notebooks/08-shots_follow_poisson_distribution.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import os\n",
    "from mplsoccer import Pitch, add_image\n",
    "from scipy.special import factorial\n",
    "import seaborn as sns\n",
    "from PIL import Image\n",
    "sns.set(font_scale=2)\n",
    "from urllib.request import urlopen\n",
    "sns.set_style(\"whitegrid\")\n",
    "%config InlineBackend.figure_format='retina'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "EVENTS_PATH = os.path.join('..','data','statsbomb','event.parquet')\n",
    "df_events = pd.read_parquet(EVENTS_PATH)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "team_goals_from_events = df_events[((df_events.outcome_name=='Goal')|\n",
    "                                    (df_events.type_name=='Own Goal For'))&(df_events.period!=5)]\n",
    "team_goals_from_events = pd.DataFrame(team_goals_from_events.groupby(['match_id'])\n",
    "                                      .id.nunique()).reset_index()\n",
    "team_goals_from_events.rename({'id':'goals'},axis=1,inplace=True)\n",
    "df_games = df_events[['match_id']].drop_duplicates()\n",
    "df_games = df_games.merge(team_goals_from_events, how='left').fillna(0)\n",
    "df_games['goals'] = df_games['goals'].astype(np.int32)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_games = len(df_games)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "average_goals_per_game = df_games.goals.mean().round(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "goals = df_games.goals.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1252 3993 3.19\n"
     ]
    }
   ],
   "source": [
    "print(n_games, goals, average_goals_per_game)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "goals_per_game = df_games['goals'].value_counts().sort_index()\n",
    "goals_per_game.index.name = 'goals in game'\n",
    "df_goals_per_game = goals_per_game.reset_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "goals_from = goals_per_game.index.min()\n",
    "goals_to = goals_per_game.index.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "t = np.arange(goals_from, goals_to+1, 1)\n",
    "d = np.exp(-average_goals_per_game)*np.power(average_goals_per_game, t)/factorial(t)\n",
    "goal_dist = (d * n_games).round(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_predicted = pd.DataFrame({'goals in game':t,f'predicted via Poisson({average_goals_per_game})':goal_dist})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_predicted = (df_predicted.merge(df_goals_per_game,how='outer')\n",
    "                .fillna(0)\n",
    "                .rename({'total_goals':'actual'},axis=1).set_index('goals in game')\n",
    "                .sort_index())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "IMAGE_URL = '/~https://github.com/statsbomb/open-data/blob/master/stats-bomb-logo.png?raw=true'\n",
    "logo = np.array(Image.open('SB_Regular.png'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 1600x900 with 2 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 796,
       "width": 1360
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(figsize=(16,9))\n",
    "df_predicted.plot(kind='bar',color=['#ffcd00','black'],ax=ax)\n",
    "ax.set_xlabel('Number of goals in a match')\n",
    "ax.set_ylabel(f'Number of matches (out of {n_games})')\n",
    "ax_image = add_image(logo, fig, left=0.7, bottom=0.2, width=0.15, alpha=0.9, interpolation='hanning')\n",
    "fig.savefig(os.path.join('..', 'figures', '01_goals_follow_poisson_dist.png'), bbox_inches = 'tight', pad_inches = 0.2)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}