For a project, I am looking for idea to model for the distribution of corners in football matches. I know that the number of goals can be model by a Poisson distribution, but for the number of corners, the distribution has larger tails. I think it is partly due to the fact that after a corner, the ball is put back in the game on one extrema of the field and this makes the probability of a second corner more likely. Would any of you have an idea of a model I could use?

Precisions on the model I plan to use My initial idea is to adapt the Maher Model for the number of goals in soccer matches. In this model the number of corners of scored by team $T$ when playing vs team $T'$ is assumed to follow a Poisson distribution with Parameter $a_T d_{T'}$ where $a_T$ and $d_T$ are the attack and defense scores of team $T$ which are estimated from the data using maximum likelihood.

I am looking for a distribution different from the Poisson distribution (fatter tails) which generalizes the Maher model to the distribution of corners. A distribution for which estimating the parameters via maximal likelihood is possible would be perfect.

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    $\begingroup$ You can try negative binomial distribution. It has the property of overdispersion (large right tail). $\endgroup$ – stans Jan 21 '18 at 22:55
  • $\begingroup$ No simple distribution will be an exact match. Do you particularly need a specific distribution for something? There are a number of heavier-tailed distributions that might be a reasonable approximation. I'd probably start with a negative binomial if it was actually necessary to have one at all. $\endgroup$ – Glen_b Jan 21 '18 at 22:56
  • $\begingroup$ Sure, but that is just a starting point for your creative process. In your place, I would try negative binomial regression, then play with a mixture of distributions, perhaps. $\endgroup$ – stans Jan 21 '18 at 23:05
  • $\begingroup$ I just edited the initial message with more precisions $\endgroup$ – Robin Nicole Jan 21 '18 at 23:13

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