So for all who were really interested in the zone, I submitted a ticket and was told this:

A zone defense is generally going to give up more rebounds to the offensive team purely because it's hard to box out everyone when there aren't designated matchups. Having good rebounders obviously helps offset that disadvantage, but over time a zone is going to give up more rebounds than a man-to-man. For defense, the effect on the offense is basically a combination of players instead of a single player. The advantage then is that you can hide a really bad defender somewhat.
1/24/2012 10:23 PM	reddyred
So when you say "combination" are you saying that the average def rating among these combo players is what is used to decide the outcome of a possession?
1/25/2012 8:18 AM	Customer Support
Yes, although it's not just a straight average of defensive ratings. There are some other factors involved, such as where on the floor the offensive player is.

There was some debate as to whether the zone used random defenders or if there was an average of def. ratings. 

There still will be.  I have been told the opposite thing in no uncertain terms by admin already and am fairly certain at least 1 or 2 other owners will attest that they have been as well.

Is there any way you could post what you were told in this thread for all to see?

i am not sure exactly what you guys are talking about. are you basically saying, there are 1 of 2 scenarios? 1 - when your selected shooter gets the ball, his defender is the average of some players on the team. 2 - a player is randomly picked, and that is the defender.

from a programming standpoint - in a way - that could be the same thing. in 1), which players would be chosen? think like a programmer for a second (ok, maybe thats not fair. i am a programmer, i really have no idea how well other people can think like a programmer if they are not?). is it really reasonable to say, im just going to have the guards defend this guard? no, i dont think so. that guard could drive. he could be a terrible perimeter shooter and only take shots for the most part, within 10 feet of the basket. so, you are probably going to say, ok, let me assign some weight to the different players, and average their ratings. IN THE LONG RUN - that is exactly identical to randomly picking a player, according the same weightings you used when averaging the players in the first place.

my disclaimer is i have no idea how to play zone and have never really tried. so i can't suggest from my experience how that works. its just that when i saw your post - i thought, those don't sound so different to me. probably just depends how the staff understood the original explanation, how they present it to you.

all in all, im not really sure how knowing which of the above is the case would really help anybody. it does affect volatility i suppose, if there is a random factor or not - they are only identical in the long run (but the expectation is the same in the short run as well, as it must be). its also possible players are randomly chosen to use to average their ratings - in which case - both explanations would be absolutely correct :)

From a mathematical standpoint, they are the same. Randomly picking a player on the perimeter to guard a 20 ft jump shot is the same as averaging all the defenders on the perimeter. I would argue this holds even in small sample size. Assume the following scenario for the final shot:

Against a defender with 1 def rating, your probability of making the shot is 99%; against 99 defense rating, it's 1%; everything in between is linear.

Assume your opponent is playing 3-2 defense and you are taking a 20 ft jumper, your opponent has 2x players with 1 defense rating, 1 player with 99 defense rating. Now, your probability of making the final shot assuming randomly assigning defender is simply 99*1/3 + 99*1/3 + 1*1/3, which is 33% + 33% + 0.33%, 66.33%. Your probability of making the shot by averaging all 3 defenders is the same: (99 + 99 + 1)/3 =  66.33

On the flip side though, defense is not the only rating. Think of this - 

Same 3-2 zone, same 20 ft jumpshot.

Defender A has a 99 defense, but a 1 speed and 1 athleticism. Can we agree he's get torched, despite the 99 defense? I certainly expect he would be.
Defender B has a 99 speed, but a 1 defense and 1 athleticism. Again, he's toast. I expect he might generate some steals over time, because speed seems to me to be the biggest factor for those, but if the shooter gets a shot off, I'd expect *very* high rate of success.
Defender C has 99 athleticism, but 1 speed and 1 defense. That's a poor defensive center guarding the 3-point line (not a recipe for success).

So, if a defender is randomly chosen, I would expect even a marginal offensive threat to have a field day all day long, making almost any shot he took and drawing a ton of fouls.

If averaged, though, you'd looking at a ~33 speed, ~33 ath, ~33 D combo, and while that would be bad, I think three of those players would prove to be far more effective overall than my Defenders A, B, and C above.

Extreme example, yes, but it works for illustrative purposes. So, unless you are going to really argue that the defense rating is the only one that impacts defense/opponent's FG%/whatever, you can't really say that (mathematically or otherwise) random selection and averaging work out to be the same thing.

You can though, because both sides use a mathematical equation to generate efficiency. Can we agree on this? What I mean is, offensive efficiency is a function such that OE = f(ath,spd,per,lp,bh, other players' passing), while defensive efficiency is a function of the defenders attributes such that defensive efficiencey (DE) =
f(ath,spd,de,blk).

So you end up with a raw efficiency number on defense for each defender. This means that random assignment or averaging will reproduce the same result as I posted above. Just substitute defensive efficiency into defense and everything still holds. 

Your example is not similar to what I posted, because all 3 players will generate extremely low defensive efficiency number. 

Do you think the engine actually aggregates the individual ratings into an OE or DE though? Or is that mathematical equation just something we could use to get a feel for how the engine ends up producing results based on the individual ratings?

Maybe I'm missing something, but I don't think it's the same at all from a mathematical standpoint.

Let's say you are playing a 2-3 zone with one strong defensive guard and one weak defensive guard.

Your opponent shoots from the perimeter. How could averaging the defensive effectiveness of the two guards be the same as randomly picking one of them to be the defender on that play? It's not at all.

Posted by girt25 on 1/27/2012 9:11:00 AM (view original):
Maybe I'm missing something, but I don't think it's the same at all from a mathematical standpoint.

Let's say you are playing a 2-3 zone with one strong defensive guard and one weak defensive guard.

Your opponent shoots from the perimeter. How could averaging the defensive effectiveness of the two guards be the same as randomly picking one of them to be the defender on that play? It's not at all.

I think he's saying that over time it's the same.  If he shoots 100% against the weak one and 0% against the strong one, over time, that's 50%, which would be the same as if you average the strong and weak.  Obviously that's extreme, and there are a ton of variables in there, but I think the point is about averaging over time, not on an individual shot.

Posted by zbrent716 on 1/27/2012 8:08:00 AM (view original):
Do you think the engine actually aggregates the individual ratings into an OE or DE though? Or is that mathematical equation just something we could use to get a feel for how the engine ends up producing results based on the individual ratings?

Even if it compares individual ratings match up, how do you think the engine decides in the end of which side is ahead. Suppose the offensive player has 30point edge in ath, but 50 point deficiency in spd, 85 per, while the defender has 95 defense, how would the engine rectify this? It has to assign a weight to the various deficiencies and then aggregate all the factors to come out with a number. This final number determines the probability (shooting %) of whether the shot goes in, misses, or the player is fouled. 

Posted by ike1024 on 1/27/2012 9:52:00 AM (view original):

Posted by girt25 on 1/27/2012 9:11:00 AM (view original):
Maybe I'm missing something, but I don't think it's the same at all from a mathematical standpoint.

Let's say you are playing a 2-3 zone with one strong defensive guard and one weak defensive guard.

Your opponent shoots from the perimeter. How could averaging the defensive effectiveness of the two guards be the same as randomly picking one of them to be the defender on that play? It's not at all.

I think he's saying that over time it's the same.  If he shoots 100% against the weak one and 0% against the strong one, over time, that's 50%, which would be the same as if you average the strong and weak.  Obviously that's extreme, and there are a ton of variables in there, but I think the point is about averaging over time, not on an individual shot.

Sure, I guess in a large sample size things will even out.

But in a smaller sample size -- say, an individual game -- it often wouldn't even be close.

FWIW, everything I've heard from both TK and seble over the years is that an average is taken. I think a lower level CS person may have put out some misinformation at some point.

Let's take an individual shots against 2 perimeter defenders, how would random assignment against averaging change the probability of the outcome?

Posted by coach_billyg on 1/27/2012 12:53:00 AM (view original):
i am not sure exactly what you guys are talking about. are you basically saying, there are 1 of 2 scenarios? 1 - when your selected shooter gets the ball, his defender is the average of some players on the team. 2 - a player is randomly picked, and that is the defender.

from a programming standpoint - in a way - that could be the same thing. in 1), which players would be chosen? think like a programmer for a second (ok, maybe thats not fair. i am a programmer, i really have no idea how well other people can think like a programmer if they are not?). is it really reasonable to say, im just going to have the guards defend this guard? no, i dont think so. that guard could drive. he could be a terrible perimeter shooter and only take shots for the most part, within 10 feet of the basket. so, you are probably going to say, ok, let me assign some weight to the different players, and average their ratings. IN THE LONG RUN - that is exactly identical to randomly picking a player, according the same weightings you used when averaging the players in the first place.

my disclaimer is i have no idea how to play zone and have never really tried. so i can't suggest from my experience how that works. its just that when i saw your post - i thought, those don't sound so different to me. probably just depends how the staff understood the original explanation, how they present it to you.

all in all, im not really sure how knowing which of the above is the case would really help anybody. it does affect volatility i suppose, if there is a random factor or not - they are only identical in the long run (but the expectation is the same in the short run as well, as it must be). its also possible players are randomly chosen to use to average their ratings - in which case - both explanations would be absolutely correct :)

Hey coach, I agree there is a random factor that comes in to play based on where the shot is taken. But being that it's zone my understanding from this ticket was that more than one defender would be involved for the possibility of hiding a bad defender and then these ratings from the combination of players would be averaged to determine whether the possession is successful. The debate in the past was average vs random assignment (either on or the other) and it seems to be a combination of both but averages must be involved according to this ticket.