#Monte Carlo Simulation

I was looking to try and predict the chance of two football teams in the UK Premier league reaching 37 points which is the normal level that teams need to reach to avoid being relegated.

#Why Monte Carlo ?

Well, with 10 games to go - it is possible that a team will win all 10 games, but not likely.

What I want to do is run the statistical model, and decide if it was a success of a failure. Then repeat this a number of times (i.e. 1 Million) - now taking the average, I should have a better approximation as to the real chance of the result.

#Scenario

There are 10 games left, and 2 teams have 25 and 23 points respectfully.

Each team performs (rather badly I am afraid to say) with different success.

Team 1, on average wins 15% of their games, and draws 40%. Team 2, on average wins 40% of their games, and draws 20%.

##Scoring

In Football (US readers, convert that to soccer), the game is scored as

• win, 3 points
• draw, 1 point
• loose, 0 points

#How will they fare ?

What are the chances of each team reaching 37 points ?

In order to calculate this, I need to develop a function which will run through the remaining 10 matches, use the percentages, and return a True/False answer as to have we reached 37 points.

##Simulator function

The simulator function requires a dictionary - I create this using a specific method.

#Setup the array for Middlebrough
def setup_vals_boro():
    return {'team':'Middlesbrough','points':25,'games':10,'winpct':0.3,'drawpct':0.6}

This dictionary is passed into the final_points (see below) method.

def final_points(g):
    '''
    Pass a dictionary with the values needed for the simulation
    '''
    points=g['points']
    for n in range(0,g['games']):
        result=random()
        if result <= g['winpct']:
            points += 3
        elif result <= g['drawpct']+g['winpct']:
            points += 1
    if points > 37:
        return True
    else:
        return False

The rest of the code is general plumbing.

#Code listing

from montecarlo import montecarlo
from random import random


#This is the function to calculate the final points
#Generally 37 points is the survival minimum

def final_points(g):
    '''
    Pass a dictionary with the values needed for the simulation
    '''
    points=g['points']
    for n in range(0,g['games']):
        result=random()
        if result <= g['winpct']:
            points += 3
        elif result <= g['drawpct']+g['winpct']:
            points += 1
    if points > 37:
        return True
    else:
        return False

#Setup the array for Middlebrough

def setup_vals_boro():
    return {'team':'Middlesbrough','points':25,'games':10,'winpct':0.15,'drawpct':0.4}

#Setup the array for Sunderland
def setup_vals_sund():
    return {'team':'Sunderland','points':23,'games':10,'winpct':0.4,'drawpct':0.2}

def output_result(success, iterations, final=False):
    if final:
        print("After {} Iterations chance of reaching 37 points {:3.2F}% ".format(iterations,montecarlo.probability(success, iterations)*100.0))
        
mc = montecarlo(final_points,setup=setup_vals_boro,output=output_result)
print("Calculating chances for Middlesbrough")
mc.run(iterations=50000,output_every=50000)

mc = montecarlo(final_points,setup=setup_vals_sund,output=output_result)
print("Calculating chances for Sunderland")
mc.run(iterations=50000,output_every=50000)

The output should be close to this....

Calculating chances for Middlesbrough
After 50000 Iterations chance of reaching 37 points 76.94% 
Calculating chances for Sunderland
After 50000 Iterations chance of reaching 37 points 76.22% 

#Summary

Monte Carlo simulation is an interesting way to test simulation theories, and I hope this will give you the confidence to have a go yourself.

The main simulator function is obviously too simplistic - but getting that to be more accurate will require much more data, and more complexity.