Predict Fantasy Football Points.ipynb

{
 "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": "iVBORw0KGgoAAAANSUhEUgAAAfUAAAG3CAYAAACt2Mx2AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c830650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfEAAAFPCAYAAABd8vd4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nq+5+XQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ccc7fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfgAAAFeCAYAAABpbQ2MAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEYmg/w+7iC/GJsx00AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d5fb650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfgAAAFeCAYAAABpbQ2MAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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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": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEXCAYAAACqIS9uAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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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."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}