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There are not two types of shots, every shot has a different probability of success. You did mention a specific probability for a player to take a shot, which did not change depending on pace.

Most certainly. On the other hand, it's easier to understand the situation with simplifying assumptions. I am not looking to reproduce all details of the GE here, just to develop an understanding on how the outcomes work, in general.

There are only three possibilities using a 2-3 zone keeps the overall probability of a shot going in:

1) the same
2) increases it
3) decreases it

Against a base offense, I personally expect it to be #1. Perhaps an argument could be made for #2, but it still makes your example moot. If #3 held, then 2-3 zone would be the system of choice to defend a base offense, which it does not seem to be.

There are too many variables that affect "overall probability" in a broad statement such as this. That's why you can't make any meaningful analysis of what's going on.

I'm not sure what "ex-ante" has to do with anything. Sure, the probability of a shot going in changes as a game goes along, as players come in and out, as the coach makes adjustments, etc. Is that what you mean? I thought we were disregarding that for the moment?

Before the game starts, you can't know what shots will be taken and what the skills of the players involved will be, therefore you can't set a defensive tactic and say with certainty how it will affect the overall probability of shots going in. Therefore, in order for the zone to give you roughly the same overall probability to make a shot, the zone itself should be in-game adaptive (that's ignoring coach adjustments). I don't think this is the case, so how the zone affects the overall probability of a shot to go in is cannot be determined before the game has ended. Hopefully this made sense.

I suspect it is more like: for a specific pace, a basket should on average be scored by time x on the shot clock. The "calibration" as you call it might be used to determine the quality of shot the offense is willing to accept (x pts on average). But I don't see how the pace can change as the game goes along (in fact, in my experience, it doesn't, except maybe at the end of the game when a team is trying to take quick shots).

What I meant is the following: determine the in-game effects of zones on player skills, take a bunch of generic teams, and run multiple simulations with and without zones. Calculate the average "time to a good shot" in both cases, compare, and determine how the zone has affected time to a shot.

If the result is not satisfactory, you can "calibrate" the outcome by playing around with th the value of the initial parameter (the effect of zones on player skills).

I am not looking to reproduce all details of the GE here, just to develop an understanding on how the outcomes work, in general.

Me neither, which goes to my following point.

There are too many variables that affect "overall probability" in a broad statement such as this. That's why you can't make any meaningful analysis of what's going on.

Agreed. However, you were the one who started with a simplification. So what's your solution? That we not talk about it at all?

Before the game starts, you can't know what shots will be taken and what the skills of the players involved will be, therefore you can't set a defensive tactic and say with certainty how it will affect the overall probability of shots going in.

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 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).

Therefore, in order for the zone to give you roughly the same overall probability to make a shot, the zone itself should be in-game adaptive (that's ignoring coach adjustments). I don't think this is the case, so how the zone affects the overall probability of a shot to go in is cannot be determined before the game has ended. Hopefully this made sense.

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.

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).

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

which you readily dismiss.

Ok - I can't agrue with that.

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.

I still don't see the difference between this and your arguments. In my mind, both models are essentially worthless once you break them down.

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.

Yes, both offenses and defenses adapt. Yes, many other things are going on at the same time. There are probably also many different types of shots (driving shots, pull-up jumpers, hook shots, etc) which adds even more complexity. So I guess neither of our models is really workable so really what's the point in continuing to discuss it?

I still don't see the difference between this and your arguments. In my mind, both models are essentially worthless once you break them down.

Well, the point was to try to come up with something we agree is close tow workable model, no?

Well, the point was to try to come up with something we agree is close tow workable model, no?

Yeah, I just got a headache thinking about it and then someone else here at work is trying to explain to me all the demographic models that we use, so I think I need a break. ;-)

Actually, I don't really know anything and your points are valid so I don't have anything else to add.

Wow.

Is this thread still about Stamina?

Wow.

Is this thread still about Stamina?

not any longer