{ "cells": [ { "cell_type": "markdown", "id": "81215b75-f5f8-4c17-9cd4-08b1b0ed4234", "metadata": {}, "source": [ "# Poisson\n", "\n", "The Poisson model is a widely-used statistical approach for predicting football match outcomes by modeling the number of goals scored by each team as independent Poisson-distributed events. \n", "\n", "This model is particularly effective because it captures the randomness inherent in goal-scoring, allowing users to accurately estimate match result probabilities, goal totals, and various betting markets, including over/under goals and Asian handicaps. \n", "\n", "Its simplicity, interpretability, and robustness have made it a foundational tool in football analytics and betting." ] }, { "cell_type": "code", "execution_count": 1, "id": "1f931497-c1f9-4cb4-969a-058676e42a24", "metadata": { "tags": [] }, "outputs": [], "source": [ "import penaltyblog as pb" ] }, { "cell_type": "markdown", "id": "4a1b5c76-8f47-4f59-8351-d5add2f69309", "metadata": {}, "source": [ "## Get data from football-data.co.uk" ] }, { "cell_type": "code", "execution_count": 2, "id": "949b129d-e4e5-4975-8318-dd601d918e90", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "
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datedatetimeseasoncompetitiondivtimeteam_hometeam_awayfthgftag...b365_cahhb365_cahapcahhpcahamax_cahhmax_cahaavg_cahhavg_cahagoals_homegoals_away
id
1565308800---liverpool---norwich2019-08-092019-08-09 20:00:002019-2020ENG Premier LeagueE020:00LiverpoolNorwich41...1.911.991.941.981.992.071.901.9941
1565395200---bournemouth---sheffield_united2019-08-102019-08-10 15:00:002019-2020ENG Premier LeagueE015:00BournemouthSheffield United11...1.951.951.981.952.001.961.961.9211
1565395200---burnley---southampton2019-08-102019-08-10 15:00:002019-2020ENG Premier LeagueE015:00BurnleySouthampton30...1.872.031.892.031.902.071.862.0230
1565395200---crystal_palace---everton2019-08-102019-08-10 15:00:002019-2020ENG Premier LeagueE015:00Crystal PalaceEverton00...1.822.081.971.962.032.081.961.9300
1565395200---tottenham---aston_villa2019-08-102019-08-10 17:30:002019-2020ENG Premier LeagueE017:30TottenhamAston Villa31...2.101.702.181.772.211.872.081.8031
\n", "

5 rows × 111 columns

\n", "
" ], "text/plain": [ " date datetime \\\n", "id \n", "1565308800---liverpool---norwich 2019-08-09 2019-08-09 20:00:00 \n", "1565395200---bournemouth---sheffield_united 2019-08-10 2019-08-10 15:00:00 \n", "1565395200---burnley---southampton 2019-08-10 2019-08-10 15:00:00 \n", "1565395200---crystal_palace---everton 2019-08-10 2019-08-10 15:00:00 \n", "1565395200---tottenham---aston_villa 2019-08-10 2019-08-10 17:30:00 \n", "\n", " season competition \\\n", "id \n", "1565308800---liverpool---norwich 2019-2020 ENG Premier League \n", "1565395200---bournemouth---sheffield_united 2019-2020 ENG Premier League \n", "1565395200---burnley---southampton 2019-2020 ENG Premier League \n", "1565395200---crystal_palace---everton 2019-2020 ENG Premier League \n", "1565395200---tottenham---aston_villa 2019-2020 ENG Premier League \n", "\n", " div time team_home \\\n", "id \n", "1565308800---liverpool---norwich E0 20:00 Liverpool \n", "1565395200---bournemouth---sheffield_united E0 15:00 Bournemouth \n", "1565395200---burnley---southampton E0 15:00 Burnley \n", "1565395200---crystal_palace---everton E0 15:00 Crystal Palace \n", "1565395200---tottenham---aston_villa E0 17:30 Tottenham \n", "\n", " team_away fthg ftag \\\n", "id \n", "1565308800---liverpool---norwich Norwich 4 1 \n", "1565395200---bournemouth---sheffield_united Sheffield United 1 1 \n", "1565395200---burnley---southampton Southampton 3 0 \n", "1565395200---crystal_palace---everton Everton 0 0 \n", "1565395200---tottenham---aston_villa Aston Villa 3 1 \n", "\n", " ... b365_cahh b365_caha pcahh \\\n", "id ... \n", "1565308800---liverpool---norwich ... 1.91 1.99 1.94 \n", "1565395200---bournemouth---sheffield_united ... 1.95 1.95 1.98 \n", "1565395200---burnley---southampton ... 1.87 2.03 1.89 \n", "1565395200---crystal_palace---everton ... 1.82 2.08 1.97 \n", "1565395200---tottenham---aston_villa ... 2.10 1.70 2.18 \n", "\n", " pcaha max_cahh max_caha \\\n", "id \n", "1565308800---liverpool---norwich 1.98 1.99 2.07 \n", "1565395200---bournemouth---sheffield_united 1.95 2.00 1.96 \n", "1565395200---burnley---southampton 2.03 1.90 2.07 \n", "1565395200---crystal_palace---everton 1.96 2.03 2.08 \n", "1565395200---tottenham---aston_villa 1.77 2.21 1.87 \n", "\n", " avg_cahh avg_caha goals_home \\\n", "id \n", "1565308800---liverpool---norwich 1.90 1.99 4 \n", "1565395200---bournemouth---sheffield_united 1.96 1.92 1 \n", "1565395200---burnley---southampton 1.86 2.02 3 \n", "1565395200---crystal_palace---everton 1.96 1.93 0 \n", "1565395200---tottenham---aston_villa 2.08 1.80 3 \n", "\n", " goals_away \n", "id \n", "1565308800---liverpool---norwich 1 \n", "1565395200---bournemouth---sheffield_united 1 \n", "1565395200---burnley---southampton 0 \n", "1565395200---crystal_palace---everton 0 \n", "1565395200---tottenham---aston_villa 1 \n", "\n", "[5 rows x 111 columns]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fb = pb.scrapers.FootballData(\"ENG Premier League\", \"2019-2020\")\n", "df = fb.get_fixtures()\n", "\n", "df.head()" ] }, { "cell_type": "markdown", "id": "9257f0fc-5f2b-402f-9209-d005d14880be", "metadata": {}, "source": [ "## Train the model" ] }, { "cell_type": "code", "execution_count": 3, "id": "7d39d92f-6fa0-4a2a-8a48-22d214e38efc", "metadata": { "tags": [] }, "outputs": [], "source": [ "clf = pb.models.PoissonGoalsModel(\n", " df[\"goals_home\"], df[\"goals_away\"], df[\"team_home\"], df[\"team_away\"]\n", ")\n", "clf.fit()" ] }, { "cell_type": "markdown", "id": "63a12589-0066-431f-8444-92e2944b55a4", "metadata": {}, "source": [ "## The model's parameters" ] }, { "cell_type": "code", "execution_count": 4, "id": "1831867d-c26e-4970-9586-a9e23e75cfed", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "Module: Penaltyblog\n", "\n", "Model: Poisson\n", "\n", "Number of parameters: 41\n", "Log Likelihood: -1057.712\n", "AIC: 2197.424\n", "\n", "Team Attack Defence \n", "------------------------------------------------------------\n", "Arsenal 1.133 -0.937 \n", "Aston Villa 0.84 -0.618 \n", "Bournemouth 0.813 -0.65 \n", "Brighton 0.777 -0.837 \n", "Burnley 0.87 -0.91 \n", "Chelsea 1.349 -0.806 \n", "Crystal Palace 0.543 -0.922 \n", "Everton 0.899 -0.795 \n", "Leicester 1.306 -1.084 \n", "Liverpool 1.536 -1.283 \n", "Man City 1.721 -1.206 \n", "Man United 1.286 -1.216 \n", "Newcastle 0.755 -0.766 \n", "Norwich 0.391 -0.521 \n", "Sheffield United 0.761 -1.163 \n", "Southampton 1.052 -0.719 \n", "Tottenham 1.218 -0.953 \n", "Watford 0.706 -0.669 \n", "West Ham 1.014 -0.688 \n", "Wolves 1.031 -1.125 \n", "------------------------------------------------------------\n", "Home Advantage: 0.229" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "clf" ] }, { "cell_type": "code", "execution_count": 5, "id": "fc93ec32-d113-4155-a516-abfe58dc8469", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "{'attack_Arsenal': np.float64(1.1331228901941925),\n", " 'attack_Aston Villa': np.float64(0.8398879945877571),\n", " 'attack_Bournemouth': np.float64(0.8130891418922739),\n", " 'attack_Brighton': np.float64(0.7765246201514078),\n", " 'attack_Burnley': np.float64(0.8703020733730807),\n", " 'attack_Chelsea': np.float64(1.3487330505653232),\n", " 'attack_Crystal Palace': np.float64(0.542542658860153),\n", " 'attack_Everton': np.float64(0.8994384134087898),\n", " 'attack_Leicester': np.float64(1.3056835701150769),\n", " 'attack_Liverpool': np.float64(1.5361418198993209),\n", " 'attack_Man City': np.float64(1.7212739991171064),\n", " 'attack_Man United': np.float64(1.2855299321448665),\n", " 'attack_Newcastle': np.float64(0.7545391466661135),\n", " 'attack_Norwich': np.float64(0.39112619748378996),\n", " 'attack_Sheffield United': np.float64(0.7614765214466674),\n", " 'attack_Southampton': np.float64(1.0516113492381278),\n", " 'attack_Tottenham': np.float64(1.217789270936845),\n", " 'attack_Watford': np.float64(0.706464518130879),\n", " 'attack_West Ham': np.float64(1.0135091468268111),\n", " 'attack_Wolves': np.float64(1.0312136849518139),\n", " 'defense_Arsenal': np.float64(-0.9373592173792837),\n", " 'defense_Aston Villa': np.float64(-0.61838890813481),\n", " 'defense_Bournemouth': np.float64(-0.6497773955489574),\n", " 'defense_Brighton': np.float64(-0.8366635726155827),\n", " 'defense_Burnley': np.float64(-0.9096437372541103),\n", " 'defense_Chelsea': np.float64(-0.8056792271120288),\n", " 'defense_Crystal Palace': np.float64(-0.9217221459400613),\n", " 'defense_Everton': np.float64(-0.7950817796413925),\n", " 'defense_Leicester': np.float64(-1.0841102810145857),\n", " 'defense_Liverpool': np.float64(-1.2833717774714317),\n", " 'defense_Man City': np.float64(-1.2063222477241144),\n", " 'defense_Man United': np.float64(-1.2156318569089062),\n", " 'defense_Newcastle': np.float64(-0.7660202258760153),\n", " 'defense_Norwich': np.float64(-0.5206704779032895),\n", " 'defense_Sheffield United': np.float64(-1.162693150527101),\n", " 'defense_Southampton': np.float64(-0.7187475334394907),\n", " 'defense_Tottenham': np.float64(-0.9533484235323105),\n", " 'defense_Watford': np.float64(-0.6693845588122723),\n", " 'defense_West Ham': np.float64(-0.6878743729022483),\n", " 'defense_Wolves': np.float64(-1.125240717318774),\n", " 'home_advantage': np.float64(0.22925183510740513)}" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "clf.get_params()" ] }, { "cell_type": "markdown", "id": "43bb1f12-7010-421b-bf93-bb8e1dba2df6", "metadata": {}, "source": [ "## Predict Match Outcomes" ] }, { "cell_type": "code", "execution_count": 6, "id": "3a047b77-707d-46b6-bcf8-57f3356efee3", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "Module: Penaltyblog\n", "\n", "Class: FootballProbabilityGrid\n", "\n", "Home Goal Expectation: [1.89677094]\n", "Away Goal Expectation: [0.77712187]\n", "\n", "Home Win: 0.6385320878305208\n", "Draw: 0.21487358807665044\n", "Away Win: 0.1465943221683105" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "probs = clf.predict(\"Liverpool\", \"Wolves\")\n", "probs" ] }, { "cell_type": "markdown", "id": "2a5274e7-d13e-455b-8e77-a6f51ba6f830", "metadata": {}, "source": [ "### 1x2 Probabilities" ] }, { "cell_type": "code", "execution_count": 7, "id": "cc1d6199-c35e-4ea3-bf82-a89c31a7277d", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "[np.float64(0.6385320878305208),\n", " np.float64(0.21487358807665044),\n", " np.float64(0.1465943221683105)]" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "probs.home_draw_away" ] }, { "cell_type": "code", "execution_count": 8, "id": "eef96983-d83d-4c39-bd49-47cb4a704ab4", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "np.float64(0.6385320878305208)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "probs.home_win" ] }, { "cell_type": "code", "execution_count": 9, "id": "e08561b2-07ed-47b3-89d7-14c0a05cf854", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "np.float64(0.21487358807665044)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "probs.draw" ] }, { "cell_type": "code", "execution_count": 10, "id": "594e21a7-9a75-49a3-b3e8-50fa4bd8ac51", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "np.float64(0.1465943221683105)" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "probs.away_win" ] }, { "cell_type": "markdown", "id": "9996be1b-acf8-4305-9bf0-6e4832505d47", "metadata": {}, "source": [ "### Probablity of Total Goals >1.5" ] }, { "cell_type": "code", "execution_count": 11, "id": "8da5ea91-ff28-4c6d-b6bf-0d5ef417da2b", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "np.float64(0.7465632504485541)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "probs.total_goals(\"over\", 1.5)" ] }, { "cell_type": "markdown", "id": "5a0876d3-9d69-4b63-ae8a-d2b3b8f40aa6", "metadata": {}, "source": [ "### Probability of Asian Handicap 1.5" ] }, { "cell_type": "code", "execution_count": 12, "id": "280e7570-5010-4b39-8104-71ca27e4005a", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "np.float64(0.3844258513443399)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "probs.asian_handicap(\"home\", 1.5)" ] }, { "cell_type": "markdown", "id": "f1205e38-8afc-45fc-ba5f-59292aad9e21", "metadata": {}, "source": [ "## Probability of both teams scoring" ] }, { "cell_type": "code", "execution_count": 13, "id": "1b63af09-9383-4c5a-ae1c-dadb1a57193a", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "np.float64(0.4592035336970112)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "probs.both_teams_to_score" ] } ], "metadata": { "kernelspec": { "display_name": "venv", "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": "3.13.1" } }, "nbformat": 4, "nbformat_minor": 5 }