Football_Forecasting.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b76cad9c",
   "metadata": {},
   "source": [
    "# WDSC-Football Forecasting 2023"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d2ab9b42",
   "metadata": {},
   "source": [
    "# Importing libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f8ad18ac",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dependencies\n",
    "from scipy.stats import poisson \n",
    "from sklearn.metrics import r2_score, mean_squared_error\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": "accc9e96",
   "metadata": {},
   "source": [
    "# Gathering our data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9653432e",
   "metadata": {},
   "source": [
    "# Data for the week calendar "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "94bced18",
   "metadata": {},
   "outputs": [],
   "source": [
    "calendar = pd.read_csv(\"./epl-2022-UTC.csv\", sep=\",\", encoding=\"utf-8\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5c518343",
   "metadata": {},
   "outputs": [],
   "source": [
    "calendar = calendar[['Round Number','Date','Home Team','Away Team']].copy()\n",
    "calendar=calendar.fillna(0)\n",
    "calendar_week=calendar[calendar['Round Number']==28]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "51ca1e40",
   "metadata": {},
   "outputs": [
    {
     "data": {
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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>Round Number</th>\n",
       "      <th>Date</th>\n",
       "      <th>Home Team</th>\n",
       "      <th>Away Team</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>270</th>\n",
       "      <td>28</td>\n",
       "      <td>18/03/2023 15:00</td>\n",
       "      <td>Arsenal</td>\n",
       "      <td>Crystal Palace</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>271</th>\n",
       "      <td>28</td>\n",
       "      <td>18/03/2023 15:00</td>\n",
       "      <td>Aston Villa</td>\n",
       "      <td>Bournemouth</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>272</th>\n",
       "      <td>28</td>\n",
       "      <td>18/03/2023 15:00</td>\n",
       "      <td>Brentford</td>\n",
       "      <td>Leicester</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>273</th>\n",
       "      <td>28</td>\n",
       "      <td>18/03/2023 15:00</td>\n",
       "      <td>Brighton</td>\n",
       "      <td>Man Utd</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>274</th>\n",
       "      <td>28</td>\n",
       "      <td>18/03/2023 15:00</td>\n",
       "      <td>Chelsea</td>\n",
       "      <td>Everton</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>275</th>\n",
       "      <td>28</td>\n",
       "      <td>18/03/2023 15:00</td>\n",
       "      <td>Liverpool</td>\n",
       "      <td>Fulham</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>276</th>\n",
       "      <td>28</td>\n",
       "      <td>18/03/2023 15:00</td>\n",
       "      <td>Man City</td>\n",
       "      <td>West Ham</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>277</th>\n",
       "      <td>28</td>\n",
       "      <td>18/03/2023 15:00</td>\n",
       "      <td>Nottingham Forest</td>\n",
       "      <td>Newcastle</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>278</th>\n",
       "      <td>28</td>\n",
       "      <td>18/03/2023 15:00</td>\n",
       "      <td>Southampton</td>\n",
       "      <td>Spurs</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>279</th>\n",
       "      <td>28</td>\n",
       "      <td>18/03/2023 15:00</td>\n",
       "      <td>Wolves</td>\n",
       "      <td>Leeds</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Round Number              Date          Home Team       Away Team\n",
       "270            28  18/03/2023 15:00            Arsenal  Crystal Palace\n",
       "271            28  18/03/2023 15:00        Aston Villa     Bournemouth\n",
       "272            28  18/03/2023 15:00          Brentford       Leicester\n",
       "273            28  18/03/2023 15:00           Brighton         Man Utd\n",
       "274            28  18/03/2023 15:00            Chelsea         Everton\n",
       "275            28  18/03/2023 15:00          Liverpool          Fulham\n",
       "276            28  18/03/2023 15:00           Man City        West Ham\n",
       "277            28  18/03/2023 15:00  Nottingham Forest       Newcastle\n",
       "278            28  18/03/2023 15:00        Southampton           Spurs\n",
       "279            28  18/03/2023 15:00             Wolves           Leeds"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "calendar_week"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "74fd34c1",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/var/folders/lw/wf82f57x0rs9dlnjr6z3l0s80000gn/T/ipykernel_20748/3054149329.py:5: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  calendar_week.replace({'Home Team': dict}, inplace=True)\n",
      "/var/folders/lw/wf82f57x0rs9dlnjr6z3l0s80000gn/T/ipykernel_20748/3054149329.py:6: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  calendar_week.replace({'Away Team': dict}, inplace=True)\n"
     ]
    }
   ],
   "source": [
    "dict = {'Nottingham Forest': \"Nott'm Forest\",\n",
    "       'Man Utd': 'Man United',\n",
    "       'Spurs': 'Tottenham'}\n",
    "\n",
    "calendar_week.replace({'Home Team': dict}, inplace=True)\n",
    "calendar_week.replace({'Away Team': dict}, inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "367cf847",
   "metadata": {},
   "source": [
    "# Data for our predictions "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ab083add",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Div</th>\n",
       "      <th>Date</th>\n",
       "      <th>Time</th>\n",
       "      <th>HomeTeam</th>\n",
       "      <th>AwayTeam</th>\n",
       "      <th>FTHG</th>\n",
       "      <th>FTAG</th>\n",
       "      <th>FTR</th>\n",
       "      <th>HTHG</th>\n",
       "      <th>HTAG</th>\n",
       "      <th>...</th>\n",
       "      <th>AvgC&lt;2.5</th>\n",
       "      <th>AHCh</th>\n",
       "      <th>B365CAHH</th>\n",
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       "      <th>PCAHH</th>\n",
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       "      <th>MaxCAHA</th>\n",
       "      <th>AvgCAHH</th>\n",
       "      <th>AvgCAHA</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>E0</td>\n",
       "      <td>13/08/2021</td>\n",
       "      <td>20:00</td>\n",
       "      <td>Brentford</td>\n",
       "      <td>Arsenal</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>H</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1.62</td>\n",
       "      <td>0.50</td>\n",
       "      <td>1.75</td>\n",
       "      <td>2.05</td>\n",
       "      <td>1.81</td>\n",
       "      <td>2.13</td>\n",
       "      <td>2.05</td>\n",
       "      <td>2.17</td>\n",
       "      <td>1.80</td>\n",
       "      <td>2.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>E0</td>\n",
       "      <td>14/08/2021</td>\n",
       "      <td>12:30</td>\n",
       "      <td>Man United</td>\n",
       "      <td>Leeds</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>H</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>2.25</td>\n",
       "      <td>-1.00</td>\n",
       "      <td>2.05</td>\n",
       "      <td>1.75</td>\n",
       "      <td>2.17</td>\n",
       "      <td>1.77</td>\n",
       "      <td>2.19</td>\n",
       "      <td>1.93</td>\n",
       "      <td>2.10</td>\n",
       "      <td>1.79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>E0</td>\n",
       "      <td>14/08/2021</td>\n",
       "      <td>15:00</td>\n",
       "      <td>Burnley</td>\n",
       "      <td>Brighton</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>A</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1.62</td>\n",
       "      <td>0.25</td>\n",
       "      <td>1.79</td>\n",
       "      <td>2.15</td>\n",
       "      <td>1.81</td>\n",
       "      <td>2.14</td>\n",
       "      <td>1.82</td>\n",
       "      <td>2.19</td>\n",
       "      <td>1.79</td>\n",
       "      <td>2.12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>E0</td>\n",
       "      <td>14/08/2021</td>\n",
       "      <td>15:00</td>\n",
       "      <td>Chelsea</td>\n",
       "      <td>Crystal Palace</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>H</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1.94</td>\n",
       "      <td>-1.50</td>\n",
       "      <td>2.05</td>\n",
       "      <td>1.75</td>\n",
       "      <td>2.12</td>\n",
       "      <td>1.81</td>\n",
       "      <td>2.16</td>\n",
       "      <td>1.93</td>\n",
       "      <td>2.06</td>\n",
       "      <td>1.82</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>E0</td>\n",
       "      <td>14/08/2021</td>\n",
       "      <td>15:00</td>\n",
       "      <td>Everton</td>\n",
       "      <td>Southampton</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>H</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1.67</td>\n",
       "      <td>-0.50</td>\n",
       "      <td>2.05</td>\n",
       "      <td>1.88</td>\n",
       "      <td>2.05</td>\n",
       "      <td>1.88</td>\n",
       "      <td>2.08</td>\n",
       "      <td>1.90</td>\n",
       "      <td>2.03</td>\n",
       "      <td>1.86</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>256</th>\n",
       "      <td>E0</td>\n",
       "      <td>11/03/2023</td>\n",
       "      <td>17:30</td>\n",
       "      <td>Crystal Palace</td>\n",
       "      <td>Man City</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>A</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1.98</td>\n",
       "      <td>1.50</td>\n",
       "      <td>1.84</td>\n",
       "      <td>2.09</td>\n",
       "      <td>1.84</td>\n",
       "      <td>2.09</td>\n",
       "      <td>1.90</td>\n",
       "      <td>2.13</td>\n",
       "      <td>1.84</td>\n",
       "      <td>2.05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>257</th>\n",
       "      <td>E0</td>\n",
       "      <td>12/03/2023</td>\n",
       "      <td>14:00</td>\n",
       "      <td>Fulham</td>\n",
       "      <td>Arsenal</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>A</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>...</td>\n",
       "      <td>2.10</td>\n",
       "      <td>1.25</td>\n",
       "      <td>1.97</td>\n",
       "      <td>1.96</td>\n",
       "      <td>1.96</td>\n",
       "      <td>1.96</td>\n",
       "      <td>1.97</td>\n",
       "      <td>2.05</td>\n",
       "      <td>1.90</td>\n",
       "      <td>1.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>258</th>\n",
       "      <td>E0</td>\n",
       "      <td>12/03/2023</td>\n",
       "      <td>14:00</td>\n",
       "      <td>Man United</td>\n",
       "      <td>Southampton</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>D</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>2.61</td>\n",
       "      <td>-1.75</td>\n",
       "      <td>1.99</td>\n",
       "      <td>1.94</td>\n",
       "      <td>2.04</td>\n",
       "      <td>1.88</td>\n",
       "      <td>2.04</td>\n",
       "      <td>1.95</td>\n",
       "      <td>1.98</td>\n",
       "      <td>1.90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>259</th>\n",
       "      <td>E0</td>\n",
       "      <td>12/03/2023</td>\n",
       "      <td>14:00</td>\n",
       "      <td>West Ham</td>\n",
       "      <td>Aston Villa</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>D</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1.73</td>\n",
       "      <td>-0.25</td>\n",
       "      <td>2.04</td>\n",
       "      <td>1.89</td>\n",
       "      <td>2.06</td>\n",
       "      <td>1.88</td>\n",
       "      <td>2.06</td>\n",
       "      <td>1.97</td>\n",
       "      <td>1.99</td>\n",
       "      <td>1.89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>260</th>\n",
       "      <td>E0</td>\n",
       "      <td>12/03/2023</td>\n",
       "      <td>16:30</td>\n",
       "      <td>Newcastle</td>\n",
       "      <td>Wolves</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>H</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>1.73</td>\n",
       "      <td>-0.75</td>\n",
       "      <td>1.82</td>\n",
       "      <td>2.11</td>\n",
       "      <td>1.85</td>\n",
       "      <td>2.09</td>\n",
       "      <td>1.85</td>\n",
       "      <td>2.13</td>\n",
       "      <td>1.82</td>\n",
       "      <td>2.07</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1021 rows × 106 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Div        Date   Time        HomeTeam        AwayTeam  FTHG  FTAG FTR  \\\n",
       "0    E0  13/08/2021  20:00       Brentford         Arsenal     2     0   H   \n",
       "1    E0  14/08/2021  12:30      Man United           Leeds     5     1   H   \n",
       "2    E0  14/08/2021  15:00         Burnley        Brighton     1     2   A   \n",
       "3    E0  14/08/2021  15:00         Chelsea  Crystal Palace     3     0   H   \n",
       "4    E0  14/08/2021  15:00         Everton     Southampton     3     1   H   \n",
       "..   ..         ...    ...             ...             ...   ...   ...  ..   \n",
       "256  E0  11/03/2023  17:30  Crystal Palace        Man City     0     1   A   \n",
       "257  E0  12/03/2023  14:00          Fulham         Arsenal     0     3   A   \n",
       "258  E0  12/03/2023  14:00      Man United     Southampton     0     0   D   \n",
       "259  E0  12/03/2023  14:00        West Ham     Aston Villa     1     1   D   \n",
       "260  E0  12/03/2023  16:30       Newcastle          Wolves     2     1   H   \n",
       "\n",
       "     HTHG  HTAG  ... AvgC<2.5  AHCh  B365CAHH  B365CAHA  PCAHH  PCAHA  \\\n",
       "0       1     0  ...     1.62  0.50      1.75      2.05   1.81   2.13   \n",
       "1       1     0  ...     2.25 -1.00      2.05      1.75   2.17   1.77   \n",
       "2       1     0  ...     1.62  0.25      1.79      2.15   1.81   2.14   \n",
       "3       2     0  ...     1.94 -1.50      2.05      1.75   2.12   1.81   \n",
       "4       0     1  ...     1.67 -0.50      2.05      1.88   2.05   1.88   \n",
       "..    ...   ...  ...      ...   ...       ...       ...    ...    ...   \n",
       "256     0     0  ...     1.98  1.50      1.84      2.09   1.84   2.09   \n",
       "257     0     3  ...     2.10  1.25      1.97      1.96   1.96   1.96   \n",
       "258     0     0  ...     2.61 -1.75      1.99      1.94   2.04   1.88   \n",
       "259     1     1  ...     1.73 -0.25      2.04      1.89   2.06   1.88   \n",
       "260     1     0  ...     1.73 -0.75      1.82      2.11   1.85   2.09   \n",
       "\n",
       "     MaxCAHH  MaxCAHA  AvgCAHH  AvgCAHA  \n",
       "0       2.05     2.17     1.80     2.09  \n",
       "1       2.19     1.93     2.10     1.79  \n",
       "2       1.82     2.19     1.79     2.12  \n",
       "3       2.16     1.93     2.06     1.82  \n",
       "4       2.08     1.90     2.03     1.86  \n",
       "..       ...      ...      ...      ...  \n",
       "256     1.90     2.13     1.84     2.05  \n",
       "257     1.97     2.05     1.90     1.97  \n",
       "258     2.04     1.95     1.98     1.90  \n",
       "259     2.06     1.97     1.99     1.89  \n",
       "260     1.85     2.13     1.82     2.07  \n",
       "\n",
       "[1021 rows x 106 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Taking all data from the last five years excluding 2020\n",
    "\n",
    "# Get data from the 2018/2019 season\n",
    "data1819 = pd.read_csv(\"https://www.football-data.co.uk/mmz4281/2122/E0.csv\", sep=',', engine='python',quoting=3) \n",
    "\n",
    "# Get data from the 2021/2022 season\n",
    "data2122 = pd.read_csv(\"https://www.football-data.co.uk/mmz4281/2122/E0.csv\", sep=',', engine='python',quoting=3) \n",
    "\n",
    "# Get data from the 2022/2023 season\n",
    "data2223 = pd.read_csv(\"https://www.football-data.co.uk/mmz4281/2223/E0.csv\", sep=',', engine='python',quoting=3) \n",
    "\n",
    "frames = [data1819, data2122, data2223]\n",
    "  \n",
    "data = pd.concat(frames)\n",
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "79e8d711",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Brentford', 'Man United', 'Burnley', 'Chelsea', 'Everton',\n",
       "       'Leicester', 'Watford', 'Norwich', 'Newcastle', 'Tottenham',\n",
       "       'Liverpool', 'Aston Villa', 'Crystal Palace', 'Leeds', 'Man City',\n",
       "       'Brighton', 'Southampton', 'Wolves', 'Arsenal', 'West Ham',\n",
       "       'Fulham', 'Bournemouth', \"Nott'm Forest\"], dtype=object)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.HomeTeam.unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b379de17",
   "metadata": {},
   "source": [
    "# Light Cleaning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "300cd124",
   "metadata": {},
   "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": 9,
   "id": "e65e31e4",
   "metadata": {
    "scrolled": true
   },
   "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>Brentford</td>\n",
       "      <td>Arsenal</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>H</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Man United</td>\n",
       "      <td>Leeds</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>H</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Burnley</td>\n",
       "      <td>Brighton</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>A</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Chelsea</td>\n",
       "      <td>Crystal Palace</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>H</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Everton</td>\n",
       "      <td>Southampton</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>H</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     HomeTeam        AwayTeam  HomeGoals  AwayGoals Result\n",
       "0   Brentford         Arsenal          2          0      H\n",
       "1  Man United           Leeds          5          1      H\n",
       "2     Burnley        Brighton          1          2      A\n",
       "3     Chelsea  Crystal Palace          3          0      H\n",
       "4     Everton     Southampton          3          1      H"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Remove final week of fixtures\n",
    "data[:-10]\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24818496",
   "metadata": {},
   "source": [
    "# Understanding our dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "05e24f32",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Number of Goals Scored Per Match')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "sns.set()\n",
    "\n",
    "max_goals = 10\n",
    "plt.hist(\n",
    "    data[[\"HomeGoals\", \"AwayGoals\"]].values, range(max_goals), label=[\"Home\", \"Away\"], density=True\n",
    ")\n",
    "plt.xticks([i - 0.5 for i in range(max_goals)], [i for i in range(max_goals)])\n",
    "plt.xlabel(\"Goals\")\n",
    "plt.ylabel(\"Proportion of matches\")\n",
    "plt.legend(loc=\"upper right\", fontsize=13)\n",
    "plt.title(\"Number of Goals Scored Per Match\", size=14, fontweight=\"bold\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2b5de9f",
   "metadata": {},
   "source": [
    "# Home Team Avantage"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "8d90d150",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "HomeGoals    1.531832\n",
       "AwayGoals    1.255632\n",
       "dtype: float64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute the average number of home and away goals \n",
    "data[['HomeGoals', 'AwayGoals']].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7f0d5eb",
   "metadata": {},
   "source": [
    "# Towards a match prediction model "
   ]
  },
  {
   "cell_type": "raw",
   "id": "6af95a3b",
   "metadata": {},
   "source": [
    "#The poisson regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "0b470503",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "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": "code",
   "execution_count": 13,
   "id": "12f4ee0f",
   "metadata": {},
   "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",
    "\n",
    "# Separate home 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": 14,
   "id": "50a004d2",
   "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>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>Brentford</td>\n",
       "      <td>Arsenal</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Man United</td>\n",
       "      <td>Leeds</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Burnley</td>\n",
       "      <td>Brighton</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Chelsea</td>\n",
       "      <td>Crystal Palace</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Everton</td>\n",
       "      <td>Southampton</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         team        opponent  goals  home\n",
       "0   Brentford         Arsenal      2     1\n",
       "1  Man United           Leeds      5     1\n",
       "2     Burnley        Brighton      1     1\n",
       "3     Chelsea  Crystal Palace      3     1\n",
       "4     Everton     Southampton      3     1"
      ]
     },
     "execution_count": 14,
     "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": "e7ec8294",
   "metadata": {},
   "source": [
    "# Build the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "6504c9b4",
   "metadata": {},
   "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": 16,
   "id": "26faf638",
   "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>  2042</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                  <td>GLM</td>       <th>  Df Residuals:      </th>  <td>  1996</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model Family:</th>         <td>Poisson</td>     <th>  Df Model:          </th>  <td>    45</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> -2920.4</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>            <td>Wed, 15 Mar 2023</td> <th>  Deviance:          </th> <td>  2230.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                <td>09:46:39</td>     <th>  Pearson chi2:      </th> <td>1.93e+03</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Iterations:</th>          <td>5</td>        <th>  Pseudo R-squ. (CS):</th>  <td>0.2222</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>    0.3109</td> <td>    0.120</td> <td>    2.580</td> <td> 0.010</td> <td>    0.075</td> <td>    0.547</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Aston Villa]</th>        <td>   -0.2794</td> <td>    0.113</td> <td>   -2.465</td> <td> 0.014</td> <td>   -0.502</td> <td>   -0.057</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Bournemouth]</th>        <td>   -0.5472</td> <td>    0.214</td> <td>   -2.558</td> <td> 0.011</td> <td>   -0.966</td> <td>   -0.128</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Brentford]</th>          <td>   -0.2757</td> <td>    0.113</td> <td>   -2.433</td> <td> 0.015</td> <td>   -0.498</td> <td>   -0.054</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Brighton]</th>           <td>   -0.3233</td> <td>    0.115</td> <td>   -2.812</td> <td> 0.005</td> <td>   -0.549</td> <td>   -0.098</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Burnley]</th>            <td>   -0.6856</td> <td>    0.142</td> <td>   -4.823</td> <td> 0.000</td> <td>   -0.964</td> <td>   -0.407</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Chelsea]</th>            <td>   -0.0253</td> <td>    0.105</td> <td>   -0.240</td> <td> 0.810</td> <td>   -0.231</td> <td>    0.181</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Crystal Palace]</th>     <td>   -0.3955</td> <td>    0.117</td> <td>   -3.375</td> <td> 0.001</td> <td>   -0.625</td> <td>   -0.166</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Everton]</th>            <td>   -0.5360</td> <td>    0.122</td> <td>   -4.386</td> <td> 0.000</td> <td>   -0.775</td> <td>   -0.296</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Fulham]</th>             <td>   -0.1928</td> <td>    0.179</td> <td>   -1.077</td> <td> 0.281</td> <td>   -0.544</td> <td>    0.158</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Leeds]</th>              <td>   -0.4291</td> <td>    0.119</td> <td>   -3.604</td> <td> 0.000</td> <td>   -0.662</td> <td>   -0.196</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Leicester]</th>          <td>   -0.1013</td> <td>    0.108</td> <td>   -0.936</td> <td> 0.349</td> <td>   -0.313</td> <td>    0.111</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Liverpool]</th>          <td>    0.2450</td> <td>    0.099</td> <td>    2.485</td> <td> 0.013</td> <td>    0.052</td> <td>    0.438</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Man City]</th>           <td>    0.3538</td> <td>    0.096</td> <td>    3.681</td> <td> 0.000</td> <td>    0.165</td> <td>    0.542</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Man United]</th>         <td>   -0.1458</td> <td>    0.109</td> <td>   -1.334</td> <td> 0.182</td> <td>   -0.360</td> <td>    0.068</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Newcastle]</th>          <td>   -0.3492</td> <td>    0.116</td> <td>   -3.008</td> <td> 0.003</td> <td>   -0.577</td> <td>   -0.122</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Norwich]</th>            <td>   -1.0465</td> <td>    0.165</td> <td>   -6.339</td> <td> 0.000</td> <td>   -1.370</td> <td>   -0.723</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Nott'm Forest]</th>      <td>   -0.7587</td> <td>    0.231</td> <td>   -3.284</td> <td> 0.001</td> <td>   -1.211</td> <td>   -0.306</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Southampton]</th>        <td>   -0.5216</td> <td>    0.122</td> <td>   -4.271</td> <td> 0.000</td> <td>   -0.761</td> <td>   -0.282</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Tottenham]</th>          <td>    0.0248</td> <td>    0.104</td> <td>    0.238</td> <td> 0.812</td> <td>   -0.179</td> <td>    0.229</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Watford]</th>            <td>   -0.6617</td> <td>    0.142</td> <td>   -4.654</td> <td> 0.000</td> <td>   -0.940</td> <td>   -0.383</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.West Ham]</th>           <td>   -0.2218</td> <td>    0.111</td> <td>   -1.990</td> <td> 0.047</td> <td>   -0.440</td> <td>   -0.003</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>team[T.Wolves]</th>             <td>   -0.6414</td> <td>    0.126</td> <td>   -5.089</td> <td> 0.000</td> <td>   -0.888</td> <td>   -0.394</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Aston Villa]</th>    <td>    0.1871</td> <td>    0.123</td> <td>    1.521</td> <td> 0.128</td> <td>   -0.054</td> <td>    0.428</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Bournemouth]</th>    <td>    0.4372</td> <td>    0.168</td> <td>    2.609</td> <td> 0.009</td> <td>    0.109</td> <td>    0.766</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Brentford]</th>      <td>    0.1912</td> <td>    0.123</td> <td>    1.550</td> <td> 0.121</td> <td>   -0.051</td> <td>    0.433</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Brighton]</th>       <td>   -0.0115</td> <td>    0.129</td> <td>   -0.089</td> <td> 0.929</td> <td>   -0.265</td> <td>    0.242</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Burnley]</th>        <td>    0.1457</td> <td>    0.133</td> <td>    1.093</td> <td> 0.274</td> <td>   -0.116</td> <td>    0.407</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Chelsea]</th>        <td>   -0.2670</td> <td>    0.139</td> <td>   -1.928</td> <td> 0.054</td> <td>   -0.538</td> <td>    0.004</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Crystal Palace]</th> <td>    0.0084</td> <td>    0.128</td> <td>    0.066</td> <td> 0.948</td> <td>   -0.242</td> <td>    0.259</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Everton]</th>        <td>    0.3137</td> <td>    0.119</td> <td>    2.632</td> <td> 0.008</td> <td>    0.080</td> <td>    0.547</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Fulham]</th>         <td>    0.1290</td> <td>    0.188</td> <td>    0.685</td> <td> 0.494</td> <td>   -0.240</td> <td>    0.498</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Leeds]</th>          <td>    0.4932</td> <td>    0.115</td> <td>    4.275</td> <td> 0.000</td> <td>    0.267</td> <td>    0.719</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Leicester]</th>      <td>    0.3061</td> <td>    0.120</td> <td>    2.548</td> <td> 0.011</td> <td>    0.071</td> <td>    0.542</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Liverpool]</th>      <td>   -0.3627</td> <td>    0.144</td> <td>   -2.523</td> <td> 0.012</td> <td>   -0.644</td> <td>   -0.081</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Man City]</th>       <td>   -0.4194</td> <td>    0.146</td> <td>   -2.873</td> <td> 0.004</td> <td>   -0.706</td> <td>   -0.133</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Man United]</th>     <td>    0.1961</td> <td>    0.123</td> <td>    1.598</td> <td> 0.110</td> <td>   -0.044</td> <td>    0.436</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Newcastle]</th>      <td>    0.1532</td> <td>    0.124</td> <td>    1.237</td> <td> 0.216</td> <td>   -0.090</td> <td>    0.396</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Norwich]</th>        <td>    0.5962</td> <td>    0.119</td> <td>    4.990</td> <td> 0.000</td> <td>    0.362</td> <td>    0.830</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Nott'm Forest]</th>  <td>    0.3558</td> <td>    0.173</td> <td>    2.062</td> <td> 0.039</td> <td>    0.018</td> <td>    0.694</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Southampton]</th>    <td>    0.3524</td> <td>    0.118</td> <td>    2.976</td> <td> 0.003</td> <td>    0.120</td> <td>    0.584</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Tottenham]</th>      <td>   -0.0393</td> <td>    0.130</td> <td>   -0.303</td> <td> 0.762</td> <td>   -0.294</td> <td>    0.215</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Watford]</th>        <td>    0.5200</td> <td>    0.122</td> <td>    4.272</td> <td> 0.000</td> <td>    0.281</td> <td>    0.759</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.West Ham]</th>       <td>    0.1193</td> <td>    0.125</td> <td>    0.953</td> <td> 0.340</td> <td>   -0.126</td> <td>    0.365</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>opponent[T.Wolves]</th>         <td>   -0.0253</td> <td>    0.128</td> <td>   -0.197</td> <td> 0.844</td> <td>   -0.277</td> <td>    0.226</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>home</th>                       <td>    0.2001</td> <td>    0.038</td> <td>    5.310</td> <td> 0.000</td> <td>    0.126</td> <td>    0.274</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:                 2042\n",
       "Model:                            GLM   Df Residuals:                     1996\n",
       "Model Family:                 Poisson   Df Model:                           45\n",
       "Link Function:                    Log   Scale:                          1.0000\n",
       "Method:                          IRLS   Log-Likelihood:                -2920.4\n",
       "Date:                Wed, 15 Mar 2023   Deviance:                       2230.8\n",
       "Time:                        09:46:39   Pearson chi2:                 1.93e+03\n",
       "No. Iterations:                     5   Pseudo R-squ. (CS):             0.2222\n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================================\n",
       "                                 coef    std err          z      P>|z|      [0.025      0.975]\n",
       "----------------------------------------------------------------------------------------------\n",
       "Intercept                      0.3109      0.120      2.580      0.010       0.075       0.547\n",
       "team[T.Aston Villa]           -0.2794      0.113     -2.465      0.014      -0.502      -0.057\n",
       "team[T.Bournemouth]           -0.5472      0.214     -2.558      0.011      -0.966      -0.128\n",
       "team[T.Brentford]             -0.2757      0.113     -2.433      0.015      -0.498      -0.054\n",
       "team[T.Brighton]              -0.3233      0.115     -2.812      0.005      -0.549      -0.098\n",
       "team[T.Burnley]               -0.6856      0.142     -4.823      0.000      -0.964      -0.407\n",
       "team[T.Chelsea]               -0.0253      0.105     -0.240      0.810      -0.231       0.181\n",
       "team[T.Crystal Palace]        -0.3955      0.117     -3.375      0.001      -0.625      -0.166\n",
       "team[T.Everton]               -0.5360      0.122     -4.386      0.000      -0.775      -0.296\n",
       "team[T.Fulham]                -0.1928      0.179     -1.077      0.281      -0.544       0.158\n",
       "team[T.Leeds]                 -0.4291      0.119     -3.604      0.000      -0.662      -0.196\n",
       "team[T.Leicester]             -0.1013      0.108     -0.936      0.349      -0.313       0.111\n",
       "team[T.Liverpool]              0.2450      0.099      2.485      0.013       0.052       0.438\n",
       "team[T.Man City]               0.3538      0.096      3.681      0.000       0.165       0.542\n",
       "team[T.Man United]            -0.1458      0.109     -1.334      0.182      -0.360       0.068\n",
       "team[T.Newcastle]             -0.3492      0.116     -3.008      0.003      -0.577      -0.122\n",
       "team[T.Norwich]               -1.0465      0.165     -6.339      0.000      -1.370      -0.723\n",
       "team[T.Nott'm Forest]         -0.7587      0.231     -3.284      0.001      -1.211      -0.306\n",
       "team[T.Southampton]           -0.5216      0.122     -4.271      0.000      -0.761      -0.282\n",
       "team[T.Tottenham]              0.0248      0.104      0.238      0.812      -0.179       0.229\n",
       "team[T.Watford]               -0.6617      0.142     -4.654      0.000      -0.940      -0.383\n",
       "team[T.West Ham]              -0.2218      0.111     -1.990      0.047      -0.440      -0.003\n",
       "team[T.Wolves]                -0.6414      0.126     -5.089      0.000      -0.888      -0.394\n",
       "opponent[T.Aston Villa]        0.1871      0.123      1.521      0.128      -0.054       0.428\n",
       "opponent[T.Bournemouth]        0.4372      0.168      2.609      0.009       0.109       0.766\n",
       "opponent[T.Brentford]          0.1912      0.123      1.550      0.121      -0.051       0.433\n",
       "opponent[T.Brighton]          -0.0115      0.129     -0.089      0.929      -0.265       0.242\n",
       "opponent[T.Burnley]            0.1457      0.133      1.093      0.274      -0.116       0.407\n",
       "opponent[T.Chelsea]           -0.2670      0.139     -1.928      0.054      -0.538       0.004\n",
       "opponent[T.Crystal Palace]     0.0084      0.128      0.066      0.948      -0.242       0.259\n",
       "opponent[T.Everton]            0.3137      0.119      2.632      0.008       0.080       0.547\n",
       "opponent[T.Fulham]             0.1290      0.188      0.685      0.494      -0.240       0.498\n",
       "opponent[T.Leeds]              0.4932      0.115      4.275      0.000       0.267       0.719\n",
       "opponent[T.Leicester]          0.3061      0.120      2.548      0.011       0.071       0.542\n",
       "opponent[T.Liverpool]         -0.3627      0.144     -2.523      0.012      -0.644      -0.081\n",
       "opponent[T.Man City]          -0.4194      0.146     -2.873      0.004      -0.706      -0.133\n",
       "opponent[T.Man United]         0.1961      0.123      1.598      0.110      -0.044       0.436\n",
       "opponent[T.Newcastle]          0.1532      0.124      1.237      0.216      -0.090       0.396\n",
       "opponent[T.Norwich]            0.5962      0.119      4.990      0.000       0.362       0.830\n",
       "opponent[T.Nott'm Forest]      0.3558      0.173      2.062      0.039       0.018       0.694\n",
       "opponent[T.Southampton]        0.3524      0.118      2.976      0.003       0.120       0.584\n",
       "opponent[T.Tottenham]         -0.0393      0.130     -0.303      0.762      -0.294       0.215\n",
       "opponent[T.Watford]            0.5200      0.122      4.272      0.000       0.281       0.759\n",
       "opponent[T.West Ham]           0.1193      0.125      0.953      0.340      -0.126       0.365\n",
       "opponent[T.Wolves]            -0.0253      0.128     -0.197      0.844      -0.277       0.226\n",
       "home                           0.2001      0.038      5.310      0.000       0.126       0.274\n",
       "==============================================================================================\n",
       "\"\"\""
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poisson_model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1b3168f",
   "metadata": {},
   "source": [
    "# Computing the expected goals for each team"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "c359b91b",
   "metadata": {},
   "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",
    "    # Creating DataFrame for away team features\n",
    "    X_away = pd.DataFrame(data={\"team\": away_team,\n",
    "                                \"opponent\": home_team,\n",
    "                                \"home\": 0\n",
    "                                }, index=[1])\n",
    "    \n",
    "    return X_home, X_away"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d3d938ec",
   "metadata": {},
   "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": 19,
   "id": "350d6032",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average Home Goals:  1.7220310969045303\n",
      "Average Away Goals:  0.6317518625725689\n"
     ]
    }
   ],
   "source": [
    "# Predicting average goals for Chelsea Man City match\n",
    "X_home, X_away =  create_X('Brighton', \"Nott'm Forest\")\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": "7be49b91",
   "metadata": {},
   "source": [
    "# Computing the distribution of match scores"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "a5ba56f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "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\n",
    "\n",
    "# Predicting distribution of match scores\n",
    "X_home, X_away =  create_X('Brighton', \"Nott'm Forest\")\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(\"Brighton goals\", labelpad=6)\n",
    "plt.ylabel(\"Nott'm Forest goals\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9580a7c",
   "metadata": {},
   "source": [
    "# Forecasting the distribution mode¶"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "b4d652d1",
   "metadata": {},
   "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": 22,
   "id": "233c070e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1- Match predicted results:  Arsenal  and  Crystal Palace\n",
      "Score Forecast:  (1, 0)\n",
      "1- Match predicted results:  Aston Villa  and  Bournemouth\n",
      "Score Forecast:  (1, 0)\n",
      "1- Match predicted results:  Brentford  and  Leicester\n",
      "Score Forecast:  (1, 1)\n",
      "1- Match predicted results:  Brighton  and  Man United\n",
      "Score Forecast:  (1, 1)\n",
      "1- Match predicted results:  Chelsea  and  Everton\n",
      "Score Forecast:  (2, 0)\n",
      "1- Match predicted results:  Liverpool  and  Fulham\n",
      "Score Forecast:  (2, 0)\n",
      "1- Match predicted results:  Man City  and  West Ham\n",
      "Score Forecast:  (2, 0)\n",
      "1- Match predicted results:  Nott'm Forest  and  Newcastle\n",
      "Score Forecast:  (0, 1)\n",
      "1- Match predicted results:  Southampton  and  Tottenham\n",
      "Score Forecast:  (0, 1)\n",
      "1- Match predicted results:  Wolves  and  Leeds\n",
      "Score Forecast:  (1, 0)\n"
     ]
    }
   ],
   "source": [
    "for i in range(0, len(calendar_week)):\n",
    "    print (\"1- Match predicted results:  \"+ calendar_week['Home Team'].iloc[i]+\"  and  \"+ calendar_week['Away Team'].iloc[i])\n",
    "    X_home, X_away =  create_X(calendar_week['Home Team'].iloc[i],calendar_week['Away Team'].iloc[i])\n",
    "    score_pred =  predict_score(X_home, X_away, poisson_model)\n",
    "    print('Score Forecast: ', score_pred)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c055f4f9",
   "metadata": {},
   "source": [
    "# Accuracy of our predictions : Determining Weighting "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "4bcacafa",
   "metadata": {},
   "outputs": [],
   "source": [
    "def mse(y_true, ypred):\n",
    "    np.square(np.subtract(Y_true,Y_pred)).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "e1faceab",
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'CatBoostRegressor' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "Cell \u001b[0;32mIn [27], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m model \u001b[38;5;241m=\u001b[39m \u001b[43mCatBoostRegressor\u001b[49m(objective\u001b[38;5;241m=\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mPoisson\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m      3\u001b[0m model\u001b[38;5;241m.\u001b[39mfit(training_data, plot\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m, eval_set\u001b[38;5;241m=\u001b[39mval_pool, verbose\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m500\u001b[39m)\n\u001b[1;32m      5\u001b[0m actual_counts \u001b[38;5;241m=\u001b[39m df_test\u001b[38;5;241m.\u001b[39mfavorite_count\u001b[38;5;241m.\u001b[39mvalues\u001b[38;5;241m.\u001b[39mastype(\u001b[38;5;28mint\u001b[39m) \n",
      "\u001b[0;31mNameError\u001b[0m: name 'CatBoostRegressor' is not defined"
     ]
    }
   ],
   "source": [
    "model = CatBoostRegressor(objective='Poisson')\n",
    "\n",
    "model.fit(training_data, plot=True, eval_set=val_pool, verbose=500)\n",
    "\n",
    "actual_counts = df_test.favorite_count.values.astype(int) \n",
    "predicted_counts_poisson = model.predict(test_pool) * 100\n",
    "r2_poisson = r2_score(actual_counts, predicted_counts_poisson)\n",
    "rmse_score_poisson_model = np.sqrt(mean_squared_error(actual_counts, predicted_counts_poisson))\n",
    "print('R2 score: {:.3f}\\nRMSE score: {:.2f}'.format(r2_poisson, rmse_score_poisson_model))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ee78aee1",
   "metadata": {},
   "outputs": [],
   "source": [
    "print(accuracy_score(ytest, model.predict(xtest)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a7c65795",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "accuracy = metrics.accuracy_score(y_test, preds)\n",
    "accuracy "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f8621d4",
   "metadata": {},
   "source": [
    "# Webscrapping - team results of the previous weeks "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d99bce76",
   "metadata": {},
   "outputs": [],
   "source": [
    "#webscrapping - team results of the weeks \n",
    "import requests\n",
    "import pandas as pd\n",
    "from bs4 import BeautifulSoup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dc1c55f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "url = \"https://fixturedownload.com/results/epl-2022\"\n",
    "data = requests.get(url).text"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9981debe",
   "metadata": {},
   "outputs": [],
   "source": [
    "import requests\n",
    "import lxml.html as lh\n",
    "import pandas as pd\n",
    "\n",
    "url='https://fixturedownload.com/results/epl-2022'\n",
    "#Create a handle, page, to handle the contents of the website\n",
    "page = requests.get(url)\n",
    "#Store the contents of the website under doc\n",
    "doc = lh.fromstring(page.content)\n",
    "#Parse data that are stored between <tr>..</tr> of HTML\n",
    "tr_elements = doc.xpath('//tr')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1d81f795",
   "metadata": {},
   "outputs": [],
   "source": [
    "tr_elements = doc.xpath('//tr')\n",
    "#Create empty list\n",
    "col=[]\n",
    "i=0\n",
    "#For each row, store each first element (header) and an empty list\n",
    "for t in tr_elements[0]:\n",
    "    i+=1\n",
    "    name=t.text_content()\n",
    "    print ('%d:\"%s\"'%(i,name))\n",
    "    col.append((name,[]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5afb8599",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Since out first row is the header, data is stored on the second row onwards\n",
    "for j in range(1,len(tr_elements)):\n",
    "    #T is our j'th row\n",
    "    T=tr_elements[j]\n",
    "    \n",
    "    #If row is not of size 10, the //tr data is not from our table \n",
    "    if len(T)!=6:\n",
    "        break\n",
    "    \n",
    "    #i is the index of our column\n",
    "    i=0\n",
    "    \n",
    "    #Iterate through each element of the row\n",
    "    for t in T.iterchildren():\n",
    "        data=t.text_content() \n",
    "        #Check if row is empty\n",
    "        if i>0:\n",
    "        #Convert any numerical value to integers\n",
    "            try:\n",
    "                data=int(data)\n",
    "            except:\n",
    "                pass\n",
    "        #Append the data to the empty list of the i'th column\n",
    "        col[i][1].append(data)\n",
    "        #Increment i for the next column\n",
    "        i+=1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d23bded2",
   "metadata": {},
   "outputs": [],
   "source": [
    "Dict={title:column for (title,column) in col}\n",
    "update_score=pd.DataFrame(Dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "390fe04a",
   "metadata": {},
   "outputs": [],
   "source": [
    "dict = {'Nottingham Forest': \"Nott'm Forest\",\n",
    "       'Man Utd': 'Man United',\n",
    "       'Spurs': 'Tottenham'}\n",
    "\n",
    "update_score.replace({'Home Team': dict}, inplace=True)\n",
    "update_score.replace({'Away Team': dict}, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "06ff138b",
   "metadata": {},
   "outputs": [],
   "source": [
    "update_score.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "71f1afd7",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(0, len(update_score)):\n",
    "    my_string = update_score['Result'].iloc[i]\n",
    "    value1, value2 = my_string.split(\"-\")\n",
    "    update_score.loc[i, ['True_Home_Score']] = value1\n",
    "    update_score.loc[i, ['True_Away_Score']] = value2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0afc9e37",
   "metadata": {},
   "outputs": [],
   "source": [
    "update_score.dropna()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "37414527",
   "metadata": {},
   "outputs": [],
   "source": [
    "update_score['Round Number']= update_score['Round Number'].astype(int)\n",
    "update_score=update_score[update_score['Round Number'] >= 12]\n",
    "update_score=update_score[update_score['Round Number'] <= 15]\n",
    "update_score.reset_index(inplace = True, drop = True)\n",
    "update_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "25a660f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(0, len(update_score)):\n",
    "    X_home, X_away =  create_X(update_score['Home Team'].iloc[i],update_score['Away Team'].iloc[i])\n",
    "    score_pmf = predict_score(X_home, X_away, poisson_model)\n",
    "    my_string = str(score_pmf)\n",
    "    value1, value2 = my_string.split(\",\")\n",
    "    update_score.loc[i, ['Predicted_Home_Score']] = value1\n",
    "    update_score.loc[i, ['Predicted_Away_Score']] = value2\n",
    "    print(score_pmf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5025aa35",
   "metadata": {},
   "outputs": [],
   "source": [
    "update_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0b0c0975",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0d4cd078",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "#we need numbers \n",
    "update_score['Predicted_Home_Score']=update_score.Predicted_Home_Score.str.strip('()')\n",
    "update_score['Predicted_Home_Score']=update_score['Predicted_Home_Score'].fillna(0)\n",
    "update_score['Predicted_Home_Score']= update_score['Predicted_Home_Score'].astype(int)\n",
    "update_score['Predicted_Away_Score']=update_score.Predicted_Away_Score.str.strip('()')\n",
    "update_score['Predicted_Away_Score']=update_score['Predicted_Away_Score'].fillna(0)\n",
    "update_score['Predicted_Away_Score']= update_score['Predicted_Away_Score'].astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "db570c41",
   "metadata": {},
   "outputs": [],
   "source": [
    "update_score=update_score.drop(update_score.index[3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e94fbab3",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "update_score = update_score[:34]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "59588c08",
   "metadata": {},
   "outputs": [],
   "source": [
    "update_score['True_Home_Score']= update_score['True_Home_Score'].astype(int)\n",
    "update_score['True_Away_Score']= update_score['True_Away_Score'].astype(int)\n",
    "update_score['Predicted_Home_Score']= update_score['Predicted_Home_Score'].astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "10efdf7e",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "update_score.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1e87c1e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "update_score.reset_index(inplace = True, drop = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "972ea285",
   "metadata": {},
   "outputs": [],
   "source": [
    "#add a prediction columns + real score \n",
    "# and compute the accuracy !!!!!!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b5aae0d0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def accuracy_competition(homepred,awaypred,truehome,trueaway):\n",
    "    a = 1-(((homepred-truehome)^2 + (awaypred-trueaway)^2 )/(1+homepred+awaypred+truehome+trueaway))\n",
    "    return a "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "76d0e276",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(0, len(update_score)):\n",
    "    a = 1-(((update_score['Predicted_Home_Score'].loc[i]-update_score['True_Home_Score'].loc[i])^2 + (update_score['Predicted_Away_Score'].loc[i]-update_score['True_Away_Score'].loc[i])^2 )/(1+update_score['Predicted_Away_Score'].loc[i]+update_score['True_Away_Score'].loc[i]+update_score['Predicted_Home_Score'].loc[i]+update_score['True_Home_Score'].loc[i]))\n",
    "    update_score.loc[i, ['Accuracy']] = a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1686c09f",
   "metadata": {},
   "outputs": [],
   "source": [
    "#my\n",
    "large5 = update_score.nlargest(10, \"Accuracy\")\n",
    "large5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7f391ac5",
   "metadata": {},
   "outputs": [],
   "source": [
    "lowest10 = update_score.set_index('Home Team').groupby('Accuracy', as_index=False).idxmax()\n",
    "lowest10\n",
    "print(\"The top 3 : Highest predictions accuracy are for the home team\")\n",
    "print(lowest10.loc[15])\n",
    "print(lowest10.loc[14])\n",
    "print(lowest10.loc[13])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "97605d03",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "lowest10 = update_score.set_index('Away Team').groupby('Accuracy', as_index=False).idxmax()\n",
    "lowest10\n",
    "print(\"The top 3 : Highest predictions accuracy are for the away team\")\n",
    "print(lowest10.loc[15])\n",
    "print(lowest10.loc[14])\n",
    "print(lowest10.loc[13])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d604d67f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# for week 16 , we weight our prediction taking into the both top 3 \n",
    "#Nott'm Forest, Crystal Palace, Brighton, Liverpool, Wolves, Chelsea\n",
    "#we give each team who plays 15 weight"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3e42ba47",
   "metadata": {},
   "outputs": [],
   "source": [
    "calendar_week"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6f0f3294",
   "metadata": {},
   "outputs": [],
   "source": [
    "number_of_games = calendar_week.shape\n",
    "number_of_games[0]"
   ]
  }
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