Archive for FIFA

Poisson-Belgium 0-0

Posted in Statistics with tags , , , , , , , , , , , , , , , , , , , on December 5, 2022 by xi'an

“Statistical match predictions are more accurate than many people realize (…) For the upcoming Qatar World Cup, Penn’s model suggests that Belgium (…) has the highest chances of raising the famous trophy, followed by Brazil”

Even Nature had to get entries on the current football World cup, with a paper on data-analytics reaching football coaches and teams. This is not exactly prime news, as I remember visiting the Department of Statistics of the University of Glasgow in the mid 1990’s and chatting with a very friendly doctoral student who was consulting for the Glasgow Rangers (or Celtics?!) on the side at the time. And went back to Ireland to continue with a local team (Galway?!).

The paper reports on different modellings, including one double-Poisson model by (PhD) Matthew Penn from Oxford and (maths undergraduate) Joanna Marks from Warwick, which presumably resemble the double-Poisson version set by Leonardo Egidi et al. and posted on Andrews’ blog a few days ago. Following an earlier model by my friends Karlis & Ntzoufras in 2003. While predictive models can obviously fail, this attempt is missing Belgium, Germany, Switzerland, Mexico, Uruguay, and Denmark early elimination from the cup. One possible reason imho is that national teams do not play that often when players are employed by different clubs in many counties, hence are hard to assess, but I cannot claim any expertise or interest in the game.

a football post?!

Posted in Statistics with tags , , , , , , , , , , , , , , on June 22, 2022 by xi'an

I am not interested in football, neither as a player (a primary school trauma when I was the last being picked!) or as a fan, contrary to my dad (who was a football referee in his youth) and my kids, but Gareth Roberts (University of Warwick) and Jeff Rosenthal wrote a paper on football draws for the (FIFA) World Cup, infamously playing in Qatar by the end of the year, which Gareth presented in a Warwick seminar.

For this tournament, there are 32 teams, first playing against opponent teams supposedly drawn from a uniform distribution over all draw assignments, within 8 groups of 4 teams, with constraints like 1-2 EU teams per group, 0-1 from the other regions. As done at the moment and on TV, the tournament is filled one team at time by drawing from Pot 1, then Pot 2, then Pot 3, & Pot 4. &tc.. Applying the constraints one draw at a time, conditional on the past draws and the constraints, rather obviously creates non-uniformity! Uniformity would be achievable by rejection sampling (with a success probability of 1/540!) But this is not televisesque enough…

A debiasing solution is found by using several balls for each team in the right proportion, correcting for the sequential draws. Still impractical when requiring 10¹⁴ balls…!

The fun in their paper is that the problem can be formulated as a particle filter, estimating the right probabilities by randomising the number of balls [hidden randomness] and estimating the probability for team j to be included by a few thousands draws. With some stratified sampling on the side to minimise randomness. Removing the need for the (intractable?) distribution is thus achieved by retrospective sampling, as in pseudo-marginal MCMC. Alternatively, one could swap pairs of teams by a simplistic MCMC algorithm, with no worry about stationarity and the possibility of on-screen draws. (Jeff devised a Java applet to simulate an actual draw.) Obviously, it is still a far stretch that this proposal will be implemented for the next World Cup. If so, I will watch it!

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