Theory on how the sim works Topic

Posted by trobone on 7/1/2013 12:26:00 PM (view original):
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.
it is, you are definitely right. i think what jet is getting at is more along the lines of, what should you expect in the long run (evening out the dice rolls) from that 75/75 guy vs the 50/50 guy. and more specifically, is that even a reasonable way to consider things - if those guys are on different teams? or do you look at the whole team? or what?
7/1/2013 12:36 PM
Posted by gillispie on 7/1/2013 12:20:00 PM (view original):
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.
I know exactly what you're saying, and i probably could have phrased it better...the higher ratings being exponentially more valuable isn't my conclusion, rather my initial hypothesis. i pitched this discussion as i think it's an important one to have before i continue my train of thought on the issue. I picked rebounds just because I thought it would be easy to put in simple terms.

to elaborate on said train of thought, my initial idea was concerned with prospect evaluation for pro basketball. namely, how players with one or two elite skills are more valuable than jack-of-all-trades players. these jack-of-all-trades players were good enough at 'everything' to be great at college, but can do effectively nothing in the pros. there are at least two technical explanations for this that i can think of:
1. NBA teams need certain roles to be filled as efficiently as possible (i.e. it's better to have three great shooters than nine OK shooters.)
2. Skills aren't worth anything unless they can overcome an opponent's ability to negate that skill (and NBA opponents are damn good)

Point #2 is where I think this gets interesting. Imagine Player A with a low post scoring ability of 75, and Player B has a low post defense ability of 80. You could make the argument that the 80 will ALWAYS stop the 75 in a vacuum. Most people would disagree, but you could at least make the argument. This kind of fits in the real life example, at least. If you assume a poisson distribution of skill for all players across the planet, the 99.9th percentile of any skill has NBA value in that it can overcome what 99.9% of the rest of the world cannot overcome. If you're not above something like the 98th percentile, you cannot overcome anyone in the NBA and your skill is useless. Meanwhile, the 98% is perfectly acceptable in NCAA D1 and the 99.9% is overkill, but below 90% is useless again.

More conservatively, i think it makes sense to apply somewhat of a Pythagorean Win Expectation here...going back to the 75 LP vs. 80 LP Def, something like Player A's 'success' percentage is =75^2/(75^2+80^2). This would work on both ends of the spectrum, where a 75 won't always lose to an 80...but if you're talking about a 15 vs. an 80 and a 5 vs. an 80, essentially they 'both suck' and would never really score against the 80.

If the pythagorean model were to work in some capacity (again, TBD because the offensive/defensive rebound and team rebound elements) that would mean the value of skills would increase exponentially EVEN WITH a linear formulation. If what Trentonjoe said is correct, we're talking about a compounded exponential for skill performance vs. rating.

The "85" comment OR made makes sense in that maybe 85 is the aforementioned "95th percentile" for NCAA D1 (and if there we an NBA sim that used HD players, a rating of 95 or so might be the aforementioned "98th percentile"). This would correlate perfectly with the 80-always-beats-75 notion, or at least that simply "being better" than your opponent more important than "how much better".

So maybe it's a combination of you said, you get better and better up to a point where it's capped. Maybe 25% of rebounds are randomly assigned so the best you could ever do is get 74.9% of the rebounds.

Nonetheless, the exponential balancing effect you're speaking of...i see it, but i don't think it would cancel out a compounded exponential skill performance.
7/1/2013 3:48 PM
i see what you are saying jet, and if a pythagorean type formula was used, i think i would agree with the conclusion. but i dont think that is what is happening, the ability for a moderate defender to defend a great scorer is just too high, it seems to me a more linear model has to be in play. i agree the abilities are not linearly formulated, across the range, but for high end ratings i do think it becomes linear or close to linear, with a gentle upwards slope. 

edit: i will say that i think your model does apply to the real life NCAA/NBA situation you described, where the reality is once you are decently worse than a guy, you are basically useless. i just dont think the HD sim works that way.
7/2/2013 9:07 AM (edited)
its even worse than linear, its like as the gap gets bigger, you asymptotically approach a maximum, resulting in almost no benefit from continued improvement. it may not actually be asymptotic but i think its close enough to think about it like that. in fact, that is basically the cornerstone of my theory on how to be successful in HD. like ive said in the interview and a million other places, team planning is the most important part of the game, and the essence of team planning is hitting the "sweet spot" in the major areas - offense, defense, rebounding, ball control - getting the major gains in each area before substantial diminishing returns kick in. i often say defense is the one area where real diminishing returns never kick in, thats not exactly true, they definitely kick in, but its just not nearly as hard. that 5th great defender on the court is dramatically more useful than the 5th great scorer.

anyway, i guess that is more of a "team ability" standpoint, but given that players just play into the whole in so many cases (scoring being the notable exception, and only half way so), i think it applies to players from that standpoint. and further, on the individual level, where a 90/90/90 player is about as good as a 100/100/100 player. so i guess while my expression above is from a team standpoint, i also believe its true (albeit without the 100% conviction) from an individual standpoint.
7/2/2013 9:05 AM
Well the pythagorean model isn't really something HD would "use", per se. it applies for assessing 'linear' probabilities. (example - for the 75 vs 80 example, if its scorer random number from 0-75 vs. defender random number 0-80, then the pythagorean model works for expected wins for the scorer. but if it's a random number from 0-155 and if it's below 75 the scorer wins and above 75 the defender wins, it would not work. i am 90% sure i'm correct on this.)

I can see a new level of profoundity to your "team ability" recommendations though. A mathematical explanation for it seems more within reach now...I always prefer an 'organic' mathematical explanation than the classic "they cap it" explanation.
7/2/2013 11:20 AM
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