    "\n",
    "## RMSE Distribution\n",
    "\n",
    "Looking at the second graph you will see both distributions of RMSE. ESPN is doing a better job of getting more of their prediction errors close to zero. While my model has less area in the tail, so doesn't have as many big prediction errors as ESPN does. I also have more prediction errors in the 5-10 value range. These results can also be seen in the scatter plots. ESPN's predictions don't perform very well with very high actual fantasy point values. My model also suffers from this problem. This seems to make sense; these are most likely big games for these players with above average results that would be hard to predict with any confidence. My big win seems to be for players performing in the 5-15 point range. My model handles these better than ESPN with less low predictions in this range. Both models also have a lot of errors when players have low actual values. My model tends to over predict these, while ESPN has over and under predictions. These are probably players with bad games, so my model based on past, better performance is over shoting. ESPN probably has some better domain knowledge that can sometimes lead to over predicting a bad performance. \n",
    "\n",
    "## Feature Importance\n",
    "\n",
    "I found these results to be very fascinating. You will immediately notice that **next_opponent_points** is very important in my model. This variable is the average fantasy points that the opponent team the player will be against in week 3 has allowed for the player's position in the previous weeks for the season. I think this is sometimes called points against and it is very important. This is something I really overlooked in my drafting. I didn't really consider a player's schedule at all. These results suggest that analyzing a player's schedule can be extremely important. A great running back could have some bad fantasy games if up against some good run defenses.\n",
    "\n",
    "The next variable, **total_points** is the player's average fantasy points thus far in the season. **Opponent_points** is like **next_opponent_points** but it is the average value for that player's team for all the teams he has played thus far in the season. **Next_opponent_factor** is just the actual team the player will be playing in week 3. **Team_factor** is the player's team. **Team_score** is the average score for the player's team for past games. **Position_factor** is the player's position. **Opponent_score** is the same as **team_score** but for the player's opponents. **At_home** is average number of games at home. **Next_at_home** is whether next game is at home. **Won_game** is average number of games won in the past."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = week_3_proj_all.combined_test_df\n",
    "data['my_error'] = np.sqrt((data['my_prediction'] - data['actual_points'])**2)\n",
    "data['espn_error'] = np.sqrt((data['predicted_points'] - data['actual_points'])**2)\n",
    "data = data[['position', 'my_error', 'espn_error']]\n",
    "data = pd.melt(data, id_vars=['position'], value_vars=['my_error', 'espn_error'])\n",
    "data.columns = ['position', 'type', 'error']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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W1xF86vt5lv/jEpFOUPDHiJkdAaxz9+3prkVE0kfBLyISM3G9uCsiElsKfhGR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\nMaPgFxGJmf8Pc7z+BY5/TtYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f1a8a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.barplot(x='position', y='error', hue='type', data=data)\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Results by Position"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above bar chart shows how the models do by position. There are not too many surprises here. Less volatile positions like K and TE have lower average errors while positions like QB and RB have higher average errors. ESPN beats me across the board on average except for RB (but all values are close). One sort of interesting point is that my model has a noteable smaller standard deviation for QBs. But again, all differences are slight."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion\n",
    "\n",
    "Predicting fantasy points is hard. On average the models are only off by about 6.5 points, but can miss pretty big when players do very well or poorly, which is really what you usually care about. This is inheritely a challenging problem - how do you use past data to try and determine a future performance that differs from that past (like a break out game or a slump)? On some level, I imagine this is impossible, but think we could maybe do better. For instance, my model doesn't account for injury at all. Knowing that a player is coming off an injury could be very valuable. Or knowing that a key offensive lineman is out could really affect a RBs performance. I think the NFL has a lot of cool work that could be done with the right data and some deep thought about how these data could be used to understand performance.\n",
    "\n",
    "Second, I was very happy to gain some more insight into what variables seem to matter when trying to predict a player's fantasy points. In the future, I will be paying a lot more attention to a player's opponents.\n",
    "\n",
    "Lastly, I think it is really cool that with only a handful of variables a model could be developed that performs very similar to ESPN's prediction model. This is what I **love** about data science. I was able to use data to gain a much deeper undertanding of an area in which I am far from an expert. I have no idea how ESPN creates their predictions, but I imagine they put some effort into it, and I think it is awesome that with just my laptop and some data I could create a competing model. If anyone from ESPN is reading this...I'd love to connect and learn some more about your model :). \n",
    "\n",
    "P.S. - I will try and post some updates on the performance of the models as the season progresses if anyone is interested."
   ]
  }
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