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

.. only:: html

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

        Click :ref:`here <sphx_glr_download_gallery_lesson5_plot_simulatematch.py>`
        to download the full example code

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

.. _sphx_glr_gallery_lesson5_plot_simulatematch.py:


Simulating a match
==================

Before we get started, we are going to simulate a football match
using a very simple model. One in which goals occur completely at random
during the match.

.. GENERATED FROM PYTHON SOURCE LINES 10-16

.. code-block:: default


    import numpy as np
    import numpy.random as rnd
    import time
    import pylab as plt








.. GENERATED FROM PYTHON SOURCE LINES 17-20

Setting parameters
----------------------------
Lets set up the basic scoring rates for football

.. GENERATED FROM PYTHON SOURCE LINES 20-30

.. code-block:: default


    #Length of match
    match_minutes = 90
    #Average goals per match
    goals_per_match = 2.79
    #Probability of a goal per minute
    prob_per_minute = np.array(goals_per_match/match_minutes)
    print('The probability of a goal per minute is %5.5f. \n' % prob_per_minute )






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

 .. code-block:: none

    The probability of a goal per minute is 0.03100. 





.. GENERATED FROM PYTHON SOURCE LINES 31-36

Simulating a single game
----------------------------
Now we simulate a single game. Goals go in with the same probability every minute.
Run the simulation below 10 times. How many times were there 3 goals in a match?


.. GENERATED FROM PYTHON SOURCE LINES 36-57

.. code-block:: default


    #Count of the number of goals
    goals=0

    for minute in range(match_minutes):

      #Generate a random number between 0 and 1.
      r=rnd.rand(1,1)

      #Prints an X when there is a goal and a zero otherwise.
      if (r < prob_per_minute):
        #Goal - if the random number is less than the goal probability.
        print('X', end = ' ')
        goals=goals+1
        time.sleep(1)  #Longer pause
      else:
        print('o', end = ' ')
        time.sleep(0.1)  #Short pause
    print('\n')
    print('Final whistle. \n \nThere were ' + str(goals) + ' goals.')





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

 .. code-block:: none

    o o o o o o o o o o o X o o o o o o o o o o o X o o o o o o o o o o o X o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o 

    Final whistle. 
 
    There were 3 goals.




.. GENERATED FROM PYTHON SOURCE LINES 58-60

It is likely that about 2 or 3 of your simulations ended with 3 goals.
Most matches have between 0 and 5 goals. It is likely you saw at most one match with 0 goals.

.. GENERATED FROM PYTHON SOURCE LINES 63-65

Simulating goals over a season
----------------------------

.. GENERATED FROM PYTHON SOURCE LINES 65-116

.. code-block:: default


    #  We now simulate 380 matches of a football season and look at how well it predicts the
    #  distribution of the number of goals. This is done in the code below: we loop over 380 matches,
    #  store the number of goals for each match in array and then we make a histogram of the number of goals.
    #


    def simulateMatch(n, p):
      # n - number of time units
      # p - probability per time unit of a goal
      # display_match == True then display simulation output for match.

      # Count the number of goals
      goals = 0

      for minute in range(n):
          # Generate a random number between 0 and 1.
          r = rnd.rand(1, 1)
          # Prints an X when there is a goal and a zero otherwise.
          if (r < p):
            # Goal - if the random number is less than the goal probability.
            goals = goals + 1

      return goals

    # Number of matches
    num_matches = 380

    # Loop over all the matches and print the number of goals.
    goals = np.zeros(num_matches)
    for i in range(num_matches):
      goals[i] = simulateMatch(match_minutes, prob_per_minute)
      #print('In match ' + str(i+1) + ' there were ' + str(int(goals[i])) + ' goals.')

    # Create a histogram

    fig, ax = plt.subplots(num=1)

    histogram_range = np.arange(-0.5, 10.51, 1)
    histogram_goals = np.histogram(goals, histogram_range)

    ax.bar(histogram_goals[1][:-1] + 0.5, histogram_goals[0], color='white', edgecolor='black', linestyle='-', alpha=0.5)
    ax.set_ylim(0, 100)
    ax.spines['top'].set_visible(False)
    ax.spines['right'].set_visible(False)
    ax.set_xticks(np.arange(0, 11, step=1))
    ax.set_yticks(np.arange(0, 101, step=20))
    ax.set_xlabel('Number of goals')
    ax.set_ylabel('Number of matches')
    plt.show()




.. image-sg:: /gallery/lesson5/images/sphx_glr_plot_simulatematch_001.png
   :alt: plot simulatematch
   :srcset: /gallery/lesson5/images/sphx_glr_plot_simulatematch_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 117-118

Run the code a few times and look at the resulting histogram.
Now we have seen this simulation, we can look at football...


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

   **Total running time of the script:** ( 0 minutes  11.797 seconds)


.. _sphx_glr_download_gallery_lesson5_plot_simulatematch.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_simulatematch.py <plot_simulatematch.py>`

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

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


.. only:: html

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

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