Posted by tianyi7886 on 1/27/2012 10:23:00 AM (view original):

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. 

I'm not as certain as you that it *must* aggregate all the factors to come out with a certain number.

If that was the case, I think you'd see more instances of one or more ratings being absurdly high "covering" for a deficiency.

Take Ath, for example, which is certainly vital. A 100 Ath, particularly if weighted more heavily, might do a fantastic job of covering for a deficiency in speed. While I think it can to some extent, I think there is also a level for speed below which a player's effectiveness is much more harshly punished, even if he has great ratings at everything else.

I not sure the 100 Ath, 100 Def, 100 SB, 5 Spd would be effective at stopping a reasonably talented 75 SPD player, even though he might have good "aggregate" ratings.

do we know that these ratings have linear effects?  if the ratings have nonlinear effects - diminishing returns - or if other variables are nonlinear than averages will differ from other methods

Posted by zbrent716 on 1/27/2012 10:44:00 AM (view original):

Posted by tianyi7886 on 1/27/2012 10:23:00 AM (view original):

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. 

I'm not as certain as you that it *must* aggregate all the factors to come out with a certain number.

If that was the case, I think you'd see more instances of one or more ratings being absurdly high "covering" for a deficiency.

Take Ath, for example, which is certainly vital. A 100 Ath, particularly if weighted more heavily, might do a fantastic job of covering for a deficiency in speed. While I think it can to some extent, I think there is also a level for speed below which a player's effectiveness is much more harshly punished, even if he has great ratings at everything else.

I not sure the 100 Ath, 100 Def, 100 SB, 5 Spd would be effective at stopping a reasonably talented 75 SPD player, even though he might have good "aggregate" ratings.

I never said that they weigh every rating the same. With the engine geared toward ath/spd, of course that wouldn't hold. If ath gets a value of 0.25 and spd a value of 0.22, while def gets 0.08 and SB gets 0.02, of course the 100 def/SB can't overcome the 75 SPD. 

There has to be a final number right? Otherwise, how does the engine determine who's the better player on an exact possession?

Use the following example:

Offensive player: 85 ath, 35 spd, 55 lp, 55 per, 65 bh, passers on court = 40 passing rating
Defender: 75 ath, 95 spd, 95 defense, 65 sb. 

You would say the defender wins this battle right? Because he's only 10 points behind in ath but has a 60 point edge in spd, and 95 defense. How do you make this decision that the defender is better when you cannnot compare apples to apples (defender doesn't have the equivalent lp/per/bh/etc ratings, and vice versa for the offensive player) and when one player is not overwhelmingly dominant in every category?

You made this decision by weighing the relative attributes and coming up with a comparison using the every category. Essentially, you assigned an overall efficiency # to both players and just compared them. Without doing so, you cannot make any comparisons. 

Posted by tianyi7886 on 1/27/2012 10:38:00 AM (view original):
Let's take an individual shots against 2 perimeter defenders, how would random assignment against averaging change the probability of the outcome?

It doesn't on a given shot.  But if there is a random assignment, and that random assignment doesn't randomly assign equally throughout the course of a game (i.e. one player gets "randomly" assigned more throughout any given game), then the results are certainly different than if based on an average.

Posted by isack24 on 1/27/2012 11:03:00 AM (view original):

Posted by tianyi7886 on 1/27/2012 10:38:00 AM (view original):
Let's take an individual shots against 2 perimeter defenders, how would random assignment against averaging change the probability of the outcome?

It doesn't on a given shot.  But if there is a random assignment, and that random assignment doesn't randomly assign equally throughout the course of a game (i.e. one player gets "randomly" assigned more throughout any given game), then the results are certainly different than if based on an average.

If the random assignment isn't assigned randomly, how is that "random assignment?"

Posted by tianyi7886 on 1/27/2012 12:21:00 PM (view original):

Posted by isack24 on 1/27/2012 11:03:00 AM (view original):

Posted by tianyi7886 on 1/27/2012 10:38:00 AM (view original):
Let's take an individual shots against 2 perimeter defenders, how would random assignment against averaging change the probability of the outcome?

It doesn't on a given shot.  But if there is a random assignment, and that random assignment doesn't randomly assign equally throughout the course of a game (i.e. one player gets "randomly" assigned more throughout any given game), then the results are certainly different than if based on an average.

If the random assignment isn't assigned randomly, how is that "random assignment?"

I said if it doesn't "randomly assign equally throughout."

Presumably, if it is truly random, it's won't be equal.  If the random assignments aren't equal throughout the course of a game, then there could be a significant difference between the averaged ratings of the defenders and a weighted average based on which player is assigned more often.

If the system uses weighted probability to assign a "random" defender, why would you think the system won't use weighted average based on the probability of assignment?

Or if you mean that in a given game, the distribution could be 65% to player A and 35% to player B based on some kind of randomness in the binary distribution, so what? Would you prefer the random assignment over the averaging on any given possession if you know that the probability of getting player A is 50%? I would be indifferent because the random process could just as easily generate 35% to player A and 65% to player B. Expected value is the same for both processes. 

Posted by tianyi7886 on 1/27/2012 1:03:00 PM (view original):
If the system uses weighted probability to assign a "random" defender, why would you think the system won't use weighted average based on the probability of assignment?

Or if you mean that in a given game, the distribution could be 65% to player A and 35% to player B based on some kind of randomness in the binary distribution, so what? Would you prefer the random assignment over the averaging on any given possession if you know that the probability of getting player A is 50%? I would be indifferent because the random process could just as easily generate 35% to player A and 65% to player B. Expected value is the same for both processes. 

Yes, your "player A" example is what I meant.

The question isn't whether I would care, it's whether it produces mathematically different results. 

It wouldn't as long as they modeled it properly, especially the part regarding standard deviation. 

Posted by isack24 on 1/27/2012 1:06:00 PM (view original):

Posted by tianyi7886 on 1/27/2012 1:03:00 PM (view original):
If the system uses weighted probability to assign a "random" defender, why would you think the system won't use weighted average based on the probability of assignment?

Or if you mean that in a given game, the distribution could be 65% to player A and 35% to player B based on some kind of randomness in the binary distribution, so what? Would you prefer the random assignment over the averaging on any given possession if you know that the probability of getting player A is 50%? I would be indifferent because the random process could just as easily generate 35% to player A and 65% to player B. Expected value is the same for both processes. 

Yes, your "player A" example is what I meant.

The question isn't whether I would care, it's whether it produces mathematically different results. 

Whether you care though, is a valid concern as well.

It is certainly possible I would construct a team differently, or perhaps juggle a lineup, based on the answer.

Particularly during a NT run, is that sub-par defender worth the risk if there is a chance the RNG hits him up as the target defender 65% of the time?

Knowing which way it works (random pick or average) allows owners to create more informed game plans.

zbrent, as long as they model the standard deviation correctly, the rng hitting the worst defender for 65% of the time in random assignment will be reflected in the same way of a weighted average. 

Posted by tianyi7886 on 1/27/2012 1:03:00 PM (view original):
If the system uses weighted probability to assign a "random" defender, why would you think the system won't use weighted average based on the probability of assignment?

Or if you mean that in a given game, the distribution could be 65% to player A and 35% to player B based on some kind of randomness in the binary distribution, so what? Would you prefer the random assignment over the averaging on any given possession if you know that the probability of getting player A is 50%? I would be indifferent because the random process could just as easily generate 35% to player A and 65% to player B. Expected value is the same for both processes. 

Well, we can agree or disagree if that is a big deal or not (your 65/35 example) but most certainly it is different than simply taking the average, and that's what we had been debating. (EDIT: I see that isaack made this same point.) 

And I think there is more than enough randomness in the engine, I don't need wins and losses decided by further randomness related to which defender of the two is randomly assigned more. (And that zbrent made this one.)

Posted by tianyi7886 on 1/27/2012 1:19:00 PM (view original):
zbrent, as long as they model the standard deviation correctly, the rng hitting the worst defender for 65% of the time in random assignment will be reflected in the same way of a weighted average. 

That I don't believe is true.  I would think that in a weighted average the two guards, for example, would always carry exactly equal weights on any shot, whereas in the random selection scenario they aren't guaranteed to do the same for any given player.  Probably the same with the PF and C.  I've always noticed that SFs are slightly more likely to be guarded by SFs in the text associated with zone defense; whether this reflects any significant engine logic is obviously up for debate.  So based on position on the floor a weighted average might be 80% of the average of the guards, 10% of the SF, 10% of the average of the post guys.  But I doubt there'd be any case in which a weighted average would give 65% weight to the SG and 35% weight to the PG.  There really would be no reason to program it that way.

There's two ways to do this. They could simply use a pure average, which wouldn't involve standard deviation. Or they could use the average of the 3 defenders to form an expected value to from a probability distribution function, which allows for a standard deviation to come into play. How they actually set up the game, we would never know, but from a mathematical standpoint, I really don't see any real difference between a random assignment/weighted assignment to taking an average of the defenders. 

There are a lot of good posts in this thread - one of the better threads I've seen, to be honest. Tiyanis point about having defense be a function of some factors is exactly what I meant. And truthfully, from a programming standpoint, you could deal with things in one of two ways. One, you can use an aggregate of ratings, like tiyani is suggesting. Or u could compare individual stats, where a 1 spd 100 def 100 ath player can't guard a fast player. Two notes on that. First from a programming standpoint, the latter is incredibly more difficult, and everything I know about how this game is programmed makes me rebel against that possibility. Secondly, in my experience, while studying the engine extensively, all evidence points to an aggregate of rating being used in the normal cases, minimally. So, I think tiyani's model is absolutely correct, I'd honestly be shocked if it wasn't.

However -- that said -- the claims that averaging and randomization, within a single game, are different, is totally correct. What I said, and maintain, is they are likely the same in the long run. But volatility is higher in the random case, which favors without question the lesser team. It's hard for zone teams to rattle of long runs of sustained success, maybe that points to randomization? Anyway, the third possibility is a couple players are randomly chosen and then averaged (weighted, possibly), which can still be the same in the long run, and falls between the other two options in volatility. It seem the most correct of the three options to me, so I certainly would not rule it out, especially considering the CS responses which suggest it could be both.