.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "gallery/lesson5/plot_SimulateMatches.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_gallery_lesson5_plot_SimulateMatches.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_gallery_lesson5_plot_SimulateMatches.py:


Simulating results
==================

We now use a Poisson regression to fit a model to the Premier League
and then we use the estimated values to simulate results between
two teams.

This code is adapted from
https://dashee87.github.io/football/python/predicting-football-results-with-statistical-modelling/

.. GENERATED FROM PYTHON SOURCE LINES 12-22

.. code-block:: default


    # importing the tools required for the Poisson regression model
    import statsmodels.api as sm
    import statsmodels.formula.api as smf
    import pandas as pd
    import matplotlib.pyplot as plt
    import numpy as np
    import seaborn
    from scipy.stats import poisson,skellam








.. GENERATED FROM PYTHON SOURCE LINES 23-26

Import data
-----------
Here we use football-data.co.uk

.. GENERATED FROM PYTHON SOURCE LINES 26-34

.. code-block:: default


    epl = pd.read_csv("https://www.football-data.co.uk/mmz4281/2122/E0.csv")
    ep = epl[['HomeTeam','AwayTeam','FTHG','FTAG']]
    epl = epl.rename(columns={'FTHG': 'HomeGoals', 'FTAG': 'AwayGoals'})
    epl.head()

    epl = epl[:-10]








.. GENERATED FROM PYTHON SOURCE LINES 35-39

Perform the regression
-----------
In the fit, we include a parameter for home advantage.
Team and opponent are fixed effects.

.. GENERATED FROM PYTHON SOURCE LINES 39-50

.. code-block:: default


    goal_model_data = pd.concat([epl[['HomeTeam','AwayTeam','HomeGoals']].assign(home=1).rename(
                columns={'HomeTeam':'team', 'AwayTeam':'opponent','HomeGoals':'goals'}),
               epl[['AwayTeam','HomeTeam','AwayGoals']].assign(home=0).rename(
                columns={'AwayTeam':'team', 'HomeTeam':'opponent','AwayGoals':'goals'})])

    poisson_model = smf.glm(formula="goals ~ home + team + opponent", data=goal_model_data,
                            family=sm.families.Poisson()).fit()
    poisson_model.summary()







.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <table class="simpletable">
    <caption>Generalized Linear Model Regression Results</caption>
    <tr>
      <th>Dep. Variable:</th>         <td>goals</td>      <th>  No. Observations:  </th>  <td>   740</td> 
    </tr>
    <tr>
      <th>Model:</th>                  <td>GLM</td>       <th>  Df Residuals:      </th>  <td>   700</td> 
    </tr>
    <tr>
      <th>Model Family:</th>         <td>Poisson</td>     <th>  Df Model:          </th>  <td>    39</td> 
    </tr>
    <tr>
      <th>Link Function:</th>          <td>Log</td>       <th>  Scale:             </th> <td>  1.0000</td>
    </tr>
    <tr>
      <th>Method:</th>                <td>IRLS</td>       <th>  Log-Likelihood:    </th> <td> -1043.1</td>
    </tr>
    <tr>
      <th>Date:</th>            <td>Thu, 20 Nov 2025</td> <th>  Deviance:          </th> <td>  776.72</td>
    </tr>
    <tr>
      <th>Time:</th>                <td>07:03:14</td>     <th>  Pearson chi2:      </th>  <td>  681.</td> 
    </tr>
    <tr>
      <th>No. Iterations:</th>          <td>5</td>        <th>  Pseudo R-squ. (CS):</th>  <td>0.2498</td> 
    </tr>
    <tr>
      <th>Covariance Type:</th>     <td>nonrobust</td>    <th>                     </th>     <td> </td>   
    </tr>
    </table>
    <table class="simpletable">
    <tr>
                   <td></td>                 <th>coef</th>     <th>std err</th>      <th>z</th>      <th>P>|z|</th>  <th>[0.025</th>    <th>0.975]</th>  
    </tr>
    <tr>
      <th>Intercept</th>                  <td>    0.2470</td> <td>    0.203</td> <td>    1.214</td> <td> 0.225</td> <td>   -0.152</td> <td>    0.646</td>
    </tr>
    <tr>
      <th>team[T.Aston Villa]</th>        <td>   -0.1298</td> <td>    0.195</td> <td>   -0.666</td> <td> 0.506</td> <td>   -0.512</td> <td>    0.252</td>
    </tr>
    <tr>
      <th>team[T.Brentford]</th>          <td>   -0.1589</td> <td>    0.198</td> <td>   -0.802</td> <td> 0.423</td> <td>   -0.547</td> <td>    0.230</td>
    </tr>
    <tr>
      <th>team[T.Brighton]</th>           <td>   -0.3735</td> <td>    0.209</td> <td>   -1.788</td> <td> 0.074</td> <td>   -0.783</td> <td>    0.036</td>
    </tr>
    <tr>
      <th>team[T.Burnley]</th>            <td>   -0.5263</td> <td>    0.220</td> <td>   -2.395</td> <td> 0.017</td> <td>   -0.957</td> <td>   -0.096</td>
    </tr>
    <tr>
      <th>team[T.Chelsea]</th>            <td>    0.2714</td> <td>    0.177</td> <td>    1.529</td> <td> 0.126</td> <td>   -0.077</td> <td>    0.619</td>
    </tr>
    <tr>
      <th>team[T.Crystal Palace]</th>     <td>   -0.1370</td> <td>    0.196</td> <td>   -0.699</td> <td> 0.484</td> <td>   -0.521</td> <td>    0.247</td>
    </tr>
    <tr>
      <th>team[T.Everton]</th>            <td>   -0.2847</td> <td>    0.204</td> <td>   -1.394</td> <td> 0.163</td> <td>   -0.685</td> <td>    0.116</td>
    </tr>
    <tr>
      <th>team[T.Leeds]</th>              <td>   -0.3127</td> <td>    0.207</td> <td>   -1.507</td> <td> 0.132</td> <td>   -0.719</td> <td>    0.094</td>
    </tr>
    <tr>
      <th>team[T.Leicester]</th>          <td>    0.0481</td> <td>    0.188</td> <td>    0.256</td> <td> 0.798</td> <td>   -0.320</td> <td>    0.416</td>
    </tr>
    <tr>
      <th>team[T.Liverpool]</th>          <td>    0.4522</td> <td>    0.170</td> <td>    2.657</td> <td> 0.008</td> <td>    0.119</td> <td>    0.786</td>
    </tr>
    <tr>
      <th>team[T.Man City]</th>           <td>    0.5115</td> <td>    0.168</td> <td>    3.036</td> <td> 0.002</td> <td>    0.181</td> <td>    0.842</td>
    </tr>
    <tr>
      <th>team[T.Man United]</th>         <td>    0.0156</td> <td>    0.189</td> <td>    0.083</td> <td> 0.934</td> <td>   -0.354</td> <td>    0.385</td>
    </tr>
    <tr>
      <th>team[T.Newcastle]</th>          <td>   -0.2841</td> <td>    0.204</td> <td>   -1.389</td> <td> 0.165</td> <td>   -0.685</td> <td>    0.117</td>
    </tr>
    <tr>
      <th>team[T.Norwich]</th>            <td>   -0.8697</td> <td>    0.248</td> <td>   -3.507</td> <td> 0.000</td> <td>   -1.356</td> <td>   -0.384</td>
    </tr>
    <tr>
      <th>team[T.Southampton]</th>        <td>   -0.2770</td> <td>    0.205</td> <td>   -1.354</td> <td> 0.176</td> <td>   -0.678</td> <td>    0.124</td>
    </tr>
    <tr>
      <th>team[T.Tottenham]</th>          <td>    0.1294</td> <td>    0.183</td> <td>    0.706</td> <td> 0.480</td> <td>   -0.230</td> <td>    0.489</td>
    </tr>
    <tr>
      <th>team[T.Watford]</th>            <td>   -0.5181</td> <td>    0.220</td> <td>   -2.357</td> <td> 0.018</td> <td>   -0.949</td> <td>   -0.087</td>
    </tr>
    <tr>
      <th>team[T.West Ham]</th>           <td>    0.0398</td> <td>    0.187</td> <td>    0.213</td> <td> 0.831</td> <td>   -0.327</td> <td>    0.406</td>
    </tr>
    <tr>
      <th>team[T.Wolves]</th>             <td>   -0.4429</td> <td>    0.212</td> <td>   -2.088</td> <td> 0.037</td> <td>   -0.859</td> <td>   -0.027</td>
    </tr>
    <tr>
      <th>opponent[T.Aston Villa]</th>    <td>    0.1071</td> <td>    0.203</td> <td>    0.529</td> <td> 0.597</td> <td>   -0.290</td> <td>    0.504</td>
    </tr>
    <tr>
      <th>opponent[T.Brentford]</th>      <td>    0.1297</td> <td>    0.200</td> <td>    0.649</td> <td> 0.516</td> <td>   -0.262</td> <td>    0.521</td>
    </tr>
    <tr>
      <th>opponent[T.Brighton]</th>       <td>   -0.0994</td> <td>    0.211</td> <td>   -0.470</td> <td> 0.638</td> <td>   -0.514</td> <td>    0.315</td>
    </tr>
    <tr>
      <th>opponent[T.Burnley]</th>        <td>    0.0579</td> <td>    0.202</td> <td>    0.286</td> <td> 0.775</td> <td>   -0.339</td> <td>    0.455</td>
    </tr>
    <tr>
      <th>opponent[T.Chelsea]</th>        <td>   -0.3702</td> <td>    0.230</td> <td>   -1.613</td> <td> 0.107</td> <td>   -0.820</td> <td>    0.080</td>
    </tr>
    <tr>
      <th>opponent[T.Crystal Palace]</th> <td>   -0.0219</td> <td>    0.208</td> <td>   -0.105</td> <td> 0.916</td> <td>   -0.429</td> <td>    0.385</td>
    </tr>
    <tr>
      <th>opponent[T.Everton]</th>        <td>    0.2573</td> <td>    0.194</td> <td>    1.325</td> <td> 0.185</td> <td>   -0.123</td> <td>    0.638</td>
    </tr>
    <tr>
      <th>opponent[T.Leeds]</th>          <td>    0.4973</td> <td>    0.185</td> <td>    2.688</td> <td> 0.007</td> <td>    0.135</td> <td>    0.860</td>
    </tr>
    <tr>
      <th>opponent[T.Leicester]</th>      <td>    0.2134</td> <td>    0.197</td> <td>    1.085</td> <td> 0.278</td> <td>   -0.172</td> <td>    0.599</td>
    </tr>
    <tr>
      <th>opponent[T.Liverpool]</th>      <td>   -0.6001</td> <td>    0.248</td> <td>   -2.421</td> <td> 0.015</td> <td>   -1.086</td> <td>   -0.114</td>
    </tr>
    <tr>
      <th>opponent[T.Man City]</th>       <td>   -0.6284</td> <td>    0.251</td> <td>   -2.501</td> <td> 0.012</td> <td>   -1.121</td> <td>   -0.136</td>
    </tr>
    <tr>
      <th>opponent[T.Man United]</th>     <td>    0.1833</td> <td>    0.198</td> <td>    0.925</td> <td> 0.355</td> <td>   -0.205</td> <td>    0.572</td>
    </tr>
    <tr>
      <th>opponent[T.Newcastle]</th>      <td>    0.2445</td> <td>    0.194</td> <td>    1.258</td> <td> 0.209</td> <td>   -0.137</td> <td>    0.626</td>
    </tr>
    <tr>
      <th>opponent[T.Norwich]</th>        <td>    0.4959</td> <td>    0.185</td> <td>    2.687</td> <td> 0.007</td> <td>    0.134</td> <td>    0.858</td>
    </tr>
    <tr>
      <th>opponent[T.Southampton]</th>    <td>    0.2915</td> <td>    0.193</td> <td>    1.509</td> <td> 0.131</td> <td>   -0.087</td> <td>    0.670</td>
    </tr>
    <tr>
      <th>opponent[T.Tottenham]</th>      <td>   -0.1604</td> <td>    0.215</td> <td>   -0.744</td> <td> 0.457</td> <td>   -0.583</td> <td>    0.262</td>
    </tr>
    <tr>
      <th>opponent[T.Watford]</th>        <td>    0.4646</td> <td>    0.186</td> <td>    2.492</td> <td> 0.013</td> <td>    0.099</td> <td>    0.830</td>
    </tr>
    <tr>
      <th>opponent[T.West Ham]</th>       <td>    0.0248</td> <td>    0.206</td> <td>    0.120</td> <td> 0.904</td> <td>   -0.378</td> <td>    0.428</td>
    </tr>
    <tr>
      <th>opponent[T.Wolves]</th>         <td>   -0.1530</td> <td>    0.215</td> <td>   -0.710</td> <td> 0.477</td> <td>   -0.575</td> <td>    0.269</td>
    </tr>
    <tr>
      <th>home</th>                       <td>    0.1502</td> <td>    0.062</td> <td>    2.405</td> <td> 0.016</td> <td>    0.028</td> <td>    0.273</td>
    </tr>
    </table>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 51-54

Simulating a game
-----------------
Let's now simulate a match between City and Arsenal

.. GENERATED FROM PYTHON SOURCE LINES 54-75

.. code-block:: default


    # Set teams here
    home_team='Man City'
    away_team='Arsenal'

    #Predict for Arsenal vs. Manchester City
    home_score_rate=poisson_model.predict(pd.DataFrame(data={'team': home_team, 'opponent': away_team,
                                           'home':1},index=[1]))
    away_score_rate=poisson_model.predict(pd.DataFrame(data={'team': away_team, 'opponent': home_team,
                                           'home':0},index=[1]))
    print(home_team + ' against ' + away_team + ' expect to score: ' + str(home_score_rate))
    print(away_team + ' against ' + home_team + ' expect to score: ' + str(away_score_rate))

    #Lets just get a result
    home_goals=np.random.poisson(home_score_rate)
    away_goals=np.random.poisson(away_score_rate)
    print(home_team + ': ' + str(home_goals[0]))
    print(away_team + ': '  + str(away_goals[0]))







.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    Man City against Arsenal expect to score: 1    2.481142
    dtype: float64
    Arsenal against Man City expect to score: 1    0.682894
    dtype: float64
    Man City: 4
    Arsenal: 1




.. GENERATED FROM PYTHON SOURCE LINES 76-79

Two-dimensional histogram of scores
-----------------------------------
This gives the probability of different score lines.

.. GENERATED FROM PYTHON SOURCE LINES 79-115

.. code-block:: default



    # Code to caluclate the goals for the match.
    def simulate_match(foot_model, homeTeam, awayTeam, max_goals=10):
        home_goals_avg = foot_model.predict(pd.DataFrame(data={'team': homeTeam,
                                                               'opponent': awayTeam, 'home': 1},
                                                         index=[1])).values[0]
        away_goals_avg = foot_model.predict(pd.DataFrame(data={'team': awayTeam,
                                                               'opponent': homeTeam, 'home': 0},
                                                         index=[1])).values[0]
        team_pred = [[poisson.pmf(i, team_avg) for i in range(0, max_goals + 1)] for team_avg in
                     [home_goals_avg, away_goals_avg]]
        return (np.outer(np.array(team_pred[0]), np.array(team_pred[1])))

    #Fill in the matrix
    max_goals=5
    score_matrix=simulate_match(poisson_model, home_team, away_team,max_goals)

    fig=plt.figure()
    ax=fig.add_subplot(1,1,1)
    pos=ax.imshow(score_matrix, extent=[-0.5,max_goals+0.5,-0.5,max_goals+0.5], aspect='auto',cmap=plt.cm.Reds)
    fig.colorbar(pos, ax=ax)
    ax.set_title('Probability of outcome')
    plt.xlim((-0.5,5.5))
    plt.ylim((-0.5,5.5))
    plt.tight_layout()
    ax.set_xlabel('Goals scored by ' + away_team)
    ax.set_ylabel('Goals scored by ' + home_team)
    plt.show()

    #Home, draw, away probabilities
    homewin=np.sum(np.tril(score_matrix, -1))
    draw=np.sum(np.diag(score_matrix))
    awaywin=np.sum(np.triu(score_matrix, 1))





.. image-sg:: /gallery/lesson5/images/sphx_glr_plot_SimulateMatches_001.png
   :alt: Probability of outcome
   :srcset: /gallery/lesson5/images/sphx_glr_plot_SimulateMatches_001.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  1.057 seconds)


.. _sphx_glr_download_gallery_lesson5_plot_SimulateMatches.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example


    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_SimulateMatches.py <plot_SimulateMatches.py>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_SimulateMatches.ipynb <plot_SimulateMatches.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_