Football Monte Carlo
“As flies to wanton boys we are for the gods, they kill us for their sport. Soon the science will not only be able to slow down the ageing of the cells, soon the science will fix the cells to the state and so we will become eternal. Only accidents, crimes, wars, will still kill us but unfortunately, crimes, wars, will multiply.
I love football. Thank you.”
This project was started with the aim of predicting the most likely outcome for a given set of games following a Poisson methodology initially set out by fivethirtyeight.
With a model able to predict single game outcomes we can scale it up, simulating full seasons from varying starting points and across different seasons to answer some further problems such as:
How important really is Home Advantage and Form
Were empty stadiums as important as pundits made us believe at the time?
How accurate can we make our model
Using Scikit-Learn to improve our metrics and reduce error
General points of interest
How big was Liverpool’s well publicised collapse last season in historical terms?
Introduction: Some Charts on the last season
We run 100 simulations of the 20/21 Premier League season from both a quarter and three quarters of the way through to find the possible range of final outcomes
Pre-loaded with an optimised measure of Home and Form Advantage to minimise errors with true observed events
Monte Carlo hints towards the historically elevated competitiveness of this last season: In the end only 8 points were between the 3rd and 8th place finishers
100 simulations a quarter of the way through the 20/21 season showed a very fluid table
With a quarter of the season remaining however, some positions are as good as taken
Home Advantage (0 - 100) in the final half of the 2019/2020 season was well above the median for the past decade
Home doesn’t need to be where the crowd is
In spite of intuition, following the resumption of the 19/20 season last year in empty stadiums, teams maintained a strong Home Advantage
Surprisingly, only two seasons in the past decade had a higher measure of Home Advantage over the final games of the season
I was also surprised by this, but it seems to actually be the case
Injury of key players for Liverpool led to a wild tumble of predicted finishing position from our model until halfway through the season, from which followed an equally strong rebound in form
Liverpool: There and back again
We identify who our model predicts to finish in first place at a quarter of the way through the season for the last ten seasons and then see how that has changed at midway and three quarters completion
This shows a distinct collapse in form by Liverpool after a spate of injuries, followed by just as notable a rebound to finish in the Champion’s League spots
We get a reasonable confidence in our model by noting that 9 out of 10 predicted pole sitters at a quarter of the way through the season finished in Champions League spots, inglorious outlier being Arsenal in the 2016/2017 season
How does it all work
Getting off the ground: Better than guesswork
After pulling our data we first identify our initial aim, to simulate the result of a set of upcoming matches based on historical results. With this aim, we must keep one thing in mind.
No two match histories are the same. A team that is bottom of the table at the beginning of the season may have played all their games against last season’s top 5 away from home; moreover they may have only narrowly lost those matches scoring a goal or two in the process. A goal against the best defense in the league could easily be worth three against poorer opponents.
This introduces the need to adjust each teams history by normalising for against whom and where they have played in all games leading up to the current game.
A simple example of this is a team which has played five matches, scoring one goal in each. However each of the opposing teams that they have faced let in three goals in the matches prior to theirs, they have thus drastically underperformed the average. When this underperforming team then faces a side that only has allowed one goal a game, they may struggle to score a single goal, a conclusion a first pass of the data wouldn’t tell you. We can thus do this after each match to update our measure for goals scored and conceded by each team in the league to get an ability to predict the total sum of goals scored for each consecutive match.
So, who wins?
Armed with a predicted performance for attack and defense for each team in the league, if we are faced with a certain matchup, how do we translate this to an actual outcome? We use the Poisson distribution, with the general outline of the process displayed by this great graphic from fivethirtyeight. The code snippet below shows the simplicity of the implementation in Python and we can loop over this rapidly to simulate a large number of games while feeding in updated team performances as the season progresses.
for match in score_pred.index: i = score_pred.loc[match]['Home Goals'] j = score_pred.loc[match]['Away Goals'] poiss_i = np.random.poisson(i) poiss_j = np.random.poisson(j) df_outcome.loc[match, ['Home Goals', 'Away Goals']] = [poiss_i, poiss_j] df_outcome.index = dates
Note in our model we do not re-adjust for draws as a large number of these occur naturally with our metrics: fivethirtyeight
Not quite done yet: Quantifying a “hunch”
Before we get started in earnest, there are a few more factors that we must introduce that are important to simulating results. What if a team top of the league faces a bottom of the table side fighting relegation at home, and on top of this the worse side is actually top of the form table, ie has the best performance in the past five matches? Football purists will swear up and down that the Home Advantage and current Form is just as important as any matchup. So how do we adjust for these, and how important is each of these really? This is a great way to introduce some Scikit-learn to our process, where we can adjust the weightings of these metrics such that we minimise the overall error in our prediction of each match result, aiming to capture a metric for each and then being able to analyse any evolution over the season.
Are our invented terms actually any use?
It is all well and good defining random variables, but are any of these actually any good once introduced in increasing our predictive power? For this we can finally leverage the handy Python package Scikit-Learn, if only briefly, for the error analysis it provides.
A good predictor makes your guesses more accurate, and thus we aim to reduce the error in all our predictions by varying the influence of our Home and Form advantage in small increments to find the point at which they give the most accurate predictions, in other words where our error (Or Mean Squared Error - MSE) is at a minimum.
We can perform this process as we move forward through a season, testing each combination of Home and Form advantage to find the smallest possible error in our predictions for the remaining games. This process has a two fold benefit: we can see how stable and reasonable our measures are; if the weighting jumps around rapidly then they are of little statistical merit, but we can also see how these intuitive yet intangible measures evolve over an individual season and between years.
We can then show the error in predictions as we vary both Home and Form Advantage for the remainder of the games in the season. Finding the weighting of both which provides the smallest error means we have a rough guide of what focus we should give to both and we can also look at how these change over the season.