Posted by pepwaves007 on 2/19/2012 6:31:00 PM (view original):
From where are you getting those numbers? I've seen IQ efficiency percentages similar to yours posted on the forums, but I've never seen someone put a number to efficiency based on fatigue. 

Nevertheless...using your numbers, Steed most likely only played at 80% efficiency for about 2-4 minutes a game, and 100% efficiency for his other 26 minutes. But, Moss played at 95% for the entire game (26.8mpg).

Someone more mathematically savvy could probably come up with an average efficiency % per 40 minutes for each, but fatigue and IQ seem like they should balance each other out in this case.

My numbers are rough estimates based on the numbers I keep. As for Steed playing 100% for 26 min, that's not quite true. Fatigue is a sliding scale. He wouldn't go from 100% to 80%; he actually goes 100, 99, 98...80, then gets taken out (assuming 80% corresponds to getting tired).

I'm very confident that the biggest determinant of rebounding ability is reb, not ath. Just look at the stat leaders for D2/D3 (D1 is confounding because all the 5 star bigs have 90+ ath and reb) and you will see that pretty much everyone has 90+ reb, while ath is all over the map.

If you want more convincing data in terms of statistical evidence, let me know. I can run them for the worlds that are going into NT or have completely NT. 

Yeah I understand that fatigue is a sliding scale...but I didn't highlight that because Moss was subject to that same sliding scale. He fatigued at more or less a similar rate (maybe slightly slower due to his stamina) as Steed. Only difference is that he was not taken out at 80%...or whatever percentage corresponds to "getting tired".

The case I presented here is obviously not strong due to the small sample size (examining only two players)...nor would it be wise to generalize the results. I just found it quite interesting because it seems to suggest ATH played at least a larger role in rebounding ability than many thought...for Steed's and Moss' results.

I mean we're not talking about a small difference in REB...33 points is pretty big. And your counter arguments about fatigue and position shouldn't make as big an impact in rebounding ability as is seen here. For example, even when playing at 80% efficiency for those 4-5 minutes, Steed's REB rating would be 77. (I know it probably doesn't work quite like that). That is still 13 points greater than Moss' 64 rating. So, if the REB rating truly is as significant as everyone says it is...I don't see how it was possible that Moss would perform equally to Steed over the course of a whole season.

That said, I would love to see more convincing statistical data if you don't mind sharing. Perhaps we can just chalk up the Moss/Steed case to a statistical outlier? Until I see those results, however, I will proceed under an operating theory where ATH is almost as strongly correlated to rebounding ability as REB itself.

I would say empirically it has always been obvious to me that REB is at least roughly twice as important in determining rebounding ability as ATH, probably more.

Posted by pepwaves on 2/19/2012 8:21:00 PM (view original):
Yeah I understand that fatigue is a sliding scale...but I didn't highlight that because Moss was subject to that same sliding scale. He fatigued at more or less a similar rate (maybe slightly slower due to his stamina) as Steed. Only difference is that he was not taken out at 80%...or whatever percentage corresponds to "getting tired".

The case I presented here is obviously not strong due to the small sample size (examining only two players)...nor would it be wise to generalize the results. I just found it quite interesting because it seems to suggest ATH played at least a larger role in rebounding ability than many thought...for Steed's and Moss' results.

I mean we're not talking about a small difference in REB...33 points is pretty big. And your counter arguments about fatigue and position shouldn't make as big an impact in rebounding ability as is seen here. For example, even when playing at 80% efficiency for those 4-5 minutes, Steed's REB rating would be 77. (I know it probably doesn't work quite like that). That is still 13 points greater than Moss' 64 rating. So, if the REB rating truly is as significant as everyone says it is...I don't see how it was possible that Moss would perform equally to Steed over the course of a whole season.

That said, I would love to see more convincing statistical data if you don't mind sharing. Perhaps we can just chalk up the Moss/Steed case to a statistical outlier? Until I see those results, however, I will proceed under an operating theory where ATH is almost as strongly correlated to rebounding ability as REB itself.

Your fatigue scenario about Moss and Steed is not the same though. Moss played at fairly fresh (assume it's 90% efficiency) and got taken out when he dipped below that. Steed played until hes getting tired (say 80%). If fatigue is a linear scale (which I'm not sure about, but let's assume it is), then it means that for somewhere around 50% of the time, Steed is playing at lower efficiency than Moss. That's pretty significant. 

I actually agree with tianyi's ultimate ath/reb conclusion, but I don't think the above post is correct.

If it was, it would mean that "fairly fresh" would yield twice as much playing time as "getting tired," which obviously isn't true.

OK, maybe not twice as much, but I don't think 50% of the time is accurate.

Posted by isack24 on 2/19/2012 9:55:00 PM (view original):
I actually agree with tianyi's ultimate ath/reb conclusion, but I don't think the above post is correct.

If it was, it would mean that "fairly fresh" would yield twice as much playing time as "getting tired," which obviously isn't true.

fatigue is not linear, so that 50% number is definitely off. Steed probably played around 18-20min at fairly fresh, and then 8min between fairly fresh and getting tired. Meanwhile, Moss played 24min at fairly fresh or better. 

interesting posts. i think the relationship between ath and reb is somewhere in the 1:3 range - as in, from a rebounding perspective only, 1 point of reb = 3 points of ath. i'd agree its almost definitely 2:1 and would be surprised if it was 4:1, my best guess (not rounding for convenience) would put it somewhere in the 2.5-3 range.

the question of the two players is interesting - why the similar performance, if rebounding is so important? well, a few comments - first off, i disagree with the notion of IQ working so linearly. also IMO, IQ applies differently in different situations - it seems to be a young player is able to rebound better than they can defend, so i'd argue iq plays a smaller role in rebounding than defense. in general, i think iq is possibly smallest in rebounding. so i would not peg that difference as that significant - even though id argue the a+ to a/a- difference was larger than suggested earlier in the thread.

with fatigue, fairly fresh vs getting tired is not that terribly different. in many cases (low sta, press), players frequently go over their fatigue mark before being taken out. you can only sub at so many points in the game. zone is the closest to following the settings - as it has the smallest impact on fatigue. fatigue is definitely not linearly - where early fatigue drops are less detrimental than later drops - so zone team can use fatigue other than fairly fresh with the least impact. i would expect the average performance of a zone player going on getting tired instead of fairly fresh to be about 5%, and not more than 10%, assuming solid stamina. 5% on average - maybe its higher for rebounding? im not sure if fatigue impacts different abilities differently or not.

i do agree with the conventional wisdom that C grabs more reb than PF. however, zone is the thing i am least familiar with of all offenses and defenses - maybe in zone, the difference is less? anyway, i would expect in a man or press than a 1 reb per game difference could be explained by the positional difference. if that was true in zone, you'd be looking at something like 7reb in 27m vs 8.1 in 29m. which is decently different, but not that much.

so, in short - outside of position difference, i don't really see much difference between the two players. it could be a product of small sample size. or maybe, it could be a product of the rest of the team. one thing im not sure most coaches realize - something i am really not a fan of - is that individual rebounding ratings are to some extent window dressing. take the same guy on a super high quality team at 6.5 rpg, put him on a terrible reb team, and he can pull down12 reb. but in the first case, he might be adding 8 reb to the team, and in the later case, 9. it really clouds the issue of what makes a player a good rebounder. i think the best simple test is actually to compare team ath and team reb to team rpg - which of course will be skewed by SOS and a million other things (high ath teams being more likely to play better competition, IMO, than better rebounding team). but it wouldn't be a terrible guideline either.

the fundamental problem in the above - which exists in many places in the sim engine - is that the greater or team wide outcome goes first (which team gets a rebound, does the shot go in), and the assignment of the stat comes second. its easier to program, sure, but it results in a less realistic and understandable sim engine than the alternative. someday, someone will come along and make a more realistic sim engine that does it right. hopefully its me, but i won't know at least till the end of the year...

i'm not a math whiz, but i disagree with the core issue of this debate - specifically, you can't compare the effect of ath v reb on a player's ability to reb. ath, imho, is a multiplier, so that you wouldn't add 2REB + 1ATH to get a player's true rebounding ability; its more REB * ATH (or some variation thereof that i have absolutely no ability to generate myself). i think that's why guards and sf's with high ath (but low reb) don't end up pulling down boards (if the REB + ATH equation was correct, a player with 90 ATH and 10 REB should be as effective as a player with 10 ATH and 90 REB; but we know that's definitely not true). the examples given above are probably (as many coaches pointed out) too small a sample size to lend any credence. the same players might improve from season to season, but because the players around them improve as well, the distribution of stats spread out, potentially lowering the statistical effectiveness for the individual player in a particular area. again, i'm not a math whiz and don't keep stats like the top coaches do, but i do notice the obvious year to year differences from the statistics page on the player profile...

Very simple regression, simply regression rebounding rate/40min against 4 independent variables, ath, spd, reb, def (in case defense matters for defensive rebound, thus, affecting total rebounds). Data used are the top 25 rebounders in Allen D3. I have to do this in excel because I left my thumbdrive with Stata in my office. Of course, more advanced analysis would be better, by incorporating team rebounding performance, rebounding rate of teammates etc. But I think this elementary analysis with simply 4 variables provides some evidence that Reb rate matters the most for rebounding efficiency:

Regression Statistics
Multiple R	0.557531788
R Square	0.310841694
Adjusted R Square	0.173010033
Standard Error	1.265180884
Observations	25
ANOVA
	df	SS	MS	F	Significance F
Regression	4	14.43961158	3.6099029	2.255227	0.099280615
Residual	20	32.01365338	1.6006827
Total	24	46.45326497
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	6.726199869	3.307663024	2.0335203	0.055484	-0.173464275	13.62586	-0.17346	13.62586
Ath	0.038331281	0.027373737	1.400294	0.176748	-0.018769334	0.095432	-0.01877	0.095432
Spd	0.005850152	0.0228146	0.2564214	0.800245	-0.041740268	0.053441	-0.04174	0.053441
Reb	0.078245006	0.030536497	2.5623438	0.018577	0.014546988	0.141943	0.014547	0.141943
Def	-0.022371903	0.020219602	-1.1064463	0.281665	-0.064549253	0.019805	-0.06455	0.019805

Way to read this is, how would someone perform with 1 extra point in a category, assuming all other categories stay the same. +1 in ath increase rebound rate by 0.038/40min, 1 point in Reb = +0.078/40min. But for those more in tune with statistics, only Reb has P value below 0.05, so Reb's statistical significant is very large.

Of course, this elementary regression is full of holes, as evident by the low adjusted R-squared. 

I'm sure there are players with tremendous reb/40min that didn't make this list, simply because their rebounding average was not in the T25 (think avg 8 reb/game in 20mpg, that's a 16reb/40min but will be left out). 

A quick glance seems to suggest that Reb plays a bigger role than Ath. 

	Name	Year	Pos	School	40Min	Ath	Spd	Reb	Def
1	Steven Warren	Jr.	C	Bethany	17.18631	36	46	100	13
2	Gerald Echevarria	Sr.	C	St. Lawrence	16.36364	62	15	98	76
3	Dale Rish	Fr.	C	Thomas More	16.23431	33	21	85	32
4	William Lainez	Sr.	C	Willamette	16.12167	25	31	93	23
5	Dale Luper	Sr.	C	St. Mary's (MN)	15.93625	33	15	100	39
6	Michael Booker	Sr.	PF	Luther	15.46875	57	34	80	49
7	Brian Churchill	Sr.	C	Ithaca	15.22491	70	16	84	68
8	Richard Priolo	Sr.	PF	Gordon	15.21569	25	38	93	44
9	Eric Knott	Jr.	C	Mount St. Mary	14.58484	26	28	79	11
10	Ruben Cote	Sr.	C	Plymouth St.	14.52055	50	48	73	61
11	Philip Cooper	Sr.	C	Cornell	14.46809	60	22	95	44
12	Christopher Montgomery	Sr.	C	Elmira	14.45946	45	53	78	40
13	Benjamin Meier	Jr.	C	Eastern U.	14.41176	19	18	98	13
14	George Ceniceros	Sr.	C	N. Central	14.28571	42	33	99	37
15	Mathew Eveland	Sr.	C	La Verne	13.93728	38	9	88	43
16	John Duncan	Sr.	C	Dickinson	13.91304	26	28	89	27
17	Johnathan Engleman	Sr.	PF	Arcadia	13.87205	51	32	90	32
18	Michael Guidry	Sr.	C	MacMurray	13.56164	59	5	77	74
19	Edward Simmons	Jr.	PF	Transylvania	13.51351	51	32	75	31
20	Justin Edwards	Sr.	PF	Hope	13.42193	28	30	84	26
21	Terry Kitchens	Sr.	C	Averett	13.33333	40	40	94	61
22	Geraldo Villegas	Sr.	PF	Greensboro	13.19865	35	28	88	55
23	Clinton Guthrie	Sr.	C	McDaniel	13.19728	12	37	100	4
24	John Moore	Sr.	C	Drew	11.90184	70	33	71	86
25	James Etter	Jr.	PF	Wilkes	11.21387	43	23	72	53

Posted by tianyi7886 on 2/20/2012 3:57:00 PM (view original):
Very simple regression, simply regression rebounding rate/40min against 4 independent variables, ath, spd, reb, def (in case defense matters for defensive rebound, thus, affecting total rebounds). Data used are the top 25 rebounders in Allen D3. I have to do this in excel because I left my thumbdrive with Stata in my office. Of course, more advanced analysis would be better, by incorporating team rebounding performance, rebounding rate of teammates etc. But I think this elementary analysis with simply 4 variables provides some evidence that Reb rate matters the most for rebounding efficiency:

Regression Statistics
Multiple R	0.557531788
R Square	0.310841694
Adjusted R Square	0.173010033
Standard Error	1.265180884
Observations	25
ANOVA
	df	SS	MS	F	Significance F
Regression	4	14.43961158	3.6099029	2.255227	0.099280615
Residual	20	32.01365338	1.6006827
Total	24	46.45326497
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	6.726199869	3.307663024	2.0335203	0.055484	-0.173464275	13.62586	-0.17346	13.62586
Ath	0.038331281	0.027373737	1.400294	0.176748	-0.018769334	0.095432	-0.01877	0.095432
Spd	0.005850152	0.0228146	0.2564214	0.800245	-0.041740268	0.053441	-0.04174	0.053441
Reb	0.078245006	0.030536497	2.5623438	0.018577	0.014546988	0.141943	0.014547	0.141943
Def	-0.022371903	0.020219602	-1.1064463	0.281665	-0.064549253	0.019805	-0.06455	0.019805

Way to read this is, how would someone perform with 1 extra point in a category, assuming all other categories stay the same. +1 in ath increase rebound rate by 0.038/40min, 1 point in Reb = +0.078/40min. But for those more in tune with statistics, only Reb has P value below 0.05, so Reb's statistical significant is very large.

Of course, this elementary regression is full of holes, as evident by the low adjusted R-squared. 

thank you for posting that tianyi! very interesting. looks like it suggests that reb is roughly twice as important as ath, or slightly more. i don't think that is too far off. as you mentioned, of course, there are a million holes - so i wouldn't advise a reading user to take it at reb is twice as important as ath. it could be 1.5 or 3x. but its probably somewhere in there. for example, usually the top rebounders are on worse teams, and higher ath bigs on better teams, so the ath is probably under valued in that equation - but of course, there are probably 50 more reasons on both side of the fence why that simple regression isn't perfect. one of them being that i strongly believe individual rebounding values are somewhat of window dressing - somewhat, not completely - and i have no idea which way that could skew things.

I agree with you billgy. The 2:1 ratio could be off by quite a bit, it could be 1.5:1, 3:1, or maybe even 4:1, but the takeaway is that reb>ath in terms of rebounding ability. 

I didn't use defensive rebound as a dependent variable; I used rebound (off+def) as the dependent variable. I am not good with Excel Macros but if anyone is, and can get a Macros set up to automatically get data on every player on every team, I'll gladly run some data analysis in Stata.