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it is important to understand that yes, pace always affects the shot quality your team will look for.

I have never seen an allegation that this is _always_ the case. BB-Charles has used this example to explain how the various offensive tactics differ from each other, but I've never seen him say that pace always affects the quality of shots taken. As a matter of fact, he has never explained how defensive tactics affect pace.

To support this, here are the two sentences which immediately precede your quote from the GE section of the rules:

The offensive schemes that we give you can be broken down into combinations of two aspects, pace and focus. Pace is either faster, slower or normal, and focus is either inside, outside or normal.

I have said that pace affects the shot quality that your team will look for. This might have or not an effect of the actual quality of a shot depending on various things. And yes, they have not explained the role of pace in defensive that is why we are having this conversation. There is something needed to be remembered, while it is true than BB-Charles have talked about the effect of pace in the shot quality a team will look for(just as I have been) he has not said that pace does not affect performance through a modulation related to stamina.

Second, assuming you are right, your example can not work if my offensive was outside focused because when you make the switch to 2-3 it will be easier for me to find the HQ outside shot.

Maybe you have to re-read my example to really understand it, since it works just fine. In it, the attacking team will probably take the first possible shot if there is no zone (since both inside and outside shots are equally attractive, and both are "good" shots), and might have to spend a bit of time looking for the good shot in a 2-3 tactic (based on the fact that outside shots are "good", and inside shots have become "bad"). It's easier to hit the outside shot, not easier to find it -- these are two different things.

This is only true if I play a neutral offense. ¿How could that work when I play an outsided offesnse? (Keeping the same porcentages you already give us) The outside focus will skew the distribution of shots towards outside shots, so yes, it will be easier to find it. See? That is why I tell you that this interpretation of defensive pace will make the value of pace dependent on the offensive tactic your opponent plays.

This is consistent with the interpretation that higher pace should, in general, result in more possessions in a game, which is about the only aspect of the definition of pace which is universally applicable to both offense and defense.

While I agree about that statement regard to offensive pace I'm not sure of it for defensive pace, that like you said, BB-Charles has not talked about.

Perhaps a BB could help to clarify this dark topic and also tell us abput the unknown pace of the 1-3-1 tactic that is not listed in the english rules.



Last edited by Zero, the Magi. at 10/6/2009 7:42:35 PM

This is only true if I play a neutral offense. ¿How could that work when I play an outsided offesnse? (Keeping the same porcentages you already give us) The outside focus will skew the distribution of shots towards outside shots, so yes, it will be easier to find it. See? That is why I tell you that this interpretation of defensive pace will make the value of pace dependent on the offensive tactic your opponent plays.

Well, in my particular example this doesn't matter (which is one of the reasons why I picked it). Admittedly, there are other variations in which the offensive focus might matter, but whether it does depends largely on calibration.

Which brings me to another interesting point...

There are two ways to determine the effect of a change in the parameter of a system:

Derivation: mathematically derive the change in outcome from the change in the parameter. Adjust accordingly.

Calibration: Change the parameter, run a million or so simulations, and record how the outcome changes. Adjust the parameter, rinse, and repeat until you get the desired outcome.

While derivation is typically the better method it is often too complicated to be feasible. This is especially true in systems with multiple stochastic (random) outcomes -- which makes the BB Game Engine a perfect candidate.

Which might simply mean that the slower pace is an ex-post calibration result, which in turns means it depends a lot on precisely how it was calibrated.

Of course, I am sure there are more theoretically-oriented guys around here (programmers, mathematicians, or statisticians, to name a few possibilities) who might be able to explain this better.

This is only true if I play a neutral offense. ¿How could that work when I play an outsided offesnse? (Keeping the same porcentages you already give us) The outside focus will skew the distribution of shots towards outside shots, so yes, it will be easier to find it. See? That is why I tell you that this interpretation of defensive pace will make the value of pace dependent on the offensive tactic your opponent plays.

Well, in my particular example this doesn't matter (which is one of the reasons why I picked it). Admittedly, there are other variations in which the offensive focus might matter, but whether it does depends largely on calibration.
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Believe me, in the example the change of the offensive tactic will matter. Even if we use the values you give us (wich have a simetric change that is not real I think, when you switch to a zone you lose more that what you win). I think you are just not taking the correct effect of the altered distribution of shots when changing offensive tactics.

But there is no need to extend in that argument.

About the effect of the change in pace. I'm not really follow it... you mean the change on the probability of a shot to go in when only pace changes?

I still think defensive pace is something that has not been properly explained in the GE section(nor the forums as far as I know) and the pace of the 1-3-1 is missing in the rules.

Last edited by Zero, the Magi. at 10/6/2009 9:35:50 PM

Believe me, in the example the change of the offensive tactic will matter. Even if we use the values you give us (wich have a simetric change that is not real I think, when you switch to a zone you lose more that what you win). I think you are just not taking the correct effect of the altered distribution of shots when changing offensive tactics.

*sigh*

No, it won't matter. With the values I gave you, with no zones every shot is a good shot, so the first shot will be taken. When zone is applied, some shot become bad shots. No matter how little "some" is, it's still greater than zero.

When zone is applied, some shot become bad shots.

I still don't get your example, because some shots are bad shots no matter what defense is used. If you accept the principle that the zone doesn't affect the "average quality" of the shot - so that, on average, they are still getting the same quality of looks (ie: my defense is better against inside looks, but that is a trade-off for the outside looks), then your point still does not make sense. The variance in the amount of time it takes to find their best shot may be higher but the average time to find the best shot will be the same.

Maybe your point makes sense for a look inside vs a 2-3 zone, as my "average" shot will probably be of lower quality. I'm not sure about that, though.

In fact, because of the way that zones work, I may even be getting a higher quality shot on average against a 2-3 zone. If my opponent uses a SF with no inside d, for example.

Obviously, all sorts of mental gymnastics on this rest on simplifying assumptions. Mine was that we only have two types of shots, inside and outside. All shots of a certain type are identical, and can either be "good" or "bad", depending how they compare to the team expectation for the quality of a shot.

My example started with the condition that all shots are good if no defensive zone is applied. Therefore, it doesn't matter whether the distribution is skewed to the inside or to the outside.

Of course, you can relax this assumption, and my example will work for a lot of cases. Not for all, obviously, but I have no time or desire to go through separate examples at this point.

If you accept the principle that the zone doesn't affect the "average quality" of the shot - so that, on average, they are still getting the same quality of looks (ie: my defense is better against inside looks, but that is a trade-off for the outside looks) , then your point still does not make sense.

I don't see any justification for the acceptance of such a statement, given that it will depend on what the opposing team looks like. I don't think zones work differently based on who you're playing against. Plus, given how shot selection is determined, it's next to impossible to control the average shot quality ex-ante.

The variance in the amount of time it takes to find their best shot may be higher but the average time to find the best shot will be the same.

As I mentioned, I am starting to suspect that the determination of pace (at least for defensive tactics) is made ex-post through calibration. But then again, this is as wild a guess as there is.

Obviously, all sorts of mental gymnastics on this rest on simplifying assumptions. Mine was that we only have two types of shots, inside and outside. All shots of a certain type are identical, and can either be "good" or "bad", depending how they compare to the team expectation for the quality of a shot.

To me, it is obvious that every shot is of different quality. Otherwise, everyone would take the first shot. "Good" or "bad" is all relative.

My example started with the condition that all shots are good if no defensive zone is applied. Therefore, it doesn't matter whether the distribution is skewed to the inside or to the outside.

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.

I don't see any justification for the acceptance of such a statement, given that it will depend on what the opposing team looks like. I don't think zones work differently based on who you're playing against. Plus, given how shot selection is determined, it's next to impossible to control the average shot quality ex-ante.

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.

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?

As I mentioned, I am starting to suspect that the determination of pace (at least for defensive tactics) is made ex-post through calibration. But then again, this is as wild a guess as there is.

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).

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?