However, you were the one who started with a simplification. So what's your solution? That we not talk about it at all?
I did start with making several simplifying assumptions, which you readily dismiss. The reason I made them was not because they represented reality with pinpoint precision, but because they let me track changes and actually try to explain what happens.
Talking about "overall probability" does nothing like this. On the contrary -- it introduces a variable, about which you can't make any realistic assumptions at this point (other than "well, it depends on too many factors to be able to say for sure"), which makes the model essentially worthless.
No you can't. My assumption is that the GE on offense starts with a base value of what an acceptable shot it (depending on the overall pace of the offense and defense), and then adjusts as the game goes on. I suspect that's why some unusual things can happen at the beginning of the first quarter.
I much rather think the value of acceptable shot is static, and it's the matchups that adjust throughout the game. Of course, matchup adjustment takes place regardless of zones, so this is not quite relevant to the analysis.
I also noticed that, when bad substitutes come on, the pace of the game slows down considerably. I suspect this is because the GE is still looking for the quality of shot that your starters were taking. However, if the backups stay on for a considerable time, eventually it adapts (and lowers the tolerance for the quality of shot).
I would much rather say that this is because the defenses were adjusted to react to certain machups, and subs change the matchups, therefore the GE has to readjust.
Yes, it seems that the defenses adjust to some extent, since if you have one star player he gets covered better than the other players, for example. However, I was removing that from my equation at the moment. As you said, we have to simplify this a bit to have any kind of discussion about it. Otherwise, there is no point in talking.
And you should be, because they adjust regardless of zones -- therefore this is probably not relevant to zone analysis.
To finish: all the formulas in BB are determined before the game. So the probability of making a shot is determined in advance. Even the BBs have stated that a missed shot (or made shot) does not directly impact the outcome of the next shot, at least not on a probabilistic level (maybe it indirectly impacts, as it could alter some adjustment factors, but those adjustments are still determined before the game is run).
I can't agree with this. I don't think the probability of making a any given shot is known in advance, since we also know that defenses are adaptive. It might be, that in the sense that given the same input parameters you get the same probability for a positive outcome, but the parameters change, so you can't quite tell the exact parameter for any given shot, since shot opportunities are somewhat stochastic.
Last edited by GM-kozlodoev at 10/7/2009 12:10:56 PM"I don't know half of you half as well as I should like; and I like less than half of you half as well as you deserve."