Quote:
Originally Posted by PokerHero77
As Poission approximates a binomial distribution, it only works if the events are independent.
I don't think pitches are independent, but for your model maybe they are independent enough. For example, if a player whiffs on the first x pitches does that make it more likely the next pitch is a whiff?
I would agree with this. In actuality, yes, there are a very large number of variables that make each pitch dependent on the last. However, as the saying goes, all models are wrong, but some are useful. The actual computation power to model how many hits a player would get given the number of variables to a "near perfect" would be computationally intractable. But, I would argue that given the assumptions outlined, Poisson is "good enough," assuming one is aware of the limitations.