Serie A 2019-20 without any stop

Serie A till March 2020

Serie A is regarded as one of the best football leagues in the world and it is often depicted as the most tactical national league. During the season, which usually runs from August to May, each club plays each of the other teams twice; once at home and once away, totaling 38 games for each team by the end of the season. Thus, in Italian football a true round-robin format is used. In the first half of the season, called the andata, each team plays once against each league opponent, for a total of 19 games. In the second half of the season, called the ritorno, the teams play in exactly the same order that they did in the first half of the season, the only difference being that home and away situations are switched. In this year, due to covid-19 pandemic, Serie A competition stopped at 26th round, the seventh round of ritorno with 4 matches in 25th round to be recovered too.

predicting season final results

In order to answer the intriguing question, at least for Italian football fans and the Author alike, about the final Serie A ranking (without covid-19 pandemic), three quantitative analysis have been exploited:

• pythagorean win expectations;

• Davidson model of competition;

• Monte Carlo simulation drawing from Poisson distributions of goals scored.

pythagorean win expectation

Stealing from sabermetrics the pythagorean win expectation method, it is possible to estimate the number of points a given club would have won completing Serie A 2019-20 competition. Compared to the original idea, it is needed to take into account the result of the tie which is not an actual possibility in baseball.

Therefore the formula used is given by: \[ pytagoreanPoints = winExpectation * remainingMatches * avgPtsD istributed \]

where

• pythagorean ‘winExpectation’ is calculated as per the following formula: \[winExpectation = \frac{GoalsScored^{exponent}}{GoalsScored^{1.32} + GoalsConceded^{exponent}}\]

• remainingMatches equals 12 for every Club except Atalanta, Cagliari, Hellas Verona, Inter, Parma, Sampdoria, Sassuolo and Torino because their matches in 25th round have been postponed.

• average points distributed in a match takes in consideration the potential tie result and it is calculated for all clubs as \[avgPtsD istributed = \frac{totalSeasonPoints}{matchesPlayed}\]

which result in 2.7734375 average points distributed each match.

davidson model of competition

Stealing from tennis analytics, it is possible to make ranking predictions from pairwise comparison using Davidson extension to Bradley-Terry model of competition ¹. Davidson model takes into account the probability of a tie and home advantage as explicit predictor. The model is fitted on few data points but the graph of comparison is fully connected because the first half of the season has been already played and therefore all teams played against everyone else.

Monte Carlo simulation

In this third part of the post the idea is to simulate every remaining match by running a Monte Carlo simulation drawing the results from the fitted Poisson distributions.

‘Monte Carlo simulation’ propagates uncertainties in model inputs into uncertainties in model outputs (final standings). Monte Carlo simulation relies on the process of explicitly representing uncertainties by specifying inputs as probability distributions. If the inputs describing a system are uncertain, the prediction of future performance is necessarily uncertain. That is, the result of any analysis based on inputs represented by probability distributions is itself a probability distribution.

Inputs for this simulation are goals scored and conceded in each match. The distribution this goals should follow is a Poisson distribution as per literature. The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time (a match) if these events occur with a known constant mean rate and independently of the time since the last event [wikipedia]. Its PMF is \[ p(goals = k)=\frac{\lambda^k e^{-\lambda}}{k!}\] where \(\lambda\) is both the mean and the variance of the distribution.

In order to check this is reasonably correct, the histogram for actual total goals scored in the played matched of season 2019-20 is plotted below against the Poisson distribution with lambda parameter equals the mean of total goals scored at home and away.

Also a formal goodness of fit test confirms that actual distribution is not significantly different from Poisson checking the old fashioned p value > 0.05.

## Chi-squared statistic:  9.790972 
## Degree of freedom of the Chi-squared distribution:  5 
## Chi-squared p-value:  0.08137932 
## Chi-squared table:
##      obscounts theocounts
## <= 0  17.00000   13.88925
## <= 1  42.00000   40.47413
## <= 2  45.00000   58.97208
## <= 3  70.00000   57.28277
## <= 4  42.00000   41.73140
## <= 5  17.00000   24.32158
## > 5   23.00000   19.32879
## 
## Goodness-of-fit criteria
##                                1-mle-pois
## Akaike's Information Criterion   995.4709
## Bayesian Information Criterion   999.0161

Same check is performed for goal scored by home and by away team

The goodness of fit for the home goals distribution is confirmed by a very high p value equal to 0.4684794.

The goodness of fit for the away goals distribution is confirmed by a very high p value equal to 0.9887426.

which Team would have been the winner?

As per the 3 models above, the “scudetto” (or championship) was a matter of 2 clubs only: Juventus and Lazio. Juventus had a slight advantage in points achieved even if not reflected in the win expectations and in the club abilities according to Davidson model so Lazio chances of contending for victory was good.

Now that the championship restarts after a long period of stop no one can say anything about the current status of club abilities so it is really difficult to predict final results. The Author suggests to come back and read this post again when actual championship end just to check if any significant changes will occur.

As a side note please consider the effort of the Author, an irrational football fan, to stick to data science only while writing this post.

Feel free to email me if you would like to delve into analysis details, thanks for reading!

The analysis and simulations shown in this post have been executed using R as main computation tool together with its gorgeous ecosystem. In particular Davidson modeling relied on “gnm” and “BradleyTerry2” packages. “doParallel” package allowed to quickly perform the Monte Carlo simulation.