Some Historical Plus-Minus

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Re: Some Historical Plus-Minus 

Post#21 » by 70sFan » Mon Feb 27, 2023 4:46 pm

eminence wrote:
eminence wrote:Bit of a summary for Hakeem:

-50 games played, 24-26 (48%) over a period where the Rockets overall won 58.4% of their games, so individual and team on-court ratings lower than one would expect

102.8 Off Rating, 101.8 Def Rating (/100), +1.0 Net on/court

+43 over a period his team was -19, so in the +6 range for on/off without going through to check pace with and without


Kareem, just the '85 to '88 season samples (thought a bit too much of a jump from '78/'80 to include them)

-76 games played (or portions of games tracked I suppose), 56-20 (73.7%) vs 76.5% overall, so probably a bit more accurate On ratings, though still likely a slight underestimation

112.6 Off Rating, 101.9 Def Rating, +10.7 Net (the Lakers were good?!? Really good)

+489 for Kareem in sample, +369 for the Lakers, my estimate would be in the +4 on/off range

Really pretty impressive results for Kareem, from a sample that leans towards his '87/'88 seasons.

I wonder how big part old Kareem played in these numbers. It looks very impressive for 1988 Kareem, but I am not sure if he was still that valuable. How much of that is Kareem's impact in limited role and how much it is just sharing the court with Magic.
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Re: Some Historical Plus-Minus 

Post#22 » by Owly » Mon Feb 27, 2023 5:26 pm

First up thanks for the time and effort and for sharing this with us (haven't tended to "and1" for a long time, I think because I felt the numbers depended very much on audience size, boards posted on etc and could lead to pandering though I suppose it can be nice as an acknowledgement).

Could you clarify what you meant by ...
Squared2020 wrote:Small samples basically suggests "Players 20 through 200 are statistically nonsignificant."

I'm struggling to parse it.
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Re: Some Historical Plus-Minus 

Post#23 » by eminence » Mon Feb 27, 2023 5:50 pm

Nevermind that last one, me no type good today, me use wrong cell. +9 range for Kareems On/Off.
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Re: Some Historical Plus-Minus 

Post#24 » by Doctor MJ » Mon Feb 27, 2023 6:48 pm

Squared2020 wrote:The primary reason I despise the measure is that it does not capture what any players do on the court. A player can hide in the noise and look like a complete player without contributing anything significant. The example I give in my talks about RAPM is "Let's identify a top student in a class, but only give out group projects and use only the overall grade. Everyone knows the one slacker in the class who tends to be on some of the good groups. If they are on group projects that score 90, 95, 85, 90, 95, 90; then you might think they are high-B / low-A students." (BTW: This is the case of Johnny Newman from the 1980's Knicks who looked really appealing for the Charlotte Hornets in 1990.)


First off, glad to see your handle pop up, and I hope you're doing well Squared 2020!

Second, thank you for sharing your work in this new form!

I wanted to speak to what you're describing here.

What I've always said is that +/- stats add a new dimension to statistical analysis that is extremely useful...to be used in conjunction with other factors. Using +/- stats alone is a recipe for either a) false epiphanies or b) shrugging your shoulders and going back to your other tools.

What I've suggested is that as we get better and better player tracking data, what I'd like to see are feature-layer metrics between the player tracking and the +/- that can at least begin to suggest specific strengths and weaknesses. Still hard to imagine that it would be wise to use these exclusively, but I think it could really help triangulating "where it hurts".

Re: Group work. So two things here:

1. Clearly when sample is problematic the ability to draw individual conclusions from group samples is hindered. In the world of modern NBA basketball I think we do eventually get enough sample that we can make use of the data, but this is not a given. I've said before that I don't think getting Wilt-Russell Era +/- will shed much insight because these guys played such high MPG. If you're only ever off the floor during garbage time, then I wouldn't think regression would be a good approach to understand your impact.

2. I like your analogy, and all analogies break down so it's not damning that there's a break here, but here's the response that I can't help but think:

In a multi-player game, there is no way to truly test the players individually except for very specific skills - FT% is about all I can really think of. Hence, while group-based stats like this are challenging to use effectively, in a context that is by definition group-based, we must expect to use them.

In school, while there are skills that come from group projects that can't be expected to come any other way, the dominance of individual assessments is the focal point and yeah, it can be a real issue if a teacher overemphasizes group work.
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Re: Some Historical Plus-Minus 

Post#25 » by Doctor MJ » Mon Feb 27, 2023 6:51 pm

Owly wrote:First up thanks for the time and effort and for sharing this with us (haven't tended to "and1" for a long time, I think because I felt the numbers depended very much on audience size, boards posted on etc and could lead to pandering though I suppose it can be nice as an acknowledgement).

Could you clarify what you meant by ...
Squared2020 wrote:Small samples basically suggests "Players 20 through 200 are statistically nonsignificant."

I'm struggling to parse it.


What I interpreted it to be - which might be wrong - is that the uncertainty in the metric is larger than the player's deviation from average. Extremely valuable and extremely un-valuable players can be identified as having positive or negative value with less sample than more typical players.
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Re: Some Historical Plus-Minus 

Post#26 » by eminence » Mon Feb 27, 2023 7:40 pm

Bird, and I double checked my cells.

78-33 (70.3% vs 71.1%), so should be pretty on the nose.

111.8 Offense, 104.8 Defense

+686 for Bird, +655 for Celtics, in the +7 range for Birds On/Off
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Re: Some Historical Plus-Minus 

Post#27 » by OhayoKD » Mon Feb 27, 2023 8:06 pm

penbeast0 wrote:Hakeem in the regular season was not the reason he's a top 10 player all time though still a great player. It's his postseason.

Eh. Hakeem being top 10 in the RS isn't hard to defend. Honestly I find him a top 5 rs performer plausible considering the external context he dealt with, but even if we bind ourselves to the data, I think he has a pretty persuasive case(at least if we focus on "isolate for winning" as opposed to offensive box production).

A couple things to note with these RAPM sets:
-> Sample size is small, very small
-> When players hit a certain treshold of lift(25-30), lineup-adjusted impact has a tendency to redistribute their impact to teammates
-> Arguable disadvantage relative to various indirect or even WOWY in that teams/teammates aren't really given time to adapt to the superstar missing

When working with a dozen or less games per season for "adjusted" data, it's probably advantageous to look at the "pure" stuff(Indirect, WOWY, how sigificant player fluctuation/injuries coincide with team performance, ect ect) to maximize our sample. We can always apply various adjustments ourselves, and while this is indeed messier, at least we're working with something substantial. We can also better contextualize the echoes we get with something like RAPM here by looking at what's going on in the real-world.

With that out of the way, let's start with a basic "pure" outline applying a filter of >10 gm/season samples, keeping in mind that the sample of data being referenced is vastly larger than the RAPM set provided:
84-85, rookie hakeem sees a 29 win team become a 48 win team without notable cast change. 86, rockets are 5-5 without, and then are 51 with, and then skyrocket in the postseason notably beating the 61 win lakers in 5 with hakeem's ppg jumping off a cliff. In 87 sampson misses a bunch of games, and there's a coke crisis but the rockets are still able to win more games than a certain chicago guard. 88, rockets play like a 20 win team without and a 45 win team with, and then in 92 the rockets go 2-10 without and win 42 with him and then move to a 55 wins in 93 before b2b titles with 94 and 95.

Hakeem is one of a handful of players(post-russell, we're talking Lebron, Kareem, Robinson) to post 25+-win lift multiple times. Worth noting that this is around where RAPM tends to distribute superstar impact to role players. His peak signals are arguably era-best.

Of course, a common knock on Hakeem is his consistency as an RS performer, but even over longer periods, he looks quite good. IIRC, if you use 10-year samples...

Hakeem takes 33-win teams to 48 wins
Jordan takes 38-win teams to 53.5 wins
Magic takes 44-win teams to 59 wins

Keeping in mind that it's harder to lift better teams, Hakeem comes marginally behind Jordan, and slightly more behind Magic, but he's right up there with both.

Ben has his own(presumably more sophisticated) approach which likes Hakeem even better; "Prime WOWY" ranks Olajuwon 10th. Magic and Jordan rank 12th and 20th, respectively. Keep in mind the samples here are much, much smaller, but at least there aren't extraneous distortions to worry about as we may with something like WOWYR

Getting back to larger samples(or in this case, the largest possible sample), Drafting Hakeem produces a +5 SRS improvement for the Rockets without significant roster additions(this is special even among top-ten candidates, and better than what Magic or Jordan managed), and they've reached the final(interrupting a dynasty on the way) by year two. That start looks GOAT-worthy. Then, when various catastrophes take place starting in 1987, Hakeem still does an admiral job keeping a shipwreck afloat before capitalizing spectacularly with limited help.

Pollock did some on/off for 94-96 which looks pretty good with 1994 looking like a top 60 signal from the last 30 years. Considering the 92 Rockets were outscored by 10 points in games without Hakeem, it's not hard to see inclusion of 92/93 giving Hakeem a top top 3-year peak.

Looking at BBR, we get a full 2 seasons of "impact" data for Hakeem with his on/off in 97/98(well, well past his peak), but even there, entering his mid 30's, Dream looks pretty impactful on very good teams(that's rarified air for a 13th/14th season player, even among top-tenners).

Considering the immense external adversity at play(coke crisis, incompetent and hostile FO, co-star injured, ect.), the wear-and tear that comes with a decade-plus of continuous high-level play(no retirements here! forced or otherwise), and the absence of a complimentary superstar to tie his minutes to(Magic had Kareem, Jordan had Pippen), I'd say Hakeem has a solid case as the most valuable regular season player of his era.

As he was also arguably the nba's greatest playoff-riser(94-95 Rox played 62-win basketball vs playoff opponents, and 86 victory against the Magic is probably the best "david beats goliath" moment of the period), and a longevity giant, I feel pretty confident considering him among the best of the best, even if his resume looks a little lean.

Getting back to RAPM, besides sample size/luck, it's not hard to see Hakeem potentially being a victim of his own goodness. At a certain threshold of lift, role-players start drawing from a superstar's well, and a direct approach has him hitting that point multiple points. Sampson is the closest thing Hakeem had to a co-star, but when he missed half a season in 1987...
21-22 with and 21-18 without

...the Rockets were basically unaffected.

Color me skeptical there was much assistance at mission control.


I also think rotations may be a factor but so I'm not swinging recklessly...
Squared2020 wrote:but that doesn't mean there's nonexplainability.

Would you happen to have rotation sheets for Hakeem here, particularly his early years from 84-88? Iirc Hakeem staggered with Sampson early on, but I'd like to verify. Given the above, that may not even be notable, but if it's available, it might provide some useful context.

Regardless, I think you and doc summarize the issue with putting too much stock in this stuff(I think alot of analysis seems to see lineup-adjustment as a "holy grail") pretty well...
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Squared2020 wrote:The primary reason I despise the measure is that it does not capture what any players do on the court. A player can hide in the noise and look like a complete player without contributing anything significant. The example I give in my talks about RAPM is "Let's identify a top student in a class, but only give out group projects and use only the overall grade. Everyone knows the one slacker in the class who tends to be on some of the good groups. If they are on group projects that score 90, 95, 85, 90, 95, 90; then you might think they are high-B / low-A students." (BTW: This is the case of Johnny Newman from the 1980's Knicks who looked really appealing for the Charlotte Hornets in 1990.)

What I've always said is that +/- stats add a new dimension to statistical analysis that is extremely useful...to be used in conjunction with other factors. Using +/- stats alone is a recipe for either a) false epiphanies or b) shrugging your shoulders and going back to your other tools.

RAPM can definitely help I think(currently making use of it directly seems to lead to better predictivity and "flexibility" among the current "industry standard" all-inones), but it's a good idea to cross-reference it with other stuff. Granulars, film, historic trends, and "reaL" signals all have a part to play. But I also think it's important to not go with "every tool is created equal" and treat it like a democracy where the conclusion with the most numbers "voting" in it's favor is the most likely. To that end, the specific samples at play are very important to consider. And while I think it's great Squared has compiled this collection for us, we should probably use it as a "feather" rather than the backbone of how we assess an individual player, at least pending more data.
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Re: Some Historical Plus-Minus 

Post#28 » by Owly » Mon Feb 27, 2023 9:48 pm

OhayoKD wrote:
penbeast0 wrote:Hakeem in the regular season was not the reason he's a top 10 player all time though still a great player. It's his postseason.

Eh. Hakeem being top 10 in the RS isn't hard to defend. Honestly I find him a top 5 rs performer plausible considering the external context he dealt with, but even if we bind ourselves to the data, I think he has a pretty persuasive case(at least if we focus on "isolate for winning" as opposed to offensive box production).

A couple things to note with these RAPM sets:
-> Sample size is small, very small
-> When players hit a certain treshold of lift(25-30), adjusted impact has a tendency to redistribute their impact to teammates
-> Arguable disadvantage relative to various indirect or even WOWY in that teams/teammates aren't really given time to adapt to the superstar missing

When working with a dozen or less games per season for "adjusted" data, it's probably advantageous to look at the "pure" stuff(Indirect, WOWY, how sigificant player fluctuation/injuries coincide with team performance, ect ect) to maximize our sample. We can always apply various adjustments ourselves, and while this is indeed messier, at least we're working with something substantial. We can also better contextualize the echoes we get with something like RAPM here by looking at what's going on in the real-world.

With that out of the way, let's start with a basic "pure" outline applying a filter of >10 gm/season samples, keeping in mind that the sample of data being referenced is vastly larger than the RAPM set provided:
84-85, rookie hakeem sees a 29 win team become a 48 win team without notable cast change. 86, rockets are 5-5 without, and then are 51 with, and then skyrocket in the postseason notably beating the 61 win lakers in 5 with hakeem's ppg jumping off a cliff. In 87 sampson misses a bunch of games, and there's a coke crisis but the rockets are still able to win more games than a certain chicago guard. 88, rockets play like a 20 win team without and a 45 win team with, and then in 92 the rockets go 2-10 without and win 42 with him and then move to a 55 wins in 93 before b2b titles with 94 and 95.

Hakeem is one of a handful of players(post-russell, we're talking Lebron, Kareem, Robinson) to post 25+-win lift multiple times. Worth noting that this is around where RAPM tends to distribute superstar impact to role players. His peak signals are arguably era-best.

Of course, a common knock on Hakeem is his consistency as an RS performer, but even over longer periods, he looks quite good:
10-year WOWY
Hakeem takes 33-win teams to 48 wins
Jordan takes 38-win teams to 53.5 wins
Magic takes 44-win teams to 59 wins

Keeping in mind that it's harder to lift better teams, Hakeem comes marginally behind Jordan, and slightly more behind Magic, but he's right up there with both.

Ben has his own(presumably more sophisticated) approach which likes Hakeem even better; "Prime WOWY" ranks Olajuwon 10th. Magic and Jordan rank 12th and 20th, respectively. Keep in mind the samples here are much, much smaller, but at least there aren't extraneous distortions to worry about as we may with something like WOWYR

Getting back to larger samples(or in this case, the largest possible sample), Drafting Hakeem produces a +5 SRS improvement for the Rockets without significant roster additions(this is special even among top-ten candidates, and much better than what Magic or Jordan managed), and they've reached the final(interrupting a dynasty on the way) by year two. That start looks GOAT-worthy. Then, when various catastrophes take place starting in 1987, Hakeem still does an admiral job keeping a shipwreck afloat before capitalizing spectacularly with limited help.

We only get a full season of "impact" data for Hakeem with his on/off in 97/98(well, well past his peak), but even there, entering his mid 30's, Dream looks pretty impactful on very good teams(that's rarified air for a 13th/14th season player, even among top-tenners).

Considering the immense external adversity at play(coke crisis, incompetent and hostile FO, co-star injured, ect.), the wear-and tear that comes with a decade-plus of continuous high-level play(no retirements here! forced or otherwise), and the absence of a complimentary superstar to tie his minutes to(Magic had Kareem, Jordan had Pippen), I'd say Hakeem has a solid case as the most valuable regular season player of his era.

As he was also arguably the nba's greatest playoff-riser(94-95 Rox played 62-win basketball vs playoff opponents, and 86 victory against the Magic is probably the best "david beats goliath" moment of the period), and a longevity giant, I feel pretty confident considering him among the best of the best, even if his resume looks a little lean.

Getting back to RAPM, besides sample size/luck, it's not hard to see Hakeem potentially being a victim of his own goodness. At a certain threshold of lift, role-players start drawing from a superstar's well, and a direct approach has him hitting that point multiple points. Sampson is the closest thing Hakeem had to a co-star, but when he missed half a season in 1987...
21-22 with and 21-18 without

...the Rockets were basically unaffected.

Color me skeptical there was much assistance at mission control.


I also think rotations may be a factor but so I'm not swinging recklessly...

Coming in I'm pretty low on Olajuwon versus norms here (and elsewhere but unless mainstream stock his risen, I think he ranks highter here) and a greater RS weighter (and tend to regard variation from RS primarily as random variance, noise, though open to being wrong in general and that not being the best explanation in a specific instance and Olajuwon is one of the larger playoff samples for risers)... so, there's the context.

I'll also note defense is hard to quantify and ... that gives us greater range in general and maybe upside on Hakeem.

Still, that first line ...On top 5 there's a top 4 that many here are pretty sure of. I'd say Robinson has close to better box and better impact signals every year they're in the league together (bar '93 on box; obvs '97 he isn't functionally around though for what little it's worth the limited sample production and impact are nonetheless very strong) and I doubt otoh that his early years make up for the significant gap in box and impact as they both box peak, plus Robinson's continued big impact signals later as Hakeem falls in relevance. Or versus Garnett with with as roughly as good (or better) composites over a slightly larger sample with much greater certainty of impact. Or Wilt or ...

You get where I'm going with this? For 5 or 10 there's a lot of great players that would make top 5 pretty implausible and top 10 tricky to defend.

The old conventional wisdom gang (Jordan, Chamberlain, Russell, Johnson, Jabbar, Bird, Robertson) would leave little room for modern players and with James locked in there's little room for him and a lot of competition. Not a great means [edit: of evaluating players] but one angle that's out there. A variation would be MVP shares which skews against those earlier era guys (fewer shares distributed due to voting systems), there he ranks 22nd for NBA and ABA combined or he would be 20th passing Erving and Daniels for NBA only, though this method cheats the earliest major-league era greats, even more than noted above as the award didn't exist in the Mikan era (in the BAA/NBA bar one curious year that only sometimes is credited for Wanzer and which doesn't have shares or voting stats). [last sentence edited to complete unfinished thought]

By the box though ... he's 17th in VORP ... in the VORP era (which means ignoring about half of NBA history and hurting those who spanned across the eras). 21st by win shares (and whilst efficiency is probably mean on him here, WS's low baseline means high total minutes is helping him, too). Hollinger's EWA would probably be friendlier (as PER much higher on him as a rate measure, though replacement level, if low, isn't otoh as dreadful as WS's is). Fwiw he never leads in PER, WS/48 or BPM (or Win Shares or VORP, don't know about EWA ... his 2nd overall in minutes in '93, his most productive year might give him a shot, though Jordan has a solid PER edge and iirc EWA gives SGs a lower replacement level) can't speak to the more state of the art stuff (though career wise, like BPM I suspect they might not like the weaker passing years).

We do have hints at high impact at peak ... but the 94-96 on off data whilst promising is a long way behind Robinson but (on the average of the yearly figures) about even with Mookie Blaylock (who has more impact evidence later) and closer to the likes of Bo Outlaw and Horace Grant (who make no mistake show very strongly in these numbers) than Robinson. He is high in terms of ranking of the average. Very noisy figures.

Still, allowing for the above difficulty in quantifying defense for much of his career ... the combination of quality of competitors and, at first glance, absence of clear evidence of him as an absolute elite RS player (can't see much putting him top 10).


I will say I haven't fully ingested, properly paid attention to your pro-argument here but at first glance it seems more "he's good" than "he has a clear consistent RS case for above 6 or 11 others" (granted this is hard with differing levels of data) but I'd have to look closer.

I will say the reading on that rookie impact looks generous, on the margins because the same roster doesn't acknowledge that it's a young roster that would be expected to improve but primarily because "is special even among top-ten candidates" and with the finals appearance "GOAT-worthy" are quite strong. Olajuwon's (considered use of inverted comma's because I don't love crediting a team level stat to an individual, won't because consistent use on every player might grow tiresome but you get the idea) 4.5 SRS change is very good but less than half the change for Bird, Duncan, Robinson (all above 11) or Abdul-Jabbar. This isn't then, of itself an outlier that is "special" amongst special players, though as I noted this is a crude team level number and differing contexts (notably advantageous changes for Duncan) would make reading at face value tricky.
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Re: Some Historical Plus-Minus 

Post#29 » by Squared2020 » Tue Feb 28, 2023 12:20 am

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Re: Some Historical Plus-Minus 

Post#30 » by Squared2020 » Tue Feb 28, 2023 12:27 am

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Re: Some Historical Plus-Minus 

Post#31 » by Squared2020 » Tue Feb 28, 2023 12:34 am

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Re: Some Historical Plus-Minus 

Post#32 » by Squared2020 » Tue Feb 28, 2023 12:41 am

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Re: Some Historical Plus-Minus 

Post#33 » by Squared2020 » Tue Feb 28, 2023 12:52 am

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Re: Some Historical Plus-Minus 

Post#34 » by Moonbeam » Tue Feb 28, 2023 1:39 am

Squared2020 wrote:
Owly wrote:First up thanks for the time and effort and for sharing this with us (haven't tended to "and1" for a long time, I think because I felt the numbers depended very much on audience size, boards posted on etc and could lead to pandering though I suppose it can be nice as an acknowledgement).

Could you clarify what you meant by ...
Squared2020 wrote:Small samples basically suggests "Players 20 through 200 are statistically nonsignificant."

I'm struggling to parse it.


Doctor MJ was pretty much right on, but I'll color in some details. The RAPM model is a "shrinkage model." This means we treat the parameters of the model (coefficients that describe the +/- contribution of a player when they are on the floor) as a random variable instead of a fixed value and attempt to "shrink" lightly-sampled variables to zero. Traditional regression assumes the parameter is a true, specific value. Bayesian models suggest that these values are random about some mean with some variance.

In traditional RAPM, we assume every player (before any stints have been played) has zero contribution with a fixed variance (this is part of the "shrinking parameter") and, as stints are added to the model, the distribution of each players' parameters (players have an O and D parameter) updates to reflect the observations. So when folks ask about priors like "Rookie Prior" they are asking to adjust the value of zero to something else.

After running the regression to get final distributions (we call these posteriors), we also get variances for free. Here we see players tend to have variances between 2 and 6, depending on the number of stints they play in. Here, we can conduct a statistical test to say "Is player 20 better than player 200?" Even though the value for player 20 is better than the value for player 200, this may be due to randomness. Tradition single-season RAPM (even three season RAPM) almost always "fails to reject" and implies that player 20 and player 200 are no different.

Heavier details can be found here: https://squared2020.com/2019/10/03/exercising-error-quantifying-statistical-tests-under-rapm-part-iv/

EDIT: Forgot to include the terms "Shrink to zero"


Thank you so much for this! I'd been wanting to see a lot more detail around the technical aspects of RAPM that I hadn't seen before or were hand-waved away. Do you know whether there has been any sort of exploration of other shrinkage techniques like elastic net?
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Re: Some Historical Plus-Minus 

Post#35 » by Moonbeam » Tue Feb 28, 2023 1:40 am

I'd be keen to see the stats for Adrian Dantley if you've got them.
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Re: Some Historical Plus-Minus 

Post#36 » by OhayoKD » Tue Feb 28, 2023 1:53 am

This took longer than expected...
Owly wrote:
OhayoKD wrote:
penbeast0 wrote:Hakeem in the regular season was not the reason he's a top 10 player all time though still a great player. It's his postseason.

Eh. Hakeem being top 10 in the RS isn't hard to defend. Honestly I find him a top 5 rs performer plausible considering the external context he dealt with, but even if we bind ourselves to the data, I think he has a pretty persuasive case(at least if we focus on "isolate for winning" as opposed to offensive box production).

Coming in I'm pretty low on Olajuwon versus norms here (and elsewhere but unless mainstream stock his risen, I think he ranks highter here) and a greater RS weighter (and tend to regard variation from RS primarily as random variance, noise, though open to being wrong in general and that not being the best explanation in a specific instance and Olajuwon is one of the larger playoff samples for risers)... so, there's the context.

I'll also note defense is hard to quantify and ... that gives us greater range in general and maybe upside on Hakeem.

Still, that first line ...On top 5 there's a top 4 that many here are pretty sure of. I'd say Robinson has close to better box and better impact signals every year they're in the league together (bar '93 on box; obvs '97 he isn't functionally around though for what little it's worth the limited sample production and impact are nonetheless very strong) and I doubt otoh that his early years make up for the significant gap in box and impact as they both box peak, plus Robinson's continued big impact signals later as Hakeem falls in relevance. Or versus Garnett with with as roughly as good (or better) composites over a slightly larger sample with much greater certainty of impact. Or Wilt or ...

You get where I'm going with this? For 5 or 10 there's a lot of great players that would make top 5 pretty implausible and top 10 tricky to defend.

Well, there is a difference between finding a bunch of players who have strong arguments, and a bunch of players whose arguments stay strong using internally consistent criteria/reasoning. Also should clarify I meant "top 10" is defensible on purely empirical means, not top 5. I see top 5 as plausible via contextual considerations (the same types that are often used to explain KG's "Impact' stuff tanking in the years immediately following 04 before his role is made significantly more specific in 08, or to penalize shaq for his off-court decisions). I'm also not necessarily going for one or two years, but rather a more general case that accounts for peak, prime, and career. Hakeem may not sweep all-three but he's within range for all of them and I don't know you can really say that for everyone you've listed. Duncan has a fantastic stretch that is basically shortened significantly with injuries in 04/05. KG may as well have injured himself for 05-07 if we're describing what happened as opposed to taking signals of the better looking parts as a reason to raise everything with a predictive lens.

I'll also note that I wasn't necessarily going for strict era-relativity. If I was, good chance my top 6 features 4 players from the 60's. That said, I'll start with box since I anticipate that may actually be the biggest source of our delta on Hakeem...
By the box though ... he's 17th in VORP ... in the VORP era (which means ignoring about half of NBA history and hurting those who spanned across the eras). 21st by win shares (and whilst efficiency is probably mean on him here, WS's low baseline means high total minutes is helping him, too). Hollinger's EWA would probably be friendlier (as PER much higher on him as a rate measure, though replacement level, if low, isn't otoh as dreadful as WS's is). Fwiw he never leads in PER, WS/48 or BPM (or Win Shares or VORP, don't know about EWA ... his 2nd overall in minutes in '93, his most productive year might give him a shot, though Jordan has a solid PER edge and iirc EWA gives SGs a lower replacement level) can't speak to the more state of the art stuff (though career wise, like BPM I suspect they might not like the weaker passing years).

You cite Hakeem's defensive value as a source of uncertainty that presumably can go either way. But to me, him being a valuable defender means "box" is going to undervalue him(and two-way bigs/primary paint protectors)relative to smaller players. You see uncertainty, I see bias:
Spoiler:
DraymondGold wrote:(1) Even if steals are overrated in box-based defensive measurements (e.g. if the box stats miss the fact that the steals come expense of unnecessary gambling, as they may for Jordan), steals are still individually the most valuable defensive play someone can make.

So a couple notes here.
(1) You are combining the defensive value of a steal with the offensive value generated. On the defensive side alone, steals aren't nearly as valuable as plays at the rim. Additionally, just like blocks, "steals" from a non-big often are a byproduct of a bigger player's influence...
https://youtu.be/p5aNUS762wM?t=1165
Here, Jordan is able to get a steal because Oakley stonewalls the attacker and occupies his attention. Yet as far as these box-models are concerned, all the credit here belongs to MJ. Notably, it was Oakley's arrival that saw the Bulls become a -2 defense in 1988(the only good defense Jordan has ever anchored), and it was with Oakley's depature that the Bulls fell back to mediocrity. Charles did not rack up enough steals or blocks for stuff like "RAPTOR' to love him, but I'd argue on plays like these, its Oakley who deserves most of the credit, not steal-getter MJ.

(2) Whatever the value of a steal, these metrics have no way to account for when steal attempts fail. Considering Jordan consistently posted high-error rates(dropping to the 14th percentile in 1991 despite a drop in defensive activity), only including the positives and completely excluding the negatives will naturally inflate how good a guard looks. We can actually see this if we compare Jordan's steal-d-rating correlation with Kawhi's:
Image
Kawhi doesn't rack up as many, but because he gambles significantly less, his steals end up having a stronger influence on the quality of his team's defense.

Unless these sorts of things are somehow accounted for in these box-components,(as far as I know BBR BPM actively compounds the issue by giving smaller players more credit for blocks) I'm pretty confident high-gambling steal-getters(and to a degree, undersized block accumulators) are getting significantly juiced. However, when possible it's better to see if we can back our theories with evidence as opposed to speculation, which is probably why, contrary to whatever "consensus" you are referencing, Ben Taylor specifically argues that MJ's playoff on/off is important so we have a way to properly account for his defensive impact:
https://youtu.be/p5aNUS762wM?t=1291. And yes, on/off is "noisy", but if you're really concerned about noise...

Make a note of "just like blocks, "steals" from a non-big often are a byproduct of a bigger player's influence".

Moving on...
Spoiler:
...it's probably a good idea to reference larger samples. Maybe there is an allocation problem here, but the largest possible samples(including multiple 82 game-sets), actually have the defensive gulf being bigger than what one might extrapolate from on/off. This tracks with the Bulls going from average to #1 with Jordan's defensive activity and effiency(breakdowns/error rate) declining, them staying average defensively until Oakley's addition, his relatively unimpressive D-RAPM, the Bulls effectively being unaffected on defense by Jordan's departure, and even his D-PIPM(IIRC Ben says historic PIPM does a better job accounting for defense than similar metrics, something to do with using linear-regression as opposed to tree-branching?) which, outside of 1988, looks worse than basically all of Lebron's prime save for a couple down-years(Lebron is able to match 1988 at various points fwiw).

All considered, the real world seems to disagree with the box-one on defense with this type of archetype, and it does so consistently with the disparity not really getting any better if we look at raw individual data or even the history of great defenses.

I've put these excerpts in spoilers since they cover a "provocative" topic, but here's a quick synopsis: "All considered, the real world seems to disagree with the box-one on defense regarding this type of archetype, and it does so consistently with the disparity not really getting any better if we look at raw individual data or even the history of great defenses."

Unfortunately, I can't quote the thread, so if you want the full context of what I was replying to, you can scroll to the middle of this post:https://forums.realgm.com/boards/viewtopic.php?p=103585765#p103585765)

Anyway, remember that note you took earlier?...let's take a look at the methodology for the box-aggregate you first highlighted:
This box score information is also weighted according to what position or role the player has on the team. For instance, a block by a center is good, but a block by a guard is great.

Yeah, um:
https://youtu.be/17swk1eLLRM?t=23

When you highlight Jordan's better box, you are discussing a version of Jordan that apparently is better at defense than Kareem. The same is true for fellow stat-sheet god LeBox. At least for LeBox, the real-world suggests some defensive influence throughout his prime, JorBox? Eh. But honestly, whatever box-titan you use the box-score to champion, the real world will disagree as it has Kareem's presence coinciding with a 4-point defensive improvement for 4 straight seasons. Now replace offense-slanted Kareem with bigs who get half their value on the defensive end(further investigation may lead me to claiming some get "most" of their value on the defensive end, but let's table that now) and we may have a problem.

If you want to disregard that, fine. But my approach here is to restrict box to specific comparisons, and maybe take a peek if a player is doing better than they "should" do there. To that end, if we're going to use BPM/Vorp to assess Hakeem, then I think we should restrict it to comparisons with similar archetypes. My preference is that we don't use it at all(for Hakeem), but if we are going to use it, maybe at least consider some of the above. FWIW Hakeem ranks 5th among "two-way bigs" in average BPM(Giannis and Davis not yet experienced his post-prime) and 3rd for career.

Wilt and Russell may as well be excluded, so let's say he's really 5th. That leaves 5-spots for everyone else with Lebron and Kareem effectively being shoe-ins(there is an angle to hit Lebron, but I'll get to that later).

Is that great for a top 10 case? No. Damning? Don't think so. Do I care?

Not really(may re-assess KG though).
(Jordan, Chamberlain, Russell, Johnson, Jabbar, Bird, Robertson) would leave little room for modern players and with James locked in there's little room for him and a lot of competition.

Wasn't really looking to branch this far out, but eh. I don't know Robertson over Hakeem is actually "conventional" anymore. My impression is Hakeem as a top 10 pick is quite frequent though obviously there's a playoff-lean there. MVP shares is probably a good proxy for real-time regular-season perception, but it will obviously skew against players with lesser-casts. A method I think would be interesting for regular season "peak" perception would be to look at how much of the vote went towards a winner. I don't know here Hakeem ranks here(66% of first place votes)but I imagine you'd get unexpected results with this approach(something like Curry, Shaq, Lebron, KG, Kareem, 2 more Lebrons, Jordan, Kareem again, ect). All that said, I'm not too interested in perception but yes, if that's what we use, Hakeem isn't top 10.

We do have hints at high impact at peak ... but the 94-96 on off data whilst promising is a long way behind Robinson but (on the average of the yearly figures) about even with Mookie Blaylock (who has more impact evidence later) and closer to the likes of Bo Outlaw and Horace Grant (who make no mistake show very strongly in these numbers) than Robinson. He is high in terms of ranking of the average. Very noisy figures.

Okay so uh, if we're working off one-off flashes(you may note I generally value replication and load), Hakeem(and pretty much everyone?) gets knocked down, but I imagine we both agree Mookie and Grant aren't really serious candidates here. That being said, this is a good chance to highlight collinearity(you know, but for posterity I guess). The Hawks had extreme collinearity(played alot of minuties together) with their starters and mostly ran a platoon system(keep complimentary minuties in and out of the lineup at the same time). Coincidentally, various Hawks players look unusually good. Won't push too strongly without a rotation chart, but Hakeem staggered early on, so something like on/off may be lower on him than something like WOWY. This applies to post-injury D-Rob, Celtics Garnett(compounded by relatively low minutes), and various other greats in a way I don't think it for Hakeem(again, pretty large sample has Sampson looking quite pedestrian).

Still, allowing for the above difficulty in quantifying defense for much of his career ... the combination of quality of competitors and, at first glance, absence of clear evidence of him as an absolute elite RS player (can't see much putting him top 10).

I will say I haven't fully ingested, properly paid attention to your pro-argument here but at first glance it seems more "he's good" than "he has a clear consistent RS case for above 6 or 11 others" (granted this is hard with differing levels of data) but I'd have to look closer.

Okay, but how many players are consistently "above 6 or 11 others" for their careers(or even primes)? Lebron, Kareem, (we don't really have the data for Russell but probably him as well), who else? Duncan's stuff fluctuates. Jordan isn't hitting those highs(well from an impact perspective anyway) even when we juice him(Oakley doesn't exist! replace 93 rs with 92!), and Magic obviously doesn't have the longevity(maybe the best "prime" impact portfolio of Hakeem's contemporaries though). Being consistently "good" is probably rarer than you're giving credit for, and I think looking at a player's signals in totality by accounting for the high-end stuff, the low-end stuff(and the stuff in between) is a better way to assess impact then jumping between specific frames for different players(KG's 2004 looks godly(and his playoff on-off peaks at +50!), but if one-year rs absurdities are your cup of tea, then Magic and MJ take a tumble). That Hakeem is consistently looking good(let's define 'good" as, "within range, or top 10" when we look at other players with similar frames) and replicates outlier-strong peak stuff(88, 92/93) is a rare combination among the 20 or so players you or I would be considering for "top 10".

I will say the reading on that rookie impact looks generous, on the margins because the same roster doesn't acknowledge that it's a young roster that would be expected to improve but primarily because "is special even among top-ten candidates" and with the finals appearance "GOAT-worthy" are quite strong. Olajuwon's (considered use of inverted comma's because I don't love crediting a team level stat to an individual, won't because consistent use on every player might grow tiresome but you get the idea) 4.5 SRS change is very good but less than half the change for Bird, Duncan, Robinson (all above 11) or Abdul-Jabbar. This isn't then, of itself an outlier that is "special" amongst special players

Well, top 5 isn't bad for top 10 :wink:

FWIW, some discussion has gone into the specific roster(and player fluctuations) for early the Rockets(contrasted to the roster/player developments for the early Bulls):
https://forums.realgm.com/boards/viewtopic.php?p=101211127#p101211127
https://forums.realgm.com/boards/viewtopic.php?p=101211196#p101211196
https://forums.realgm.com/boards/viewtopic.php?p=101212621#p101212621
https://forums.realgm.com/boards/viewtopic.php?f=64&t=2224933&start=200

For what it's worth, I think this is around where alot of "Hakeem, regular season floor-raiser?" started.

I'll end this post by adding some a couple of arguments for raising bigs/paint-protectors(that logically would help Hakeem as well)

Absolute value, the idea is that all this impact stuff is tracking something akin to "value over replacement", but in absolute terms, bigs are the most valuable players and there should be some scaling for size, ect.
https://forums.realgm.com/boards/viewtopic.php?p=104409082#p104409082

Historic consistency of Impact/Winning from Paint-Protection, The idea is that
A. paint-protection has the best track-record of stacking without diminishing returns(or better than wing-scoring/helio playmaking)
B. Paint-protectors are generally the most consistent in terms of leading successful teams and individual influence(Russell/Duncan are the textbook examples of the former, Russell/Kareem/Lebron???(is that cheating) are textbook examples of the former).
https://forums.realgm.com/boards/viewtopic.php?p=104200855#p104200855

Now if you'll excuse me, I'm going to touch grass :lol:
its my last message in this thread, but I just admit, that all the people, casual and analytical minds, more or less have consencus who has the weight of a rubberized duck. And its not JaivLLLL
Squared2020
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Re: Some Historical Plus-Minus 

Post#37 » by Squared2020 » Tue Feb 28, 2023 2:10 am

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Professional History:
2012 - 2017: Consultant for several NBA front offices.
2017 - 2018: Orlando Magic
2018 - 2021: Houston Rockets
2021 - Present: NBA League Office
Squared2020
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Re: Some Historical Plus-Minus 

Post#38 » by Squared2020 » Tue Feb 28, 2023 3:25 am

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Professional History:
2012 - 2017: Consultant for several NBA front offices.
2017 - 2018: Orlando Magic
2018 - 2021: Houston Rockets
2021 - Present: NBA League Office
colts18
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Re: Some Historical Plus-Minus 

Post#39 » by colts18 » Tue Feb 28, 2023 3:37 am

Squared2020 wrote:
colts18 wrote: MJ


199 games of Jordan broken up over four seasons:

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Thanks for the work. Is there a way to get MJ's stats in relation to his teammates? Like to calculate MJ's On/Off and Offensive and Defensive On/Off numbers.

Btw, just a suggestion. I think RAPM seasons with more comprehensive number of games is much more valuable than having 50 games documented for 10 seasons. I think adding 200-300 more games to the 1991 season which gets a clear picture of season is better than doing 20 games documented for 10 different seasons like 1970 or 1980.
70sFan
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Re: Some Historical Plus-Minus 

Post#40 » by 70sFan » Tue Feb 28, 2023 7:24 am

Squared2020 wrote:
Moonbeam wrote:I'd be keen to see the stats for Adrian Dantley if you've got them.


Adrian Dantley

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Wow, you are the best, I have never thought I'd see any Dantley +/- numbers. Thank you so much!

It looks like I have quite a few more 1984/85 Jazz games, so if you ever decide to go back for that season I can help you.

I feel uncomfortable to ask for more, but do you have any data for Wilt Chamberlain and Artis Gilmore?

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