Behold, the idiocy that is John Hollinger

[grndmstr_c]

Originally Posted by chumdawg

Yes! This is the part of our discussion that I am finding most stimulating. I think there are several rich areas to mine. For example, let's say that we are tied with two minutes left, or one minute even. Or to put it in our terms, for two or four or some number of "possessions." What are the thresholds in the respective scenarios where we can say with significant certainty that a team must have been a 55/45 or 60/40 favorite rather than a coin flip, for example.

Since you are crunching numbers, let me make sure I am thinking of "possessions" in the same way that you are. Are you calling a sequence where each team gets the ball one possession or two?

I'm calling a sequence where each team gets the ball one possession, though in my simple examples where there are no ties the I'm just using the word possession to refer to the smallest unit of play from which superiority/inferiority can be decided.

While I'm at it a quick correction. I overstated the probabilities of winning 100 and 10 possessions earlier (forgot to hit the square root key). It'd actually be more like 84% and 63%, respectively, using the 55/45 base odds. The 97-98% and 75% figures should be close to the true values if the base odds are 60/40, though (those larger figures would also be applicable with 55/45 base odds and sample sizes of 400 and 40 possessions, respectively).

The range of things that can occur on a single offensive possession in basketball actually makes specifying the distributions for those hypothesis tests your talking about a fairly laborious affair. You'd need to know the probabilities for each type of shot and turnover on the offensive and defensive end for each team, you'd need to know the shooting efficiencies by type of shot on both ends, you'd need to know rebounding probabilities, and you'd need to have some model for how offensive and defensive proficiencies offset one another.