# Theory on how the sim works Topic

Imagine two opposing PF's both playing M2M defense and the same offensive style, equal distribution, etc. Basically, everything is equal except for these specific ratings...

Let's assume that rebounding is just a function of ATH and REB, for the sake of argument say its 2 parts REB and 1 part ATH.

Player A has ATH of 50 and REB of 50. Player B has ATH of 75 and REB of 75. Obviously, B will have the better rebounding rate over time...but by how much? Will he get 50% more rebounds than player A because his ratings are 50% better (so roughly a 60/40 split)? Or, since he's simply the better rebounder, will he significantly more rebounds (maybe a 75/25 split? imagine the superior rebounder boxing out the other guy each play). Does the sim match up rebounders like this, or do they put all 10 rebounders together and 'see who wins'?

Also, how would it look if B had ATH of 60 and REB of 45, so technically 'equal' rebounding? Would they be equal, or would the specific ATH or REB edge have an effect that we haven't thought about?
6/28/2013 4:24 PM (edited)
Not sure if anyone has an answer as to how superior B is over A. I think a better hypothetical would be if player B had the same athleticism but higher rebounding.

6/28/2013 4:30 PM
jet, the way the engine works is that the sim decides which team gets the rebound, and then, assigns a player the rebound statistic. if this seems a little backwards to you... i agree. essentially it disconnects the player's performance from the stats, but as long as the way a player contributes to the team's rebounding ability, is the same way an individual on a team gets weighted to get the rebound, then over time, the stats are meaningful.

the above is why if you have a bad rebounding team with a good rebounder, he will get way more rebounds than significantly better guys he plays against.

you sometimes hear coaches ask, why did my guy X who is way better than their guy Y get 5 rebounds to his 8? well, often, the other team at the 1-4 (if X and Y are centers) is just shittier, so comparing rebounds that way, by rebounds at a position from guys on a different team, is very dangerous.

i dont believe the ath/reb have different effects, instead, that a "rebounding ability" is computed based on some factors, ath reb iq and probably fatigue, would be the list (and health if you want to be picky about it).
6/28/2013 4:39 PM
I'm not sure whether gillispie's explanation incorporates the update, but from 2/16/2011:

"Added an individual player matchup component to rebounding, so that a mismatch will produce better numbers from the player with the advantage. This will in turn create a little more separation between the truly good rebounding teams and poor rebounding teams."

That seems to indicate that gillispie's hit it on the nose, but that there may be an additional algorithm that adjusts again on the individual level.  That probably doesn't answer your question though.
6/28/2013 5:25 PM
Posted by rogelio on 6/28/2013 5:25:00 PM (view original):
I'm not sure whether gillispie's explanation incorporates the update, but from 2/16/2011:

"Added an individual player matchup component to rebounding, so that a mismatch will produce better numbers from the player with the advantage. This will in turn create a little more separation between the truly good rebounding teams and poor rebounding teams."

That seems to indicate that gillispie's hit it on the nose, but that there may be an additional algorithm that adjusts again on the individual level.  That probably doesn't answer your question though.
interesting, not sure i ever read that before. well, what i described is how it was - but it sounds like things were amended to include some matchup based factors. most of what i suggested still holds true - looking at a matchup and going how come the shittier rebounder won, is still a dangerous proposition.

whats not exactly clear to me is if the change seble made affects the decision on which team gets the rebound, or the decision about which player gets assigned the rebound, or both. presumably both, but just doing the 2nd to make stats look better is a possibility... even though it makes the change purely cosmetic (which wouldnt be the first time).

anyway, interesting point regelio, thanks for bringing it up. was late in the work day friday, and had a few minutes to kill, so i figured id see if there was anything interesting on the forums. guess ill go back to being retired now :)
6/29/2013 1:59 PM
Ignore the distinction between offensive and defensive rebounds for a minute, as well as positional weights.  The simplest model would be if p_A1|A = (REB_A1)/(REB_A1+REB_A2+...), i.e. the probability of player A1 getting credit for a rebound given that team A got the rebound is proportional to relative rebounding ratings on the team.  And the simplest model for p_A|miss = (REB_A1+REB_A2+...)/(REB_A1+REB_A2+...+REB_B1+REB_B2+...), i.e. the probability that team A got the rebound given a missed shot is proportional to the relative rebounding ratings between the two teams.  In this model, p_A1|miss = p_A1|p_A * p_A|miss ~ REB_A1, so only rebounding ratings (and the probability of missed shots) should determine the number of rebounds a player gets, independently of the rebounding abilities of the other players on the floor.

The fact that many people seem to have observed that the number of rebounds a player gets is not independent of the rebounding abilities of the other players on the floor, and in particular that good rebounders on bad rebounding teams put up surprising numbers, suggests that this simple model is wrong.  If so, it is not obviously fixable with positional weights or splitting offensive and defensive rebounds.  To explain the observation, there need to be non-linearities, such that p_A1|A is greater (for good rebounders on bad teams) or pA|miss is smaller (for good rebounding teams) than the simple model indicates.  However, the only evidence we have from the 2/16/2011 update is just the opposite.

With numbers:
Team A: 50 10 10 10 10
Team B: 60 60 60 60 60

In the simple model, team B should get 3/4 of the rebounds (total = 300 vs total = 100), and A1 should get 1/2 of A's rebounds (50/100), while B1 should get 1/5 of B's rebounds (60/300).  Player A1 should get 1/2 * 1/4 = 1/8 of all rebounds, and player B1 should get 1/5 * 3/4 = 3/20 of all rebounds.  But (3/20)/(1/8) = 60/50, so this is exactly proportional to what one would expect from A1's and B1's REB ratings without considering the rest of the team.
6/29/2013 11:45 PM
I know I'm a bit slow but doesn't Team A's "numbers" above add up to 90, not 100?
6/30/2013 1:30 AM
rick, its been a while, so you'll have to help me with some of this. i get the simple model you propose... following the p_A1 | A and p_A | miss.

im struggling to  follow this part though...
p_A1|miss = p_A1|p_A * p_A|miss ~ REB_A1
prob player A1 gets the reb gives a miss = what? not familiar with the nested | or ~ terminology. can you explain?

this conclusion is not clear to me either - "
so only rebounding ratings (and the probability of missed shots) should determine the number of rebounds a player gets, independently of the rebounding abilities of the other players on the floor. "

then in your example, you use the rebounding ratings of the other team mates to figure out how many rebounds the player should get. also, you should probably minimally say, ... should determine the proportion of rebounds a player gets. otherwise you need to include # of shots.

anyway, im not sure if im reading that wrong or if its just not exactly stating what you are trying to state. in your example, it seems you are suggesting, the proportion of rebounds between two players on different teams can be figured independently of the rest of the teams ratings, which to me, is not what you conclude above. (or technically, between any 2 players, but i think we are focused on players on different teams here)

im trying to wrap my head around this, so bear with me. if what you are saying is, the rebounding proportion between two players can be figured independently of rebounding ratings of the rest of the team, which conflicts with the update - there would be no need, which disproves the simple model - well, i dont know. i guess i would start by first, checking the first statement, without the numerical example... using r_a1 to represent the rebounding ability of a1 and R_A to represent the # of rebounds by team A...
r_A1= r_A/(r_A + r_B) * r_A1/r_A = r_A1/(r_A + r_B)
similarly, r_B1 = r_B1 / (r_A + r_B)
so clearly, r_A1 / r_B1 = r_A1/(r_A + r_B) / ( r_B1 / (r_A + r_B))  = r_A1 / r_B1
so no problem there. the proportion of rebounds going to a pair of players is going to be proportional to their rebounding ratings independent of the rest of the players' rebounding ratings (using the term rebounding rating liberally to include whatever goes into calculating rebounding abilities - not just rebounding ratings). i agree this would make the update redundant, and thus, the simple model does not hold.

is that what you are saying? actually, i guess its not what you are saying, i think it would make the update redundant and thus the model cannot be the case. you seem to be saying the update suggests that non-linearities must exist already and the update somehow contradicts that. i guess i dont see it, to me we have great reason to believe (from observation and admin statements) that these non-linearities already existed, and the update was put in place to create more of a correlation between matched up players. can you elaborate on your stance?

6/30/2013 11:33 AM (edited)
what i did take away from your post is that you are suggesting its hard to expand the simple model to create a scenario in which r_A1/r_B1 (proportion of rebounds between two matched up players) is dependent on the ratings of the rest of the team - which, in our conversations in the past (and conversations independent of each other) - we have both used to suggest the simple model holds. positional weights can not create this, i agree. nor with splitting offensive and defensive rebounds - although that does significantly muddy the waters, it seems to me as i think through it - but more on the lines of rebounding proportion of two players being dependent on the scoring ratings and defensive ratings of all team mates. still, not their rebounding ratings - so i agree - but i think that muddying of the waters does create some of what we observe today.

what about this. in real life, a good deal of rebounds are gimmies, and a good deal are contested. there is a gradient, of course, but lets just assume its a dichotomy. however, the % gimmies is not fixed - its dependent on the players' rebounding ratings (among other things). now, you have a three step processes, where the first step is determining the type of rebound, the second is determining which team gets the rebound in that case, and third, which player gets it. it seems to me that is sufficient to create a model where the rebounding proportion of players on different teams are dependent on the rebounding ratings of the rest of the players. agree or disagree?
6/30/2013 11:47 AM (edited)
emy, you're right that was an arithmetic fail on my part; but make one of those 10's a 20 and then my example holds.

gillespie, my notation was a bit sloppy.  I should write p(X|Y) not p_X|Y to indicate probability of X given (or conditional on) Y.  And you can always chain conditional probabilities together, so p(X|Z) === p(X|Y) * p(Y|Z).  I used ~ to indicate proportionality, since the final expression has a denominator with everybody's rebounding ratings, and as we move from player to player only the numerator changes.  The usual proportionality symbol wasn't available (no LaTeX on the WIS forums, suprisingly).  Actually, I probably could have made one with the source editor.  Oh well.

So what I am saying is:
1) Imagine the simplest possible model (the one I proposed).
2) Many people allege to have seen a phenomenon which is incompatible with this simplest model.
3) I don't see any simple fix to the simplest model which could account for the phenomenon, including the "fix" WIS put in above.
4) Therefore, the simple model must be missing something important.

Gillespie proposed that maybe "gimmes" can account for the phenomenon.  That might work -- take it to the extreme where every rebound in the game is a gimme for the defensive team (imagine a game where the only misses are free throws).  In that scenario, maybe rebounding ratings barely matter in determining which team gets the rebound, but suppose that rebounding ratings still matter in determining which player on that team gets the rebound.  In other words, p(A1|A) is still very dependent on REB, but p(A|miss) is not.  In that case we would expect the good rebounder on the crappy rebounding team to outrebound everyone on the court, including the great rebounders on the elite rebounding team.

With that thought experiment complete, I now think it is possible that the difference between offensive and defensive rebounds may be enough to explain the phenomenon.  After all, defensive rebounds aren't "gimmes", but the defensive team certainly has a better chance than the offensive team of getting the rebound (maybe 2-3x fold).  If the effect of REB ratings on the probability of a team getting a rebound is diluted by situational factors, such as which team shot the ball, but the probability that a particular player gets that rebound, given that his team got the rebound, is not, then we can probably account for the phenomenon.

6/30/2013 11:44 PM
yeah... i wasnt sure about the off/def rebs, i figured id just give you that one, because i was confident in the "gimmie" concept. but i think you are right, the weighting of the def or off rebounds to give one team an advantage is sort of like a gimmie, and really any weighting should be enough to create the dependency on the rebounding ratings of the rest of the team. i think theres a good chance theres a bit more going on than that, but anyway, i do think we agree its not that difficult to create the phenomenon where players rebounding figures are significantly influenced by the rest of their team. and given that, that the 2011 update makes a lot of sense.

i still would be interested to hear the english version of that compound statement, especially since my first attempt was to use the |s and ~s exactly as you said :)
7/1/2013 9:18 AM
rgerkin you're definitely on to the something there, as the skew towards defensive rebounding is where the "stud amongst scrubs" rebounding numbers come from. I'm trying to wrap my mind around how the "matchup" update could work, too.

The upshot of all this is I believe a especially high ratings may be worth more than their scalar difference. i.e. when you create a "player role" you shouldn't just multiply ratings, there should be an exponent factor in there if you're truly trying to simulate impact.
7/1/2013 9:39 AM (edited)
The baseball caluculations (which they released) aren't linear, since the same person wrote the code, I don't think the basketball calculations would be.
7/1/2013 10:30 AM
trenton, which calculations are you referring to? im guessing you are talking about something like how shooting ability is not simply the linear combination of per and spd, rather, there is a multiplicative property to it. i would definitely agree with that. however, what rgerkin is talking about is the rebounding ability, not the rating, and whether the ability is linear or not in the ratings, doesnt really play into it. once you have the rebounding ability for each player, the number of rebounds you get is not linear in that ability - its dependent on the other players. maybe its because the off/def rebounds favor a certain team (its almost definitely partly because of that), maybe its partly because of something else. so i dont disagree with you, i just wanted to point out that is a lower level distinction you are making, non linear combinations of the ratings into the rebounding ability wouldnt explain the dependency on other players' rebounding abilities.

jet, i dont think i agree with the conclusion. assuming when you say, their scalar difference, you mean in the rebounding ratings themselves. in # of rebounds, absolutely. however, i sort of have the opposite conclusion. it seems to me a guy with 80 ath/reb growing to 90ath/reb adds more value than a 90 ath/reb guy going to 100 ath/reb. i personally believe that the combination of ratings is not linear, as TJ pointed out, and therefore as ratings go up, you usually get more bang for you buck. but then, things level out. if you think about it, combining all these ratings and IQ into an ability yields some value - those have to be normalized and put on some usable scale. one can accomplish that in a variety of ways, and i think the way its done in HD is such that improving abilities yield somewhat linear results until you get near some soft cap, after which, returns are diminished. i remember when i was a young coach, probably less than a year into my career, OR pointed out that he thought once you had guys with 85+ in everything, they were basically all the same. i thought he might be crazy, because in d2/d3, you clearly got the benefit of multiplicative properties in the combination of ratings, for example, 50 spd/per to 60spd/per was not nearly the improvement that 60 spd/per to 70 spd/per was. but when i got to d1, it really felt like OR was right - although id put that number in the low 90s, not at 85.

anyway, i guess ill stop rambling now. but i am curious why you feel this means especially high ratings may be worth more than their scalar difference? i dont really see the connection. to me, because a player gets less rebounds if his team mates are better, that would almost suggest a player creates less of an advantage for their team that their ratings suggest. i also definitely feel like there are diminishing returns on team rebounding, when you build a great team, there is often a lot of room between that great team (rebounding wise only) and a ridiculously awesome team - but i dont see it play out on the court. i think the setup is such that the advantages you can gain on off and def rebounds are restricted to a range - which is why, no matter how bad a team you play, they still get a decent amount of boards (i think that plays into why a good rebounder on a bad team gets a killer # of rebounds) - and why, no matter how good your team is on the boards, you can only get so much of an advantage against other teams.

all in my opinion of course, there are little known facts here. just offering my opinion, but i definitely could be wrong about some stuff, and find the different opinions offered so far to be very interesting.
7/1/2013 12:20 PM
I always thought it was like rolling dice. While the 75/75 guy is more likely to win the battle, there's nothing stopping the algoritum from giving 5 rebounds in a row to the 50/50 guy, just like while the odds are you're going to roll a 6,7,8 or most times, sometimes you roll three snake eyes in a row.
7/1/2013 12:26 PM
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