The coin flip analogy is used quite a bit, but how often it comes heads and tails is determined by any number factors; It's not an analogy so much of an example I use to try and illustrate how binomial variance(coin flip stuff) adds a layer of uncertainty to all the stats we look at in baseball (which is directly dependent on the sample size). People sometimes take that to mean I think baseball can be reduced to a coin flip, which couldn't be farther from the truth. I only begin with that uncertainty, since it's easily quantified and very large, when the sample size is small. There are many other uncertainties, many of which, the manager and coaching staff are in a prime position to try and gauge. Dave Bush has had prior success in the majors and because we expect a certain level of skill persistence, the default assumption is that he should continue to have success. There are factors that can throw a monkey wrench into that assumption of course. Injuries, change in mechanics, change in mental approach and age, to name a few. But if Yost and his staff aren't aware of any of those currently being a factor, why shouldn't they assume the most obvious and likely scenario? Bush might have simply flipped 9 heads, when 5 were expected and considering the underlying data, that sure looks to be the over riding cause of his misfortunes. If the sub-par innings mount, Yost and Melvin will have to re-evaluate the situation, since it will become less and less likely that bad luck is the cause. Furthermore, if a better option presents itself that trumps the uncertainty of recent bad performance, that could justify a move as well. Since they have to consider many different factors, there is no magic number, no definitive situation.