I have a data set of cards (yellow and red cards) shown in Spanish La Liga games since 2013/14 season. I was going to use Poisson to calculate the probability of x cards being shown in a game. However, the mean and the variance of my data are not equal.
Mean = 5.36 Variance = 4.69
I'm aware that the mean should equal the variance if I'm going to use Poisson. So what should I be using instead? Is there a different probability distribution to use in this case or is there a way to adjust the poisson distribution for the difference between the mean and variance?