Quote:
Originally Posted by grndmstr_c
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.
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On the "range of things that can occur" point, I would like to be able to neatly sum all those under one category. Something like "clutch-ness." Meaning, a catch-all for all the possible scenarios, as they impact the game.
In other words, if we are going to make the claim that the Mavs have a closing lineup that is closer to 55/45 or 60/40 than it is to a coin flip, we don't especially care *how* they get there, but *that* they get there.
Ten possessions each, if by that we mean that each team gets the ball ten times, is probably overdoing it if we want to counter Hollinger's claim that tight games are a coin flip. We'd probably need to get it down to five times each, or less, that both teams had the ball.
Given the correction you noted, with regard to the 55/45 favorite, I'm not sure how optimistic I am that the same 55/45 favorite would be expected to be that far removed from chance over the course of five possessions (or "trials").
What would the numbers be for a 55/45 team to win a five-possession-or-less game? (I realize that is a different question than "to win a five-possession game.")