METHODOLOGY
How is the card risk of a Serie A club estimated?
For each club we calculate how many cards, bookings plus sending-offs, it receives per match on average, giving more weight to recent matches, and how many fouls it commits. The model treats cards as Poisson events. For players we start from bookings per 90 minutes, pulled towards the average of their teammates when few minutes have been played.
Frequently asked questions
How much do recent matches count?
Each match is weighted by exp(−ξ × days) with ξ = 0.003: the weight halves in about 231 days. We do this because the number of cards per match changes from one season to the next, and an average that counts many seasons equally does not represent the current one.
How is the risk of an individual player estimated?
From his bookings per 90 minutes, pulled towards the average of his teammates in proportion to minutes played: the weight of the individual figure is minutes/(minutes + 450). The risk is the probability of at least one booking in a match. We list only players with at least 450 minutes.
Are derbies and the referee taken into account?
The model estimates a derby effect from the data, shown on the Discipline page, but the per-club estimates do not apply it. Referee strictness is fitted from the data, but is not applied to the per-club estimates.
Limits and missing data
If the card model has not been fitted yet, the Discipline page says so instead of showing numbers.