{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Predicting English Premier League Results\n",
    "\n",
    "I've been a fan of football for as long as I can remember, so with my quest to learn as much as possible about data science, I decided to go ahead and build a results predictor for English Premier League Matches!\n",
    "\n",
    "I'll first start off by importing commonly used data analysis libraries and importing the data into Python."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline\n",
    "\n",
    "# filter warnings, just so the jupyter notebook looks cleaner\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, to import the data. This data was collected from https://datahub.io/sports-data/english-premier-league"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "epl_1819 = pd.read_json(\"season-1819_json.json\")\n",
    "epl_1718 = pd.read_json(\"season-1718_json.json\")\n",
    "epl_1617 = pd.read_json(\"season-1617_json.json\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>AC</th>\n",
       "      <th>AF</th>\n",
       "      <th>AR</th>\n",
       "      <th>AS</th>\n",
       "      <th>AST</th>\n",
       "      <th>AY</th>\n",
       "      <th>AwayTeam</th>\n",
       "      <th>B365A</th>\n",
       "      <th>B365D</th>\n",
       "      <th>B365H</th>\n",
       "      <th>...</th>\n",
       "      <th>PSCH</th>\n",
       "      <th>PSD</th>\n",
       "      <th>PSH</th>\n",
       "      <th>Referee</th>\n",
       "      <th>VCA</th>\n",
       "      <th>VCD</th>\n",
       "      <th>VCH</th>\n",
       "      <th>WHA</th>\n",
       "      <th>WHD</th>\n",
       "      <th>WHH</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>8</td>\n",
       "      <td>0</td>\n",
       "      <td>13</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>Leicester</td>\n",
       "      <td>7.50</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.57</td>\n",
       "      <td>...</td>\n",
       "      <td>1.55</td>\n",
       "      <td>3.93</td>\n",
       "      <td>1.58</td>\n",
       "      <td>A Marriner</td>\n",
       "      <td>7.00</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.57</td>\n",
       "      <td>6.00</td>\n",
       "      <td>3.8</td>\n",
       "      <td>1.57</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>9</td>\n",
       "      <td>0</td>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Cardiff</td>\n",
       "      <td>4.50</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.90</td>\n",
       "      <td>...</td>\n",
       "      <td>1.88</td>\n",
       "      <td>3.63</td>\n",
       "      <td>1.89</td>\n",
       "      <td>K Friend</td>\n",
       "      <td>4.75</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.87</td>\n",
       "      <td>4.00</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.91</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>11</td>\n",
       "      <td>0</td>\n",
       "      <td>10</td>\n",
       "      <td>9</td>\n",
       "      <td>2</td>\n",
       "      <td>Crystal Palace</td>\n",
       "      <td>3.00</td>\n",
       "      <td>3.4</td>\n",
       "      <td>2.50</td>\n",
       "      <td>...</td>\n",
       "      <td>2.62</td>\n",
       "      <td>3.46</td>\n",
       "      <td>2.50</td>\n",
       "      <td>M Dean</td>\n",
       "      <td>3.00</td>\n",
       "      <td>3.4</td>\n",
       "      <td>2.50</td>\n",
       "      <td>2.80</td>\n",
       "      <td>3.3</td>\n",
       "      <td>2.45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>8</td>\n",
       "      <td>0</td>\n",
       "      <td>13</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>Chelsea</td>\n",
       "      <td>1.61</td>\n",
       "      <td>4.0</td>\n",
       "      <td>6.50</td>\n",
       "      <td>...</td>\n",
       "      <td>7.24</td>\n",
       "      <td>4.02</td>\n",
       "      <td>6.41</td>\n",
       "      <td>C Kavanagh</td>\n",
       "      <td>1.62</td>\n",
       "      <td>4.0</td>\n",
       "      <td>6.50</td>\n",
       "      <td>1.57</td>\n",
       "      <td>3.9</td>\n",
       "      <td>5.80</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>12</td>\n",
       "      <td>0</td>\n",
       "      <td>15</td>\n",
       "      <td>5</td>\n",
       "      <td>2</td>\n",
       "      <td>Tottenham</td>\n",
       "      <td>2.04</td>\n",
       "      <td>3.5</td>\n",
       "      <td>3.90</td>\n",
       "      <td>...</td>\n",
       "      <td>4.74</td>\n",
       "      <td>3.57</td>\n",
       "      <td>3.83</td>\n",
       "      <td>M Atkinson</td>\n",
       "      <td>2.10</td>\n",
       "      <td>3.4</td>\n",
       "      <td>3.90</td>\n",
       "      <td>2.05</td>\n",
       "      <td>3.2</td>\n",
       "      <td>3.80</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 65 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   AC  AF  AR  AS  AST  AY        AwayTeam  B365A  B365D  B365H  ...  PSCH  \\\n",
       "0   5   8   0  13    4   1       Leicester   7.50    3.9   1.57  ...  1.55   \n",
       "1   4   9   0  10    1   1         Cardiff   4.50    3.6   1.90  ...  1.88   \n",
       "2   5  11   0  10    9   2  Crystal Palace   3.00    3.4   2.50  ...  2.62   \n",
       "3   5   8   0  13    4   1         Chelsea   1.61    4.0   6.50  ...  7.24   \n",
       "4   5  12   0  15    5   2       Tottenham   2.04    3.5   3.90  ...  4.74   \n",
       "\n",
       "    PSD   PSH     Referee   VCA  VCD   VCH   WHA  WHD   WHH  \n",
       "0  3.93  1.58  A Marriner  7.00  4.0  1.57  6.00  3.8  1.57  \n",
       "1  3.63  1.89    K Friend  4.75  3.6  1.87  4.00  3.5  1.91  \n",
       "2  3.46  2.50      M Dean  3.00  3.4  2.50  2.80  3.3  2.45  \n",
       "3  4.02  6.41  C Kavanagh  1.62  4.0  6.50  1.57  3.9  5.80  \n",
       "4  3.57  3.83  M Atkinson  2.10  3.4  3.90  2.05  3.2  3.80  \n",
       "\n",
       "[5 rows x 65 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = epl_1819.append([epl_1718,epl_1617])\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that we are spoiled with data here, with over 62 columns of data for each match. However, most of this data pertains to betting odds from different websites. While we can take a look at these values for the sake of evaluation of our models, the most important data I will be looking at is as follows:\n",
    "\n",
    "1) HomeTeam\n",
    "\n",
    "2) AwayTeam\n",
    "\n",
    "3) FTHG (Full-Time Home Goals)\n",
    "\n",
    "4) FTAG (Full-Time Away Goals)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>HomeTeam</th>\n",
       "      <th>AwayTeam</th>\n",
       "      <th>FTHG</th>\n",
       "      <th>FTAG</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>Man United</td>\n",
       "      <td>Leicester</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>Bournemouth</td>\n",
       "      <td>Cardiff</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>Fulham</td>\n",
       "      <td>Crystal Palace</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>Huddersfield</td>\n",
       "      <td>Chelsea</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>Newcastle</td>\n",
       "      <td>Tottenham</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       HomeTeam        AwayTeam  FTHG  FTAG\n",
       "0    Man United       Leicester     2     1\n",
       "1   Bournemouth         Cardiff     2     0\n",
       "2        Fulham  Crystal Palace     0     2\n",
       "3  Huddersfield         Chelsea     0     3\n",
       "4     Newcastle       Tottenham     1     2"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = df[['HomeTeam','AwayTeam','FTHG','FTAG']]\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's add a column to represent the total goals scored in each game:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>HomeTeam</th>\n",
       "      <th>AwayTeam</th>\n",
       "      <th>HomeGoals</th>\n",
       "      <th>AwayGoals</th>\n",
       "      <th>TotalGoals</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>Man United</td>\n",
       "      <td>Leicester</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>Bournemouth</td>\n",
       "      <td>Cardiff</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>Fulham</td>\n",
       "      <td>Crystal Palace</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>Huddersfield</td>\n",
       "      <td>Chelsea</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>Newcastle</td>\n",
       "      <td>Tottenham</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       HomeTeam        AwayTeam  HomeGoals  AwayGoals  TotalGoals\n",
       "0    Man United       Leicester          2          1           3\n",
       "1   Bournemouth         Cardiff          2          0           2\n",
       "2        Fulham  Crystal Palace          0          2           2\n",
       "3  Huddersfield         Chelsea          0          3           3\n",
       "4     Newcastle       Tottenham          1          2           3"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['FTG'] = df['FTHG'] + df['FTAG']\n",
    "df = df.rename(columns={'FTHG': 'HomeGoals', 'FTAG': 'AwayGoals', 'FTG':'TotalGoals'})\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "HomeGoals     1.565789\n",
       "AwayGoals     1.200877\n",
       "TotalGoals    2.766667\n",
       "dtype: float64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see here that the Home Team, on average, scores more goals than the away team. This is consistent with the concept of home field advantage, which is present in most sporting events. Let's take a look at some distributions to see if we can decipher any potential statistical patterns.\n",
    "\n",
    "I want to plot the count of the number of goals for each category, just to see the data in its broadest form at first. In order to do so, instead of using matplotlib and subplots, I prefered using the Pandas.melt() function in order to use Seaborn more easily. \n",
    "\n",
    "Note: Normally, in order to properly examine distributions, I would have to normalize the y-axis to percentages (create a pmf). However, just to have an overall idea first, I will be looking at the overall distribution with count values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>variable</th>\n",
       "      <th>value</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>HomeGoals</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>HomeGoals</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>HomeGoals</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>HomeGoals</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>HomeGoals</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    variable  value\n",
       "0  HomeGoals      2\n",
       "1  HomeGoals      2\n",
       "2  HomeGoals      0\n",
       "3  HomeGoals      0\n",
       "4  HomeGoals      1"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dfMelted = pd.melt(df[['HomeGoals','AwayGoals','TotalGoals']])\n",
    "dfMelted.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a160099e8>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,8))\n",
    "sns.set_style('darkgrid')\n",
    "ax = sns.countplot(data=dfMelted,x='variable',hue='value', palette='coolwarm')\n",
    "ax.set(xlabel='Goals per Match', ylabel='Number of Matches',title='Number of Goals per Match')\n",
    "plt.legend(title=\"Number of Goals per Match\", fontsize='small', fancybox=True,facecolor='white')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "At this point, two potential distributions come to mind, purely due to the shape of the plots:\n",
    "\n",
    "1) Lognormal Distribution (similar to a normal distribution, skewed to the right)\n",
    "\n",
    "2) Poisson Distribution\n",
    "\n",
    "**The Poisson Distribution makes more sense in this case, since we previously saw that means across the HomeGoals & AwayGoals classifications differed, and would thus have distributions that more accurately represent this. Moreover, the Poisson Distribution fits our problem pretty well, since it:**\n",
    "\n",
    "1) Is a Discrete Probability Distribution, and there are a discrete number of goals to be scored in a match\n",
    "\n",
    "2) Predicts probabilities within a specific time period, which, in this case, is a 90 minute game of football\n",
    "\n",
    "3) Assumes events are independent of time (i.e. the probability of a goal being scored is not dependent on whether or not goals have already been scored in the match)\n",
    "\n",
    "The formula for the Poisson Distribution is as follows:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "$$P(x) = \\frac{e^{-\\lambda} \\lambda^{x}}{x!}, \\lambda > 0$$\n",
    "Where $ \\lambda = $ Average  Number  of  Goals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To test this, let's compare the distribution of TotalGoals with a Poisson Distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "_lambdaTotal = np.mean(df['TotalGoals'])\n",
    "_lambdaAway = np.mean(df['AwayGoals'])\n",
    "_lambdaHome = np.mean(df['HomeGoals'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Goals</th>\n",
       "      <th>Poisson Probability - Home</th>\n",
       "      <th>Poisson Probability - Away</th>\n",
       "      <th>Poisson Probability - Total</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Goals  Poisson Probability - Home  Poisson Probability - Away  \\\n",
       "0      0                         0.0                         0.0   \n",
       "1      1                         0.0                         0.0   \n",
       "2      2                         0.0                         0.0   \n",
       "3      3                         0.0                         0.0   \n",
       "4      4                         0.0                         0.0   \n",
       "5      5                         0.0                         0.0   \n",
       "6      6                         0.0                         0.0   \n",
       "7      7                         0.0                         0.0   \n",
       "8      8                         0.0                         0.0   \n",
       "\n",
       "   Poisson Probability - Total  \n",
       "0                          0.0  \n",
       "1                          0.0  \n",
       "2                          0.0  \n",
       "3                          0.0  \n",
       "4                          0.0  \n",
       "5                          0.0  \n",
       "6                          0.0  \n",
       "7                          0.0  \n",
       "8                          0.0  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poisson_pmf = pd.DataFrame({'Goals':range(max(df['TotalGoals'])),\n",
    "                            'Poisson Probability - Home':np.zeros(max(df['TotalGoals'])),\n",
    "                            'Poisson Probability - Away':np.zeros(max(df['TotalGoals'])),\n",
    "                            'Poisson Probability - Total':np.zeros(max(df['TotalGoals'])),\n",
    "                           })\n",
    "poisson_pmf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Goals</th>\n",
       "      <th>Poisson Probability - Home</th>\n",
       "      <th>Poisson Probability - Away</th>\n",
       "      <th>Poisson Probability - Total</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.208923</td>\n",
       "      <td>0.300930</td>\n",
       "      <td>0.062871</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.327129</td>\n",
       "      <td>0.361380</td>\n",
       "      <td>0.173944</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0.256108</td>\n",
       "      <td>0.216987</td>\n",
       "      <td>0.240622</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>0.133670</td>\n",
       "      <td>0.086858</td>\n",
       "      <td>0.221907</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>0.052325</td>\n",
       "      <td>0.026076</td>\n",
       "      <td>0.153486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>0.016386</td>\n",
       "      <td>0.006263</td>\n",
       "      <td>0.084929</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>0.004276</td>\n",
       "      <td>0.001254</td>\n",
       "      <td>0.039162</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>0.000957</td>\n",
       "      <td>0.000215</td>\n",
       "      <td>0.015478</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Goals  Poisson Probability - Home  Poisson Probability - Away  \\\n",
       "0      0                    0.208923                    0.300930   \n",
       "1      1                    0.327129                    0.361380   \n",
       "2      2                    0.256108                    0.216987   \n",
       "3      3                    0.133670                    0.086858   \n",
       "4      4                    0.052325                    0.026076   \n",
       "5      5                    0.016386                    0.006263   \n",
       "6      6                    0.004276                    0.001254   \n",
       "7      7                    0.000957                    0.000215   \n",
       "8      8                    0.000000                    0.000000   \n",
       "\n",
       "   Poisson Probability - Total  \n",
       "0                     0.062871  \n",
       "1                     0.173944  \n",
       "2                     0.240622  \n",
       "3                     0.221907  \n",
       "4                     0.153486  \n",
       "5                     0.084929  \n",
       "6                     0.039162  \n",
       "7                     0.015478  \n",
       "8                     0.000000  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "for i in range(max(poisson_pmf['Goals'])):\n",
    "    poisson_pmf['Poisson Probability - Home'][i] = (math.exp(-_lambdaHome)*_lambdaHome**(i)/math.factorial(i))\n",
    "    poisson_pmf['Poisson Probability - Away'][i] = (math.exp(-_lambdaAway)*_lambdaAway**(i)/math.factorial(i))\n",
    "    poisson_pmf['Poisson Probability - Total'][i] = (math.exp(-_lambdaTotal)*_lambdaTotal**(i)/math.factorial(i))\n",
    "poisson_pmf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "poisson_pmf['Observed Probability - Home'] = np.zeros(9)\n",
    "poisson_pmf['Observed Probability - Away'] = np.zeros(9)\n",
    "poisson_pmf['Observed Probability - Total'] = np.zeros(9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Goals</th>\n",
       "      <th>Poisson Probability - Home</th>\n",
       "      <th>Poisson Probability - Away</th>\n",
       "      <th>Poisson Probability - Total</th>\n",
       "      <th>Observed Probability - Home</th>\n",
       "      <th>Observed Probability - Away</th>\n",
       "      <th>Observed Probability - Total</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.208923</td>\n",
       "      <td>0.300930</td>\n",
       "      <td>0.062871</td>\n",
       "      <td>0.228947</td>\n",
       "      <td>0.338596</td>\n",
       "      <td>0.071053</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.327129</td>\n",
       "      <td>0.361380</td>\n",
       "      <td>0.173944</td>\n",
       "      <td>0.319298</td>\n",
       "      <td>0.327193</td>\n",
       "      <td>0.158772</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>0.256108</td>\n",
       "      <td>0.216987</td>\n",
       "      <td>0.240622</td>\n",
       "      <td>0.237719</td>\n",
       "      <td>0.196491</td>\n",
       "      <td>0.240351</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>0.133670</td>\n",
       "      <td>0.086858</td>\n",
       "      <td>0.221907</td>\n",
       "      <td>0.122807</td>\n",
       "      <td>0.086842</td>\n",
       "      <td>0.219298</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>0.052325</td>\n",
       "      <td>0.026076</td>\n",
       "      <td>0.153486</td>\n",
       "      <td>0.060526</td>\n",
       "      <td>0.038596</td>\n",
       "      <td>0.167544</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>0.016386</td>\n",
       "      <td>0.006263</td>\n",
       "      <td>0.084929</td>\n",
       "      <td>0.024561</td>\n",
       "      <td>0.008772</td>\n",
       "      <td>0.088596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>0.004276</td>\n",
       "      <td>0.001254</td>\n",
       "      <td>0.039162</td>\n",
       "      <td>0.005263</td>\n",
       "      <td>0.002632</td>\n",
       "      <td>0.034211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>0.000957</td>\n",
       "      <td>0.000215</td>\n",
       "      <td>0.015478</td>\n",
       "      <td>0.000877</td>\n",
       "      <td>0.000877</td>\n",
       "      <td>0.014035</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.002632</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Goals  Poisson Probability - Home  Poisson Probability - Away  \\\n",
       "0      0                    0.208923                    0.300930   \n",
       "1      1                    0.327129                    0.361380   \n",
       "2      2                    0.256108                    0.216987   \n",
       "3      3                    0.133670                    0.086858   \n",
       "4      4                    0.052325                    0.026076   \n",
       "5      5                    0.016386                    0.006263   \n",
       "6      6                    0.004276                    0.001254   \n",
       "7      7                    0.000957                    0.000215   \n",
       "8      8                    0.000000                    0.000000   \n",
       "\n",
       "   Poisson Probability - Total  Observed Probability - Home  \\\n",
       "0                     0.062871                     0.228947   \n",
       "1                     0.173944                     0.319298   \n",
       "2                     0.240622                     0.237719   \n",
       "3                     0.221907                     0.122807   \n",
       "4                     0.153486                     0.060526   \n",
       "5                     0.084929                     0.024561   \n",
       "6                     0.039162                     0.005263   \n",
       "7                     0.015478                     0.000877   \n",
       "8                     0.000000                     0.000000   \n",
       "\n",
       "   Observed Probability - Away  Observed Probability - Total  \n",
       "0                     0.338596                      0.071053  \n",
       "1                     0.327193                      0.158772  \n",
       "2                     0.196491                      0.240351  \n",
       "3                     0.086842                      0.219298  \n",
       "4                     0.038596                      0.167544  \n",
       "5                     0.008772                      0.088596  \n",
       "6                     0.002632                      0.034211  \n",
       "7                     0.000877                      0.014035  \n",
       "8                     0.000000                      0.002632  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for i in poisson_pmf['Goals']:\n",
    "    poisson_pmf['Observed Probability - Home'][i] = df['HomeGoals'][df['HomeGoals']==i].count()/df['HomeGoals'].count()\n",
    "    poisson_pmf['Observed Probability - Away'][i] = df['AwayGoals'][df['AwayGoals']==i].count()/df['AwayGoals'].count()\n",
    "    poisson_pmf['Observed Probability - Total'][i] = df['TotalGoals'][df['TotalGoals']==i].count()/df['TotalGoals'].count()\n",
    "poisson_pmf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(3, 1, figsize=(15,8))\n",
    "sns.set_style('darkgrid')\n",
    "\n",
    "axes[0].plot(poisson_pmf['Goals'],poisson_pmf['Observed Probability - Home'], label = 'Observed Probability', marker='o')\n",
    "axes[0].plot(poisson_pmf['Goals'],poisson_pmf['Poisson Probability - Home'], label = 'Poisson Probability', marker = 'x')\n",
    "axes[0].set_title('Home Goals')\n",
    "axes[0].legend(fontsize='large', fancybox=True,facecolor='white')\n",
    "axes[0].set_ylabel('Probability')\n",
    "axes[0].set_xlabel('Number of Goals in a Match')\n",
    "\n",
    "axes[1].plot(poisson_pmf['Goals'],poisson_pmf['Observed Probability - Away'], label = 'Observed Probability', marker = 'o')\n",
    "axes[1].plot(poisson_pmf['Goals'],poisson_pmf['Poisson Probability - Away'], label = 'Poisson Probability', marker = 'x')\n",
    "axes[1].set_title('Away Goals')\n",
    "axes[1].legend(fontsize='large', fancybox=True,facecolor='white')\n",
    "axes[1].set_ylabel('Probability')\n",
    "axes[1].set_xlabel('Number of Goals in a Match')\n",
    "\n",
    "axes[2].plot(poisson_pmf['Goals'],poisson_pmf['Observed Probability - Total'], label = 'Observed Probability', marker = 'o')\n",
    "axes[2].plot(poisson_pmf['Goals'],poisson_pmf['Poisson Probability - Total'], label = 'Poisson Probability', marker = 'x')\n",
    "axes[2].set_title('Total Goals')\n",
    "axes[2].legend(fontsize='large', fancybox=True,facecolor='white')\n",
    "axes[2].set_ylabel('Probability')\n",
    "axes[2].set_xlabel('Number of Goals in a Match')\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, the Poisson distribution aligns decently well with the observed distribution regarding the number of goals scored in a match. That's a good sign!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For further confirmation, let's take a look at the Skellam distribution, which represents a difference between two Poisson-Distributed variables. In this case, we'll take a look at the difference between HomeGoals and AwayGoals"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import skellam"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Difference</th>\n",
       "      <th>Skellam</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>-10</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>-9</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>-8</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>-7</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>-6</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Difference Skellam\n",
       "0         -10     NaN\n",
       "1          -9     NaN\n",
       "2          -8     NaN\n",
       "3          -7     NaN\n",
       "4          -6     NaN"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Set up a dataframe with values of \"Difference\", the difference of goals between the home team and away team,\n",
    "# from -10 to 10, just to be sure we encompass all possible values\n",
    "\n",
    "values = []\n",
    "values.extend(range(-10,11))\n",
    "skellamdf = pd.DataFrame(columns=[\"Difference\",\"Skellam\"])\n",
    "skellamdf.Difference = values\n",
    "skellamdf.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "pmf_temp = []\n",
    "for i in skellamdf['Difference']:\n",
    "    pmf_temp.append(skellam.pmf(i,  df.mean()[0],  df.mean()[1]))\n",
    "skellamdf['Skellam'] = pmf_temp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>HomeTeam</th>\n",
       "      <th>AwayTeam</th>\n",
       "      <th>HomeGoals</th>\n",
       "      <th>AwayGoals</th>\n",
       "      <th>TotalGoals</th>\n",
       "      <th>Difference</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>Man United</td>\n",
       "      <td>Leicester</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>Bournemouth</td>\n",
       "      <td>Cardiff</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>Fulham</td>\n",
       "      <td>Crystal Palace</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>-2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>Huddersfield</td>\n",
       "      <td>Chelsea</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>-3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>Newcastle</td>\n",
       "      <td>Tottenham</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>-1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       HomeTeam        AwayTeam  HomeGoals  AwayGoals  TotalGoals  Difference\n",
       "0    Man United       Leicester          2          1           3           1\n",
       "1   Bournemouth         Cardiff          2          0           2           2\n",
       "2        Fulham  Crystal Palace          0          2           2          -2\n",
       "3  Huddersfield         Chelsea          0          3           3          -3\n",
       "4     Newcastle       Tottenham          1          2           3          -1"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Difference'] = df['HomeGoals'] - df['AwayGoals']\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a distribution\n",
    "\n",
    "differenceDistribution = []\n",
    "\n",
    "for i in skellamdf['Difference']:\n",
    "    differenceDistribution.append(df['Difference'][df['Difference']==i].count()/df['Difference'].count())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "skellamdf['Observed'] = differenceDistribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Probability of Goal Difference per Match')"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Skellam vs Actual\n",
    "\n",
    "plt.figure(figsize=(15,8))\n",
    "sns.set_style('darkgrid')\n",
    "sns.barplot(data=skellamdf,x=skellamdf['Difference'], y='Observed', palette='coolwarm', label = 'Observed')\n",
    "sns.lineplot(data=skellamdf,x=skellamdf['Difference'], y='Skellam', marker='o', color='green', label = 'Skellam',)\n",
    "plt.legend(fontsize='large', fancybox=True,facecolor='white')\n",
    "plt.title('Probability of Goal Difference per Match')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Again, we see a pretty good match here! The skellam distribution mimics the observed distribution of the difference in goals between the home team and the away team. We can see that it is almost impossible for the home team to win by more than 6 goals or lose by more than 5 goals, with the most likely difference being 0, indicating a draw. However, there seems to be a higher probability for the home team winning, which is consistent with what we have seen previously."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Creating the Poisson Distribution Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>Generalized Linear Model Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>goals</td>      <th>  No. Observations:  </th>  <td>  2280</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                  <td>GLM</td>       <th>  Df Residuals:      </th>  <td>  2228</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model Family:</th>         <td>Poisson</td>     <th>  Df Model:          </th>  <td>    51</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Link Function:</th>          <td>log</td>       <th>  Scale:             </th> <td>  1.0000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>                <td>IRLS</td>       <th>  Log-Likelihood:    </th> <td> -3229.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Tue, 04 Feb 2020</td> <th>  Deviance:          </th> <td>  2433.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>19:38:27</td>     <th>  Pearson chi2:      </th> <td>2.10e+03</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Iterations:</th>          <td>5</td>        <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>     <td>nonrobust</td>    <th>                     </th>     <td> </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>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>                  <td>    0.4798</td> <td>    0.110</td> <td>    4.364</td> <td> 0.000</td> <td>    0.264</td> <td>    0.695</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Bournemouth]</th>        <td>   -0.3454</td> <td>    0.104</td> <td>   -3.306</td> <td> 0.001</td> <td>   -0.550</td> <td>   -0.141</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Brighton]</th>           <td>   -0.7580</td> <td>    0.138</td> <td>   -5.496</td> <td> 0.000</td> <td>   -1.028</td> <td>   -0.488</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Burnley]</th>            <td>   -0.6206</td> <td>    0.113</td> <td>   -5.478</td> <td> 0.000</td> <td>   -0.843</td> <td>   -0.399</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Cardiff]</th>            <td>   -0.7688</td> <td>    0.184</td> <td>   -4.168</td> <td> 0.000</td> <td>   -1.130</td> <td>   -0.407</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Chelsea]</th>            <td>   -0.0770</td> <td>    0.096</td> <td>   -0.800</td> <td> 0.424</td> <td>   -0.266</td> <td>    0.112</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Crystal Palace]</th>     <td>   -0.4210</td> <td>    0.107</td> <td>   -3.951</td> <td> 0.000</td> <td>   -0.630</td> <td>   -0.212</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Everton]</th>            <td>   -0.3369</td> <td>    0.104</td> <td>   -3.249</td> <td> 0.001</td> <td>   -0.540</td> <td>   -0.134</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Fulham]</th>             <td>   -0.7568</td> <td>    0.184</td> <td>   -4.102</td> <td> 0.000</td> <td>   -1.118</td> <td>   -0.395</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Huddersfield]</th>       <td>   -1.0707</td> <td>    0.157</td> <td>   -6.836</td> <td> 0.000</td> <td>   -1.378</td> <td>   -0.764</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Hull]</th>               <td>   -0.6882</td> <td>    0.178</td> <td>   -3.869</td> <td> 0.000</td> <td>   -1.037</td> <td>   -0.340</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Leicester]</th>          <td>   -0.3610</td> <td>    0.105</td> <td>   -3.449</td> <td> 0.001</td> <td>   -0.566</td> <td>   -0.156</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Liverpool]</th>          <td>    0.0992</td> <td>    0.092</td> <td>    1.077</td> <td> 0.281</td> <td>   -0.081</td> <td>    0.280</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Man City]</th>           <td>    0.2080</td> <td>    0.090</td> <td>    2.318</td> <td> 0.020</td> <td>    0.032</td> <td>    0.384</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Man United]</th>         <td>   -0.1929</td> <td>    0.099</td> <td>   -1.945</td> <td> 0.052</td> <td>   -0.387</td> <td>    0.002</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Middlesbrough]</th>      <td>   -1.0307</td> <td>    0.204</td> <td>   -5.050</td> <td> 0.000</td> <td>   -1.431</td> <td>   -0.631</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Newcastle]</th>          <td>   -0.6068</td> <td>    0.130</td> <td>   -4.671</td> <td> 0.000</td> <td>   -0.861</td> <td>   -0.352</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Southampton]</th>        <td>   -0.5935</td> <td>    0.112</td> <td>   -5.281</td> <td> 0.000</td> <td>   -0.814</td> <td>   -0.373</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Stoke]</th>              <td>   -0.6638</td> <td>    0.133</td> <td>   -4.991</td> <td> 0.000</td> <td>   -0.925</td> <td>   -0.403</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Sunderland]</th>         <td>   -0.9434</td> <td>    0.198</td> <td>   -4.771</td> <td> 0.000</td> <td>   -1.331</td> <td>   -0.556</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Swansea]</th>            <td>   -0.7032</td> <td>    0.135</td> <td>   -5.208</td> <td> 0.000</td> <td>   -0.968</td> <td>   -0.439</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Tottenham]</th>          <td>   -0.0019</td> <td>    0.094</td> <td>   -0.021</td> <td> 0.984</td> <td>   -0.187</td> <td>    0.183</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Watford]</th>            <td>   -0.4854</td> <td>    0.109</td> <td>   -4.458</td> <td> 0.000</td> <td>   -0.699</td> <td>   -0.272</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.West Brom]</th>          <td>   -0.6990</td> <td>    0.134</td> <td>   -5.204</td> <td> 0.000</td> <td>   -0.962</td> <td>   -0.436</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.West Ham]</th>           <td>   -0.4087</td> <td>    0.106</td> <td>   -3.844</td> <td> 0.000</td> <td>   -0.617</td> <td>   -0.200</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Wolves]</th>             <td>   -0.4672</td> <td>    0.161</td> <td>   -2.903</td> <td> 0.004</td> <td>   -0.783</td> <td>   -0.152</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Bournemouth]</th>    <td>    0.2826</td> <td>    0.109</td> <td>    2.586</td> <td> 0.010</td> <td>    0.068</td> <td>    0.497</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Brighton]</th>       <td>    0.1149</td> <td>    0.125</td> <td>    0.918</td> <td> 0.359</td> <td>   -0.130</td> <td>    0.360</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Burnley]</th>        <td>    0.0692</td> <td>    0.114</td> <td>    0.606</td> <td> 0.545</td> <td>   -0.155</td> <td>    0.293</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Cardiff]</th>        <td>    0.3037</td> <td>    0.146</td> <td>    2.074</td> <td> 0.038</td> <td>    0.017</td> <td>    0.591</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Chelsea]</th>        <td>   -0.2888</td> <td>    0.126</td> <td>   -2.284</td> <td> 0.022</td> <td>   -0.537</td> <td>   -0.041</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Crystal Palace]</th> <td>    0.1321</td> <td>    0.113</td> <td>    1.171</td> <td> 0.242</td> <td>   -0.089</td> <td>    0.353</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Everton]</th>        <td>   -0.0080</td> <td>    0.117</td> <td>   -0.069</td> <td> 0.945</td> <td>   -0.237</td> <td>    0.221</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Fulham]</th>         <td>    0.4645</td> <td>    0.139</td> <td>    3.343</td> <td> 0.001</td> <td>    0.192</td> <td>    0.737</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Huddersfield]</th>   <td>    0.2674</td> <td>    0.120</td> <td>    2.231</td> <td> 0.026</td> <td>    0.033</td> <td>    0.502</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Hull]</th>           <td>    0.4663</td> <td>    0.139</td> <td>    3.344</td> <td> 0.001</td> <td>    0.193</td> <td>    0.740</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Leicester]</th>      <td>    0.1351</td> <td>    0.113</td> <td>    1.197</td> <td> 0.231</td> <td>   -0.086</td> <td>    0.356</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Liverpool]</th>      <td>   -0.3506</td> <td>    0.129</td> <td>   -2.713</td> <td> 0.007</td> <td>   -0.604</td> <td>   -0.097</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Man City]</th>       <td>   -0.4771</td> <td>    0.135</td> <td>   -3.542</td> <td> 0.000</td> <td>   -0.741</td> <td>   -0.213</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Man United]</th>     <td>   -0.2874</td> <td>    0.126</td> <td>   -2.279</td> <td> 0.023</td> <td>   -0.535</td> <td>   -0.040</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Middlesbrough]</th>  <td>    0.0438</td> <td>    0.161</td> <td>    0.273</td> <td> 0.785</td> <td>   -0.271</td> <td>    0.359</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Newcastle]</th>      <td>   -0.0618</td> <td>    0.132</td> <td>   -0.468</td> <td> 0.640</td> <td>   -0.321</td> <td>    0.197</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Southampton]</th>    <td>    0.1126</td> <td>    0.113</td> <td>    0.995</td> <td> 0.320</td> <td>   -0.109</td> <td>    0.334</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Stoke]</th>          <td>    0.2083</td> <td>    0.122</td> <td>    1.703</td> <td> 0.089</td> <td>   -0.031</td> <td>    0.448</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Sunderland]</th>     <td>    0.3100</td> <td>    0.146</td> <td>    2.117</td> <td> 0.034</td> <td>    0.023</td> <td>    0.597</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Swansea]</th>        <td>    0.2229</td> <td>    0.122</td> <td>    1.829</td> <td> 0.067</td> <td>   -0.016</td> <td>    0.462</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Tottenham]</th>      <td>   -0.3686</td> <td>    0.130</td> <td>   -2.844</td> <td> 0.004</td> <td>   -0.623</td> <td>   -0.115</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Watford]</th>        <td>    0.2397</td> <td>    0.110</td> <td>    2.177</td> <td> 0.030</td> <td>    0.024</td> <td>    0.456</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.West Brom]</th>      <td>    0.0596</td> <td>    0.127</td> <td>    0.467</td> <td> 0.640</td> <td>   -0.190</td> <td>    0.309</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.West Ham]</th>       <td>    0.2222</td> <td>    0.111</td> <td>    2.008</td> <td> 0.045</td> <td>    0.005</td> <td>    0.439</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Wolves]</th>         <td>   -0.0898</td> <td>    0.169</td> <td>   -0.530</td> <td> 0.596</td> <td>   -0.422</td> <td>    0.242</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>home</th>                       <td>    0.2653</td> <td>    0.036</td> <td>    7.386</td> <td> 0.000</td> <td>    0.195</td> <td>    0.336</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                 Generalized Linear Model Regression Results                  \n",
       "==============================================================================\n",
       "Dep. Variable:                  goals   No. Observations:                 2280\n",
       "Model:                            GLM   Df Residuals:                     2228\n",
       "Model Family:                 Poisson   Df Model:                           51\n",
       "Link Function:                    log   Scale:                          1.0000\n",
       "Method:                          IRLS   Log-Likelihood:                -3229.2\n",
       "Date:                Tue, 04 Feb 2020   Deviance:                       2433.8\n",
       "Time:                        19:38:27   Pearson chi2:                 2.10e+03\n",
       "No. Iterations:                     5                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================================\n",
       "                                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "----------------------------------------------------------------------------------------------\n",
       "Intercept                      0.4798      0.110      4.364      0.000       0.264       0.695\n",
       "team[T.Bournemouth]           -0.3454      0.104     -3.306      0.001      -0.550      -0.141\n",
       "team[T.Brighton]              -0.7580      0.138     -5.496      0.000      -1.028      -0.488\n",
       "team[T.Burnley]               -0.6206      0.113     -5.478      0.000      -0.843      -0.399\n",
       "team[T.Cardiff]               -0.7688      0.184     -4.168      0.000      -1.130      -0.407\n",
       "team[T.Chelsea]               -0.0770      0.096     -0.800      0.424      -0.266       0.112\n",
       "team[T.Crystal Palace]        -0.4210      0.107     -3.951      0.000      -0.630      -0.212\n",
       "team[T.Everton]               -0.3369      0.104     -3.249      0.001      -0.540      -0.134\n",
       "team[T.Fulham]                -0.7568      0.184     -4.102      0.000      -1.118      -0.395\n",
       "team[T.Huddersfield]          -1.0707      0.157     -6.836      0.000      -1.378      -0.764\n",
       "team[T.Hull]                  -0.6882      0.178     -3.869      0.000      -1.037      -0.340\n",
       "team[T.Leicester]             -0.3610      0.105     -3.449      0.001      -0.566      -0.156\n",
       "team[T.Liverpool]              0.0992      0.092      1.077      0.281      -0.081       0.280\n",
       "team[T.Man City]               0.2080      0.090      2.318      0.020       0.032       0.384\n",
       "team[T.Man United]            -0.1929      0.099     -1.945      0.052      -0.387       0.002\n",
       "team[T.Middlesbrough]         -1.0307      0.204     -5.050      0.000      -1.431      -0.631\n",
       "team[T.Newcastle]             -0.6068      0.130     -4.671      0.000      -0.861      -0.352\n",
       "team[T.Southampton]           -0.5935      0.112     -5.281      0.000      -0.814      -0.373\n",
       "team[T.Stoke]                 -0.6638      0.133     -4.991      0.000      -0.925      -0.403\n",
       "team[T.Sunderland]            -0.9434      0.198     -4.771      0.000      -1.331      -0.556\n",
       "team[T.Swansea]               -0.7032      0.135     -5.208      0.000      -0.968      -0.439\n",
       "team[T.Tottenham]             -0.0019      0.094     -0.021      0.984      -0.187       0.183\n",
       "team[T.Watford]               -0.4854      0.109     -4.458      0.000      -0.699      -0.272\n",
       "team[T.West Brom]             -0.6990      0.134     -5.204      0.000      -0.962      -0.436\n",
       "team[T.West Ham]              -0.4087      0.106     -3.844      0.000      -0.617      -0.200\n",
       "team[T.Wolves]                -0.4672      0.161     -2.903      0.004      -0.783      -0.152\n",
       "opponent[T.Bournemouth]        0.2826      0.109      2.586      0.010       0.068       0.497\n",
       "opponent[T.Brighton]           0.1149      0.125      0.918      0.359      -0.130       0.360\n",
       "opponent[T.Burnley]            0.0692      0.114      0.606      0.545      -0.155       0.293\n",
       "opponent[T.Cardiff]            0.3037      0.146      2.074      0.038       0.017       0.591\n",
       "opponent[T.Chelsea]           -0.2888      0.126     -2.284      0.022      -0.537      -0.041\n",
       "opponent[T.Crystal Palace]     0.1321      0.113      1.171      0.242      -0.089       0.353\n",
       "opponent[T.Everton]           -0.0080      0.117     -0.069      0.945      -0.237       0.221\n",
       "opponent[T.Fulham]             0.4645      0.139      3.343      0.001       0.192       0.737\n",
       "opponent[T.Huddersfield]       0.2674      0.120      2.231      0.026       0.033       0.502\n",
       "opponent[T.Hull]               0.4663      0.139      3.344      0.001       0.193       0.740\n",
       "opponent[T.Leicester]          0.1351      0.113      1.197      0.231      -0.086       0.356\n",
       "opponent[T.Liverpool]         -0.3506      0.129     -2.713      0.007      -0.604      -0.097\n",
       "opponent[T.Man City]          -0.4771      0.135     -3.542      0.000      -0.741      -0.213\n",
       "opponent[T.Man United]        -0.2874      0.126     -2.279      0.023      -0.535      -0.040\n",
       "opponent[T.Middlesbrough]      0.0438      0.161      0.273      0.785      -0.271       0.359\n",
       "opponent[T.Newcastle]         -0.0618      0.132     -0.468      0.640      -0.321       0.197\n",
       "opponent[T.Southampton]        0.1126      0.113      0.995      0.320      -0.109       0.334\n",
       "opponent[T.Stoke]              0.2083      0.122      1.703      0.089      -0.031       0.448\n",
       "opponent[T.Sunderland]         0.3100      0.146      2.117      0.034       0.023       0.597\n",
       "opponent[T.Swansea]            0.2229      0.122      1.829      0.067      -0.016       0.462\n",
       "opponent[T.Tottenham]         -0.3686      0.130     -2.844      0.004      -0.623      -0.115\n",
       "opponent[T.Watford]            0.2397      0.110      2.177      0.030       0.024       0.456\n",
       "opponent[T.West Brom]          0.0596      0.127      0.467      0.640      -0.190       0.309\n",
       "opponent[T.West Ham]           0.2222      0.111      2.008      0.045       0.005       0.439\n",
       "opponent[T.Wolves]            -0.0898      0.169     -0.530      0.596      -0.422       0.242\n",
       "home                           0.2653      0.036      7.386      0.000       0.195       0.336\n",
       "==============================================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "goal_model_data = pd.concat([df[['HomeTeam','AwayTeam','HomeGoals']].assign(home=1).rename(\n",
    "            columns={'HomeTeam':'team', 'AwayTeam':'opponent','HomeGoals':'goals'}),\n",
    "           df[['AwayTeam','HomeTeam','AwayGoals']].assign(home=0).rename(\n",
    "            columns={'AwayTeam':'team', 'HomeTeam':'opponent','AwayGoals':'goals'})])\n",
    "\n",
    "poisson_model = smf.glm(formula=\"goals ~ home + team + opponent\", data=goal_model_data, \n",
    "                        family=sm.families.Poisson()).fit()\n",
    "poisson_model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This produces an output similar to a regression, where a positive \"coef\" would mean more expected goals and a negative \"coef\" would mean less goals, and values closer to 0 would indicate more neutral effects in comparison to the intercept.\n",
    "\n",
    "For example, Man City have a positive coefficient equal to 0.2080, meaning they would generally score more goals than an average team. Moreover, we see that Man City's **opponent value** is negative at -0.4771. The opponent value penalizes or rewards teams based on the value of the opposition. Man City's negative coefficient indicates that it is harder to score against them than the average opponent, while a positive coefficient would mean that it is generally easier to score against that opponent. \n",
    "\n",
    "Now, let's try predicting a match between Chelsea and Man City. To do so, I will create the predict_match function.\n",
    "\n",
    "Within this function, I will be specifying 4 variables:\n",
    "\n",
    "1) foot_model: The type of statistical model being used to model the data. In this case, we'll have the 'poisson_model'\n",
    "\n",
    "2) homeTeam: A string value containing the desired home team name.\n",
    "\n",
    "3) awayTeam: A string value containing the desired away team name.\n",
    "\n",
    "4) max_goals: The maximum number of goals allowed in the game, as a sum of homeTeam and awayTeam goals. I set this to 10."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict_match(foot_model, homeTeam, awayTeam, max_goals=10):\n",
    "    from scipy.stats import poisson\n",
    "    home_goals_avg = foot_model.predict(pd.DataFrame(data={'team': homeTeam, \n",
    "                                                            'opponent': awayTeam,'home':1},\n",
    "                                                      index=[1])).values[0]\n",
    "    away_goals_avg = foot_model.predict(pd.DataFrame(data={'team': awayTeam, \n",
    "                                                            'opponent': homeTeam,'home':0},\n",
    "                                                      index=[1])).values[0]\n",
    "    team_pred = [[poisson.pmf(i, team_avg) for i in range(0, max_goals+1)] for team_avg in [home_goals_avg, away_goals_avg]]\n",
    "    return(np.outer(np.array(team_pred[0]), np.array(team_pred[1])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, let's simulate that match between Chelsea and Man City:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.06715664, 0.10008115, 0.07457369, 0.03704484],\n",
       "       [0.08129063, 0.12114453, 0.0902687 , 0.04484141],\n",
       "       [0.04919965, 0.0733205 , 0.05463346, 0.02713944],\n",
       "       [0.01985146, 0.02958392, 0.02204393, 0.01095043]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "chelsea_city = predict_match(poisson_model, 'Chelsea', 'Man City',max_goals=3)\n",
    "chelsea_city"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This outputted array shows us the probability of each team scoring a certain amount of goals. In this case, Chelsea's number of goals are represented by rows, and Man City's number of goals are represented by columns. For example:\n",
    "\n",
    "- The first array entry at [0,0], 0.06715664, shows us the probability of Chelsea scoring 0 goals, and Man City scoring 0 goals.\n",
    "\n",
    "- The entry at [0,1], 0.10008115, shows us the probability of Chelsea scoring 0 goals, and Man City scoring 1 goal.\n",
    "\n",
    "- The entry at [2,1], 0.0733205, shows us the probability of Chelsea scoring 2 goals, and Man City scoring 1 goal.\n",
    "\n",
    "... And so on\n",
    "\n",
    "Now, let's calculate the probability of Chelsea winning. On the array, the event of Chelsea winning would be indicated by any entry on the lower triangle of the square array. The event of Man City winning would be indicated by any entry on the upper triangle. The event of a draw is represented by the diagonal entries of the array."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# For the model to completely work, we would need to assume max_goals = 10, as to encompass all possible outcomes\n",
    "chelsea_city = predict_match(poisson_model, 'Chelsea', 'Man City')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.999999414005042"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(chelsea_city)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Based off of our data, in a match of Chelsea vs. Man City at home:\n",
      "\n",
      "The probability of Chelsea winning is 0.308133\n",
      "The probability of Man City winning is 0.436653\n",
      "The probability of a draw is 0.255213\n"
     ]
    }
   ],
   "source": [
    "chelsea_prob = np.sum(np.tril(chelsea_city,-1))\n",
    "\n",
    "city_prob = np.sum(np.triu(chelsea_city,1))\n",
    "\n",
    "draw_prob = np.sum(np.diag(chelsea_city))\n",
    "\n",
    "print('''Based off of our data, in a match of Chelsea vs. Man City at home:\\n\\nThe probability of Chelsea winning is %f\n",
    "The probability of Man City winning is %f\\nThe probability of a draw is %f''' %(chelsea_prob,city_prob,draw_prob))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the actual result of the game in the 2018/19 was..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Chelsea 2 - 0 Man City\n"
     ]
    }
   ],
   "source": [
    "chelsea_goals = epl_1819[(epl_1819['HomeTeam']=='Chelsea')&(epl_1819['AwayTeam']=='Man City')]['FTHG']\n",
    "\n",
    "city_goals = epl_1819[(epl_1819['HomeTeam']=='Chelsea')&(epl_1819['AwayTeam']=='Man City')]['FTAG']\n",
    "\n",
    "print(\"Chelsea %d - %d Man City\" %(chelsea_goals,city_goals))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, reality weighed in favor of Chelsea, instead of the predicted Man City win. The football world is riddled with surprises and upsets. However, the probabilities do make logical sense, as, in the 2018-19 season, Man City ended up winning the league with 98 points, and Chelsea ended up in 3rd place with only 72 points, indicating Man City were a much better team during the season, which is exactly what the probabilities are telling us too!\n",
    "\n",
    "To test this result, we'd need to compare it with a betting company's odds, which we have handy!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Chelsea Win</th>\n",
       "      <th>Draw</th>\n",
       "      <th>Man City Win</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>154</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.8</td>\n",
       "      <td>1.95</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Chelsea Win  Draw  Man City Win\n",
       "154          4.0   3.8          1.95"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bet365odds = epl_1819[(epl_1819['HomeTeam']=='Chelsea')&(epl_1819['AwayTeam']=='Man City')][['B365H','B365D','B365A']]\n",
    "bet365odds = bet365odds.rename(columns={'B365H':'Chelsea Win','B365D':'Draw','B365A':'Man City Win'})\n",
    "bet365odds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now to convert these odds into probabilities, using the following formula: \n",
    "\n",
    "$$Probability = \\frac{1}{Decimal Odds}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Chelsea Win</th>\n",
       "      <th>Draw</th>\n",
       "      <th>Man City Win</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>154</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.263158</td>\n",
       "      <td>0.512821</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Chelsea Win      Draw  Man City Win\n",
       "154         0.25  0.263158      0.512821"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bet365odds['Chelsea Win'] = 1/bet365odds['Chelsea Win']\n",
    "bet365odds['Man City Win'] = 1/bet365odds['Man City Win']\n",
    "bet365odds['Draw'] = 1/bet365odds['Draw']\n",
    "bet365odds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Chelsea Win</th>\n",
       "      <th>Draw</th>\n",
       "      <th>Man City Win</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.308133</td>\n",
       "      <td>0.255213</td>\n",
       "      <td>0.436653</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Chelsea Win      Draw  Man City Win\n",
       "0     0.308133  0.255213      0.436653"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_prob = pd.DataFrame.from_dict({'Chelsea Win': [chelsea_prob], 'Draw': [draw_prob], 'Man City Win': [city_prob]})\n",
    "model_prob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Chelsea Win</th>\n",
       "      <th>Draw</th>\n",
       "      <th>Man City Win</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Source</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>Bet 365</td>\n",
       "      <td>0.250000</td>\n",
       "      <td>0.263158</td>\n",
       "      <td>0.512821</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>Our Model</td>\n",
       "      <td>0.308133</td>\n",
       "      <td>0.255213</td>\n",
       "      <td>0.436653</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           Chelsea Win      Draw  Man City Win\n",
       "Source                                        \n",
       "Bet 365       0.250000  0.263158      0.512821\n",
       "Our Model     0.308133  0.255213      0.436653"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bet365odds = bet365odds.append(model_prob).reset_index().rename(columns={'index':'Source'})\n",
    "bet365odds['Source'] = ['Bet 365','Our Model']\n",
    "bet365odds = bet365odds.set_index('Source')\n",
    "bet365odds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The differences between Bet 365's probabilities and our probabilities are as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Chelsea Win     0.058133\n",
       "Draw           -0.007945\n",
       "Man City Win   -0.076168\n",
       "Name: Our Model, dtype: float64"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bet365odds.diff(axis=0).loc['Our Model']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Evaluating Our Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, we weren't too far off with our calculations. We somewhat underestimated the probability of a Man City win, and that's fine! That's because Man City progressively became a better and better team with years gone by due to extensive purchases of great players, a great manager, increased team chemistry, and more! The more the data is weighted towards more recent results, the more accurate our model becomes! This indicates that sometimes, less data might indeed be better, due to the changes that happen from season to season within the sport.\n",
    "\n",
    "Moreover, as previously mentioned, the Poisson Distribution may oversimplify things. There are plenty of factors that could be taken into consideration, such as:\n",
    "\n",
    "1) The expected starting lineups of each side (i.e. Are certain players injured? Will the manager decide to start his best team?)\n",
    "\n",
    "2) Form (i.e. Assigning more weight to more recent results)\n",
    "\n",
    "3) How far along into the season are we? What does the team have to play for? Are they competing for the title, or will a win make no difference whatsoever? (i.e. Motivation)\n",
    "\n",
    "4) Historical Results between the two teams (Even if Man City are the better team now, do Chelsea have a good track record against them? Maybe Chelsea have a playing style that combats Man City's very well)\n",
    "\n",
    "5) Inability to weight data towards more recent results reasonably. Here, we could potentially use a weighted mean with higher weights on more recent results, but it wouldn't reflect the entire story.\n",
    "\n",
    "And many more!"
   ]
  }
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