demo_model_filled.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "de265c57",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# WDSS Football Forecasting Competition\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "<img src=\"logo_subtitle.png\" width=500 />"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d22b4852",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Our Sponsor\n",
    "\n",
    "<img src=\"mustard-systems-logo.png\" width=500 />"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2ac5504d",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The Competition"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0040431",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Predicting the scores of football matches isn't a new idea \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5de9ed9c",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- People try their luck at bookies daily with nothing more than guesses, however at WDSS a more data-driven approach is preferred "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24d2f3bc",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The competition aims to draw together the best implementations of these with hopes of finding the best model possible"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2432ab68",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The Format"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91fb6b15",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Weekly predictions on the **scores** of each Premier League match\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2eaa0dda",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Each week the predictions must be **ranked** from 1 to 10 in terms of confidence"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca6131ac",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Each contestor's predictions will be scored based on their weighted **mean squared error** and converted into points using a monotonously-decreasing rule "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b770449a",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The Rules"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b01e9c95",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- All weekly submissions must be accompanied by a model created in **Jupyter Notebooks (.ipynb file)** or **R Markdown notebooks (.Rmd)**"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b99c212",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Scores predicted must **match the output of your model** (we will check this and disqualify inconsistent submissions) \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b266d16",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Sources of data should be made clear within submissions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f7085a0",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- There will be some flexibility in what constitutes as a model, but please refer to today's demo model as a benchmark \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1ada204",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Have Fun! "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "992f77a3",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    },
    "tags": []
   },
   "source": [
    "## The Winner & Prize"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3e09d4d4",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The competition will be split across Term 1 & 2 with a **prize pool of £600 and £700 respectively** for each iteration "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "604cdb74",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- This prize pool will be split between the top competitors as ranked by the accuracy of their predictions \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03593fa5",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Additionally, a £100 prize will be awarded for the model that displays the most **ingenuity**, **creativity**, and **good statistical practice** "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d93593a9",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Getting Started: lets build a demo model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fedebaa2",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Today we will guide you in building a **baseline model** for our upcoming Premier League forecasting competition"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b4cd9a4e",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- This model will NOT win the competition for you, but it will help point you in the right direction"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f9490f7",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Start out with our imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8c4aad19",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# Dependencies\n",
    "from scipy.stats import poisson \n",
    "import numpy as np\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt \n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e48d8b5e",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Gathering our data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "eb8a0d6f",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# Function to retrieve EPL matches from any given year\n",
    "def get_premier_league_data(start_year):\n",
    "    season = str(start_year)[-2:] + str(start_year + 1)[-2:]\n",
    "    data = pd.read_csv(\"http://www.football-data.co.uk/mmz4281/\" + season + \"/E0.csv\") \n",
    "    return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f59b0418",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Div</th>\n",
       "      <th>Date</th>\n",
       "      <th>HomeTeam</th>\n",
       "      <th>AwayTeam</th>\n",
       "      <th>FTHG</th>\n",
       "      <th>FTAG</th>\n",
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       "      <th>HTAG</th>\n",
       "      <th>HTR</th>\n",
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       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>E0</td>\n",
       "      <td>10/08/2018</td>\n",
       "      <td>Man United</td>\n",
       "      <td>Leicester</td>\n",
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       "      <td>1.79</td>\n",
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       "      <td>1.75</td>\n",
       "      <td>1.70</td>\n",
       "      <td>2.29</td>\n",
       "      <td>2.21</td>\n",
       "      <td>1.55</td>\n",
       "      <td>4.07</td>\n",
       "      <td>7.69</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>E0</td>\n",
       "      <td>11/08/2018</td>\n",
       "      <td>Bournemouth</td>\n",
       "      <td>Cardiff</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>H</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>H</td>\n",
       "      <td>...</td>\n",
       "      <td>1.83</td>\n",
       "      <td>20</td>\n",
       "      <td>-0.75</td>\n",
       "      <td>2.20</td>\n",
       "      <td>2.13</td>\n",
       "      <td>1.80</td>\n",
       "      <td>1.75</td>\n",
       "      <td>1.88</td>\n",
       "      <td>3.61</td>\n",
       "      <td>4.70</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>E0</td>\n",
       "      <td>11/08/2018</td>\n",
       "      <td>Fulham</td>\n",
       "      <td>Crystal Palace</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>A</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>A</td>\n",
       "      <td>...</td>\n",
       "      <td>1.87</td>\n",
       "      <td>22</td>\n",
       "      <td>-0.25</td>\n",
       "      <td>2.18</td>\n",
       "      <td>2.11</td>\n",
       "      <td>1.81</td>\n",
       "      <td>1.77</td>\n",
       "      <td>2.62</td>\n",
       "      <td>3.38</td>\n",
       "      <td>2.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>E0</td>\n",
       "      <td>11/08/2018</td>\n",
       "      <td>Huddersfield</td>\n",
       "      <td>Chelsea</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>A</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>A</td>\n",
       "      <td>...</td>\n",
       "      <td>1.84</td>\n",
       "      <td>23</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1.84</td>\n",
       "      <td>1.80</td>\n",
       "      <td>2.13</td>\n",
       "      <td>2.06</td>\n",
       "      <td>7.24</td>\n",
       "      <td>3.95</td>\n",
       "      <td>1.58</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>E0</td>\n",
       "      <td>11/08/2018</td>\n",
       "      <td>Newcastle</td>\n",
       "      <td>Tottenham</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>A</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>A</td>\n",
       "      <td>...</td>\n",
       "      <td>1.81</td>\n",
       "      <td>20</td>\n",
       "      <td>0.25</td>\n",
       "      <td>2.20</td>\n",
       "      <td>2.12</td>\n",
       "      <td>1.80</td>\n",
       "      <td>1.76</td>\n",
       "      <td>4.74</td>\n",
       "      <td>3.53</td>\n",
       "      <td>1.89</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 62 columns</p>\n",
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       "  Div        Date      HomeTeam        AwayTeam  FTHG  FTAG FTR  HTHG  HTAG  \\\n",
       "0  E0  10/08/2018    Man United       Leicester     2     1   H     1     0   \n",
       "1  E0  11/08/2018   Bournemouth         Cardiff     2     0   H     1     0   \n",
       "2  E0  11/08/2018        Fulham  Crystal Palace     0     2   A     0     1   \n",
       "3  E0  11/08/2018  Huddersfield         Chelsea     0     3   A     0     2   \n",
       "4  E0  11/08/2018     Newcastle       Tottenham     1     2   A     1     2   \n",
       "\n",
       "  HTR  ... BbAv<2.5  BbAH  BbAHh  BbMxAHH  BbAvAHH  BbMxAHA  BbAvAHA  PSCH  \\\n",
       "0   H  ...     1.79    17  -0.75     1.75     1.70     2.29     2.21  1.55   \n",
       "1   H  ...     1.83    20  -0.75     2.20     2.13     1.80     1.75  1.88   \n",
       "2   A  ...     1.87    22  -0.25     2.18     2.11     1.81     1.77  2.62   \n",
       "3   A  ...     1.84    23   1.00     1.84     1.80     2.13     2.06  7.24   \n",
       "4   A  ...     1.81    20   0.25     2.20     2.12     1.80     1.76  4.74   \n",
       "\n",
       "   PSCD  PSCA  \n",
       "0  4.07  7.69  \n",
       "1  3.61  4.70  \n",
       "2  3.38  2.90  \n",
       "3  3.95  1.58  \n",
       "4  3.53  1.89  \n",
       "\n",
       "[5 rows x 62 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get data from the 2018/2019 season\n",
    "data = get_premier_league_data(2018)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1cfe9989",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Light cleaning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "672f3b72",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# Filtering columns of interest\n",
    "columns = [\"HomeTeam\", \"AwayTeam\", \"FTHG\", \"FTAG\", \"FTR\"]\n",
    "data = data[columns]\n",
    "\n",
    "# Renaming columns\n",
    "data = data.rename(\n",
    "    columns={\"FTHG\": \"HomeGoals\", \"FTAG\": \"AwayGoals\", \"FTR\": \"Result\"}\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "596161f1",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>HomeTeam</th>\n",
       "      <th>AwayTeam</th>\n",
       "      <th>HomeGoals</th>\n",
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       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Man United</td>\n",
       "      <td>Leicester</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>H</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Bournemouth</td>\n",
       "      <td>Cardiff</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>H</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Fulham</td>\n",
       "      <td>Crystal Palace</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Huddersfield</td>\n",
       "      <td>Chelsea</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>A</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Newcastle</td>\n",
       "      <td>Tottenham</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>A</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>365</th>\n",
       "      <td>Wolves</td>\n",
       "      <td>Fulham</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>H</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>366</th>\n",
       "      <td>Arsenal</td>\n",
       "      <td>Brighton</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>D</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>367</th>\n",
       "      <td>Chelsea</td>\n",
       "      <td>Watford</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>H</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>368</th>\n",
       "      <td>Huddersfield</td>\n",
       "      <td>Man United</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>D</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>369</th>\n",
       "      <td>Man City</td>\n",
       "      <td>Leicester</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>H</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>370 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "         HomeTeam        AwayTeam  HomeGoals  AwayGoals Result\n",
       "0      Man United       Leicester          2          1      H\n",
       "1     Bournemouth         Cardiff          2          0      H\n",
       "2          Fulham  Crystal Palace          0          2      A\n",
       "3    Huddersfield         Chelsea          0          3      A\n",
       "4       Newcastle       Tottenham          1          2      A\n",
       "..            ...             ...        ...        ...    ...\n",
       "365        Wolves          Fulham          1          0      H\n",
       "366       Arsenal        Brighton          1          1      D\n",
       "367       Chelsea         Watford          3          0      H\n",
       "368  Huddersfield      Man United          1          1      D\n",
       "369      Man City       Leicester          1          0      H\n",
       "\n",
       "[370 rows x 5 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Remove final week of fixtures\n",
    "data[:-10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e5401b93",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "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>Result</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Man United</td>\n",
       "      <td>Leicester</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>H</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Bournemouth</td>\n",
       "      <td>Cardiff</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>H</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Fulham</td>\n",
       "      <td>Crystal Palace</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Huddersfield</td>\n",
       "      <td>Chelsea</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Newcastle</td>\n",
       "      <td>Tottenham</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       HomeTeam        AwayTeam  HomeGoals  AwayGoals Result\n",
       "0    Man United       Leicester          2          1      H\n",
       "1   Bournemouth         Cardiff          2          0      H\n",
       "2        Fulham  Crystal Palace          0          2      A\n",
       "3  Huddersfield         Chelsea          0          3      A\n",
       "4     Newcastle       Tottenham          1          2      A"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "918ce900",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Simple analysis: Home team advantage?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "435b57f5",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "HomeGoals    1.568421\n",
       "AwayGoals    1.252632\n",
       "dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute the average number of home and away goals \n",
    "data[['HomeGoals', 'AwayGoals']].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6396f07",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Towards a match prediction model "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "18568fc7",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- One way to predict the match score is to consider the number of goals scored by each team\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb4b9907",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- We will denote the number of goals scored by a particular team in a match by $y_i$, where $i$ indicates the particular match\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e624f99",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Furthermore, we will use *regression analysis* to model $\\mathbb{E}[y_i | X_i]$ "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb3d2583",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The Poisson distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10d3afe6",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- The Poisson distribution is often used to model the probability distribution of *count events* (that is, the same event happening a specific number of times in a fixed time frame)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74f6d43c",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- It is a *discrete* distribution parametarized by a mean constant rate of occurences $\\lambda$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb5c7870",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- It assumes that event occurances within the interval are *independent* of one another"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b90a3ab4",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- It can be especially useful to model the number of goals we expect a team to score"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f630c07",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The Poisson distribution: an example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ca142a4d",
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Here we simulate 1 million samples from a Poisson distribution with a mean of two\n",
    "x = np.random.poisson(2, 1000000)\n",
    "plt.hist(x, 14, density=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "48c87944",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Formatting our data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "10bca848",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "#### PREPARE THE DATASET ####\n",
    "\n",
    "# Separate home goals data\n",
    "home_goals = data[[\"HomeTeam\", \"AwayTeam\", \"HomeGoals\"]]\n",
    "home_goals = home_goals.assign(home=1)\n",
    "home_goals = home_goals.rename(\n",
    "    columns={\"HomeTeam\": \"team\",\n",
    "             \"AwayTeam\": \"opponent\", \n",
    "             \"HomeGoals\": \"goals\"}\n",
    ")\n",
    "\n",
    "# Separate away goals data \n",
    "away_goals = data[[\"AwayTeam\", \"HomeTeam\", \"AwayGoals\"]]\n",
    "away_goals = away_goals.assign(home=0)\n",
    "away_goals = away_goals.rename(\n",
    "    columns={\"AwayTeam\": \"team\",\n",
    "             \"HomeTeam\": \"opponent\", \n",
    "             \"AwayGoals\": \"goals\"}\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "27b7c0cb",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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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>team</th>\n",
       "      <th>opponent</th>\n",
       "      <th>goals</th>\n",
       "      <th>home</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Man United</td>\n",
       "      <td>Leicester</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Bournemouth</td>\n",
       "      <td>Cardiff</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Fulham</td>\n",
       "      <td>Crystal Palace</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Huddersfield</td>\n",
       "      <td>Chelsea</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Newcastle</td>\n",
       "      <td>Tottenham</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           team        opponent  goals  home\n",
       "0    Man United       Leicester      2     1\n",
       "1   Bournemouth         Cardiff      2     1\n",
       "2        Fulham  Crystal Palace      0     1\n",
       "3  Huddersfield         Chelsea      0     1\n",
       "4     Newcastle       Tottenham      1     1"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Concatenating into training data \n",
    "training_data = pd.concat([home_goals, away_goals])\n",
    "training_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ef0c817",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## The Poisson regression model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "26d2fac0",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- To predict the number of goals each team scores, we will fit the following model using match-level data\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "87ee09b7",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "$$y_i \\sim Poisson(\\lambda_i)$$\n",
    "\n",
    "\n",
    "$$\\ln (\\lambda_i) = X_i\\beta$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77eb8da6",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Here, $\\lambda_i$ is the mean number goals scored by the home team in match $i$, which we aim to predict using variables $X_i$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "590f8f66",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Building the model\n",
    "# Poisson Regression: log-linear model\n",
    "poisson_model = smf.glm(\n",
    "    formula=\"goals ~ home + team + opponent\",\n",
    "    data=training_data,\n",
    "    family=sm.families.Poisson() \n",
    ").fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "422b5962",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "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>   760</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                  <td>GLM</td>       <th>  Df Residuals:      </th>  <td>   720</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model Family:</th>         <td>Poisson</td>     <th>  Df Model:          </th>  <td>    39</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> -1065.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Tue, 12 Oct 2021</td> <th>  Deviance:          </th> <td>  762.55</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>00:01:59</td>     <th>  Pearson chi2:      </th>  <td>  656.</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>    0.5061</td> <td>    0.188</td> <td>    2.685</td> <td> 0.007</td> <td>    0.137</td> <td>    0.876</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Bournemouth]</th>        <td>   -0.2470</td> <td>    0.178</td> <td>   -1.388</td> <td> 0.165</td> <td>   -0.596</td> <td>    0.102</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Brighton]</th>           <td>   -0.7283</td> <td>    0.206</td> <td>   -3.538</td> <td> 0.000</td> <td>   -1.132</td> <td>   -0.325</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Burnley]</th>            <td>   -0.4684</td> <td>    0.190</td> <td>   -2.468</td> <td> 0.014</td> <td>   -0.841</td> <td>   -0.096</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Cardiff]</th>            <td>   -0.7485</td> <td>    0.208</td> <td>   -3.600</td> <td> 0.000</td> <td>   -1.156</td> <td>   -0.341</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Chelsea]</th>            <td>   -0.1597</td> <td>    0.172</td> <td>   -0.927</td> <td> 0.354</td> <td>   -0.497</td> <td>    0.178</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Crystal Palace]</th>     <td>   -0.3578</td> <td>    0.183</td> <td>   -1.957</td> <td> 0.050</td> <td>   -0.716</td> <td>    0.000</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Everton]</th>            <td>   -0.3074</td> <td>    0.180</td> <td>   -1.710</td> <td> 0.087</td> <td>   -0.660</td> <td>    0.045</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Fulham]</th>             <td>   -0.7366</td> <td>    0.208</td> <td>   -3.542</td> <td> 0.000</td> <td>   -1.144</td> <td>   -0.329</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Huddersfield]</th>       <td>   -1.1778</td> <td>    0.243</td> <td>   -4.837</td> <td> 0.000</td> <td>   -1.655</td> <td>   -0.701</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Leicester]</th>          <td>   -0.3627</td> <td>    0.183</td> <td>   -1.984</td> <td> 0.047</td> <td>   -0.721</td> <td>   -0.004</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Liverpool]</th>          <td>    0.1698</td> <td>    0.158</td> <td>    1.074</td> <td> 0.283</td> <td>   -0.140</td> <td>    0.480</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Man City]</th>           <td>    0.2362</td> <td>    0.156</td> <td>    1.515</td> <td> 0.130</td> <td>   -0.069</td> <td>    0.542</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Man United]</th>         <td>   -0.1135</td> <td>    0.171</td> <td>   -0.664</td> <td> 0.507</td> <td>   -0.448</td> <td>    0.221</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Newcastle]</th>          <td>   -0.5573</td> <td>    0.194</td> <td>   -2.874</td> <td> 0.004</td> <td>   -0.937</td> <td>   -0.177</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Southampton]</th>        <td>   -0.4714</td> <td>    0.190</td> <td>   -2.483</td> <td> 0.013</td> <td>   -0.843</td> <td>   -0.099</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Tottenham]</th>          <td>   -0.0980</td> <td>    0.169</td> <td>   -0.578</td> <td> 0.563</td> <td>   -0.430</td> <td>    0.234</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Watford]</th>            <td>   -0.3324</td> <td>    0.182</td> <td>   -1.829</td> <td> 0.067</td> <td>   -0.689</td> <td>    0.024</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.West Ham]</th>           <td>   -0.3363</td> <td>    0.182</td> <td>   -1.850</td> <td> 0.064</td> <td>   -0.693</td> <td>    0.020</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Wolves]</th>             <td>   -0.4465</td> <td>    0.187</td> <td>   -2.384</td> <td> 0.017</td> <td>   -0.814</td> <td>   -0.079</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Bournemouth]</th>    <td>    0.3008</td> <td>    0.184</td> <td>    1.631</td> <td> 0.103</td> <td>   -0.061</td> <td>    0.662</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Brighton]</th>       <td>    0.1253</td> <td>    0.191</td> <td>    0.657</td> <td> 0.511</td> <td>   -0.249</td> <td>    0.499</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Burnley]</th>        <td>    0.2607</td> <td>    0.186</td> <td>    1.405</td> <td> 0.160</td> <td>   -0.103</td> <td>    0.624</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Cardiff]</th>        <td>    0.2644</td> <td>    0.185</td> <td>    1.430</td> <td> 0.153</td> <td>   -0.098</td> <td>    0.627</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Chelsea]</th>        <td>   -0.2790</td> <td>    0.213</td> <td>   -1.310</td> <td> 0.190</td> <td>   -0.697</td> <td>    0.139</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Crystal Palace]</th> <td>    0.0167</td> <td>    0.196</td> <td>    0.085</td> <td> 0.932</td> <td>   -0.368</td> <td>    0.402</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Everton]</th>        <td>   -0.1224</td> <td>    0.204</td> <td>   -0.601</td> <td> 0.548</td> <td>   -0.522</td> <td>    0.277</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Fulham]</th>         <td>    0.4252</td> <td>    0.179</td> <td>    2.374</td> <td> 0.018</td> <td>    0.074</td> <td>    0.776</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Huddersfield]</th>   <td>    0.3495</td> <td>    0.181</td> <td>    1.928</td> <td> 0.054</td> <td>   -0.006</td> <td>    0.705</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Leicester]</th>      <td>   -0.0827</td> <td>    0.201</td> <td>   -0.410</td> <td> 0.681</td> <td>   -0.477</td> <td>    0.312</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Liverpool]</th>      <td>   -0.8271</td> <td>    0.255</td> <td>   -3.239</td> <td> 0.001</td> <td>   -1.328</td> <td>   -0.327</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Man City]</th>       <td>   -0.7766</td> <td>    0.252</td> <td>   -3.088</td> <td> 0.002</td> <td>   -1.270</td> <td>   -0.284</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Man United]</th>     <td>    0.0493</td> <td>    0.196</td> <td>    0.252</td> <td> 0.801</td> <td>   -0.334</td> <td>    0.433</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Newcastle]</th>      <td>   -0.0914</td> <td>    0.201</td> <td>   -0.454</td> <td> 0.650</td> <td>   -0.486</td> <td>    0.303</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Southampton]</th>    <td>    0.2154</td> <td>    0.187</td> <td>    1.150</td> <td> 0.250</td> <td>   -0.152</td> <td>    0.583</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Tottenham]</th>      <td>   -0.2751</td> <td>    0.213</td> <td>   -1.291</td> <td> 0.197</td> <td>   -0.693</td> <td>    0.142</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Watford]</th>        <td>    0.1252</td> <td>    0.192</td> <td>    0.654</td> <td> 0.513</td> <td>   -0.250</td> <td>    0.501</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.West Ham]</th>       <td>    0.0548</td> <td>    0.195</td> <td>    0.281</td> <td> 0.778</td> <td>   -0.327</td> <td>    0.436</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Wolves]</th>         <td>   -0.1292</td> <td>    0.204</td> <td>   -0.635</td> <td> 0.526</td> <td>   -0.528</td> <td>    0.270</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>home</th>                       <td>    0.2248</td> <td>    0.061</td> <td>    3.657</td> <td> 0.000</td> <td>    0.104</td> <td>    0.345</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:                  760\n",
       "Model:                            GLM   Df Residuals:                      720\n",
       "Model Family:                 Poisson   Df Model:                           39\n",
       "Link Function:                    log   Scale:                          1.0000\n",
       "Method:                          IRLS   Log-Likelihood:                -1065.1\n",
       "Date:                Tue, 12 Oct 2021   Deviance:                       762.55\n",
       "Time:                        00:01:59   Pearson chi2:                     656.\n",
       "No. Iterations:                     5                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================================\n",
       "                                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "----------------------------------------------------------------------------------------------\n",
       "Intercept                      0.5061      0.188      2.685      0.007       0.137       0.876\n",
       "team[T.Bournemouth]           -0.2470      0.178     -1.388      0.165      -0.596       0.102\n",
       "team[T.Brighton]              -0.7283      0.206     -3.538      0.000      -1.132      -0.325\n",
       "team[T.Burnley]               -0.4684      0.190     -2.468      0.014      -0.841      -0.096\n",
       "team[T.Cardiff]               -0.7485      0.208     -3.600      0.000      -1.156      -0.341\n",
       "team[T.Chelsea]               -0.1597      0.172     -0.927      0.354      -0.497       0.178\n",
       "team[T.Crystal Palace]        -0.3578      0.183     -1.957      0.050      -0.716       0.000\n",
       "team[T.Everton]               -0.3074      0.180     -1.710      0.087      -0.660       0.045\n",
       "team[T.Fulham]                -0.7366      0.208     -3.542      0.000      -1.144      -0.329\n",
       "team[T.Huddersfield]          -1.1778      0.243     -4.837      0.000      -1.655      -0.701\n",
       "team[T.Leicester]             -0.3627      0.183     -1.984      0.047      -0.721      -0.004\n",
       "team[T.Liverpool]              0.1698      0.158      1.074      0.283      -0.140       0.480\n",
       "team[T.Man City]               0.2362      0.156      1.515      0.130      -0.069       0.542\n",
       "team[T.Man United]            -0.1135      0.171     -0.664      0.507      -0.448       0.221\n",
       "team[T.Newcastle]             -0.5573      0.194     -2.874      0.004      -0.937      -0.177\n",
       "team[T.Southampton]           -0.4714      0.190     -2.483      0.013      -0.843      -0.099\n",
       "team[T.Tottenham]             -0.0980      0.169     -0.578      0.563      -0.430       0.234\n",
       "team[T.Watford]               -0.3324      0.182     -1.829      0.067      -0.689       0.024\n",
       "team[T.West Ham]              -0.3363      0.182     -1.850      0.064      -0.693       0.020\n",
       "team[T.Wolves]                -0.4465      0.187     -2.384      0.017      -0.814      -0.079\n",
       "opponent[T.Bournemouth]        0.3008      0.184      1.631      0.103      -0.061       0.662\n",
       "opponent[T.Brighton]           0.1253      0.191      0.657      0.511      -0.249       0.499\n",
       "opponent[T.Burnley]            0.2607      0.186      1.405      0.160      -0.103       0.624\n",
       "opponent[T.Cardiff]            0.2644      0.185      1.430      0.153      -0.098       0.627\n",
       "opponent[T.Chelsea]           -0.2790      0.213     -1.310      0.190      -0.697       0.139\n",
       "opponent[T.Crystal Palace]     0.0167      0.196      0.085      0.932      -0.368       0.402\n",
       "opponent[T.Everton]           -0.1224      0.204     -0.601      0.548      -0.522       0.277\n",
       "opponent[T.Fulham]             0.4252      0.179      2.374      0.018       0.074       0.776\n",
       "opponent[T.Huddersfield]       0.3495      0.181      1.928      0.054      -0.006       0.705\n",
       "opponent[T.Leicester]         -0.0827      0.201     -0.410      0.681      -0.477       0.312\n",
       "opponent[T.Liverpool]         -0.8271      0.255     -3.239      0.001      -1.328      -0.327\n",
       "opponent[T.Man City]          -0.7766      0.252     -3.088      0.002      -1.270      -0.284\n",
       "opponent[T.Man United]         0.0493      0.196      0.252      0.801      -0.334       0.433\n",
       "opponent[T.Newcastle]         -0.0914      0.201     -0.454      0.650      -0.486       0.303\n",
       "opponent[T.Southampton]        0.2154      0.187      1.150      0.250      -0.152       0.583\n",
       "opponent[T.Tottenham]         -0.2751      0.213     -1.291      0.197      -0.693       0.142\n",
       "opponent[T.Watford]            0.1252      0.192      0.654      0.513      -0.250       0.501\n",
       "opponent[T.West Ham]           0.0548      0.195      0.281      0.778      -0.327       0.436\n",
       "opponent[T.Wolves]            -0.1292      0.204     -0.635      0.526      -0.528       0.270\n",
       "home                           0.2248      0.061      3.657      0.000       0.104       0.345\n",
       "==============================================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get a statistical summary of the poisson model\n",
    "poisson_model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8d158ef",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## A note on dummies, coefficients, and interpretation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce457966",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Computing the expected goals for each team"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "33dff13b",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# Create feature data for home and away team for the match\n",
    "def create_X(home_team, away_team):\n",
    "    X_home = pd.DataFrame(data={\"team\": home_team,\n",
    "                                \"opponent\": away_team,\n",
    "                                \"home\": 1\n",
    "                                }, index=[1])\n",
    "    \n",
    "    X_away = pd.DataFrame(data={\"team\": away_team,\n",
    "                                \"opponent\": home_team,\n",
    "                                \"home\": 0\n",
    "                                }, index=[1])\n",
    "    \n",
    "    # Creating DataFrame for away team features \n",
    "    return X_home, X_away"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "543f6bbd",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def predict_avg_goals(X_home, X_away, model):\n",
    "    # Predict the mean number of goals for home team\n",
    "    home_goals_avg = model.predict(X_home) \n",
    "    \n",
    "    # Predict the mean number of goals for away team\n",
    "    away_goals_avg = model.predict(X_away) \n",
    "    \n",
    "    return home_goals_avg, away_goals_avg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "efb1e112",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average Home Goals:  0.8143138874982507\n",
      "Average Away Goals:  1.589213139385842\n"
     ]
    }
   ],
   "source": [
    "# Predicting average goals for Chelsea Man City match\n",
    "X_home, X_away =  create_X('Chelsea', 'Man City')\n",
    "avg_goals = predict_avg_goals(X_home, X_away, poisson_model)\n",
    "print('Average Home Goals: ', avg_goals[0].values[0])\n",
    "\n",
    "# Fill in to print the average away goals\n",
    "print('Average Away Goals: ', avg_goals[1].values[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea9926a3",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Computing the distribution of match scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "bf47327b",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# Funciton to forecast a given match\n",
    "# Probability Mass Function\n",
    "def predict_score_pmf(X_home, X_away, model, max_goals):\n",
    "    \n",
    "    # Predict the average number of goals for home  and away teams\n",
    "    avg_goals = predict_avg_goals(X_home, X_away, model)\n",
    "    home_goals_avg = avg_goals[0]\n",
    "    away_goals_avg = avg_goals[1]\n",
    "\n",
    "    # Compute marginal distribution for home goals\n",
    "    home_goals_pmf = [poisson.pmf(i, home_goals_avg)\n",
    "                      for i in range(0, max_goals + 1)]\n",
    "\n",
    "    # Compute marginal distribution for away goals \n",
    "    away_goals_pmf = [poisson.pmf(i, away_goals_avg)\n",
    "                      for i in range(0, max_goals + 1)]\n",
    "\n",
    "    # Compute joint distribution for match score as outer product\n",
    "    joint_pmf = np.outer(np.array(home_goals_pmf),\n",
    "                         np.array(away_goals_pmf))\n",
    "    \n",
    "    return joint_pmf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "aaf59d16",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Predicting distribution of match scores\n",
    "X_home, X_away =  create_X('Chelsea', 'Man City')\n",
    "score_pmf = predict_score_pmf(X_home, X_away, poisson_model, 8)\n",
    "score_pmf = score_pmf.round(3)\n",
    "\n",
    "# Visualizing distribution in a heatmap\n",
    "f, axs = plt.subplots(figsize=(8, 6))\n",
    "sns.heatmap(score_pmf, annot=True)\n",
    "axs.xaxis.tick_top() # x axis on top\n",
    "axs.xaxis.set_label_position('top')\n",
    "plt.title(\"Chelsea v.s Man City score forecast\", y=1.12)\n",
    "plt.xlabel(\"Man City goals\", labelpad=6)\n",
    "plt.ylabel(\"Chelsea goals\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60556dbc",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Forecasting the distribution mode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "a90959ac",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def predict_score(X_home, X_away, model):\n",
    "    # Predicting distribution of match scores\n",
    "    score_pmf = predict_score_pmf(X_home, X_away, model,16)\n",
    "    score_pmf = score_pmf.round(3)\n",
    "    \n",
    "    # Computing distribution mode\n",
    "    home_goals_mode = np.argmax(score_pmf) // (17)\n",
    "    away_goals_mode = np.argmax(score_pmf) % (17)\n",
    "    score_pred = (home_goals_mode, away_goals_mode)\n",
    "    return score_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "dd6f3700",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Score Forecast:  (0, 1)\n"
     ]
    }
   ],
   "source": [
    "# Predicting Chelsea Man City match score\n",
    "X_home, X_away =  create_X('Chelsea', 'Man City')\n",
    "score_pred =  predict_score(X_home, X_away, poisson_model)\n",
    "print('Score Forecast: ', score_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12465c91",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Validating our predictions ... how well did we do?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e3596cc",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- To find out how our model performed, it is important to devise some form of scoring metric\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "422efcd8",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- In this workshop, we will use the mean squared error to asses this:\n",
    "$$\\text{MSE}(y, \\hat y) \\,=\\, \\frac{1}{N} \\sum_{i=1}^{N} (y_i - \\hat y_i)^2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "daba49bb",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def mse(y_true, ypred):\n",
    "    np.square(np.subtract(Y_true,Y_pred)).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "f4aa9719",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def model_eval(X, model):\n",
    "    # Predicting distribution of match scores\n",
    "    #### LEFT AS AN EXERCISE ####\n",
    "    pass"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e224e98",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Links to some data sources\n",
    "\n",
    "\n",
    "Description of football-data's column names: https://www.football-data.co.uk/notes.txt\n",
    "\n",
    "\n",
    "Future Fixtures CSV: https://fixturedownload.com/download/epl-2021-GMTStandardTime.csv\n",
    "\n",
    "\n",
    "Historical Standings: https://www.rotowire.com/soccer/league-table.php?season=2018"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "362ba132",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Next Steps"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6d2ea45",
   "metadata": {},
   "source": [
    "- Sign up and Participate in the competition!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80a21263",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Build on the benchmark\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bedd61c0",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Additional regressors (betting odds?)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3a408666",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Alternative data sources (Twitter and NLP?)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49308589",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Cross-validation of predictions\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "732f5bf5",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "- Dixon-Coles model\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3daf2c7b",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# How to sign up for the competition?"
   ]
  }
 ],
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   "display_name": "Python 3",
   "language": "python",
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