Stat guys Duncan vs Garnett (bear with me)

[Doctor MJ]

Every year from 1998-2007, Tim Duncan beat Garnett in NPI RAPM. Not sure how KG can have a huge lead if thats the case.

There was already a PI vs NPI discussion earlier in the thread. It would be fine to go into more debate on it, and I'm happy to explain more my thoughts, but long story short:

The smaller the sample, the more RAPM chops out outlier data on the grounds that it is probably a fluke. If as a result of this you see the following combination repeatedly:

Player A wins APM
Player B wins NPI RAPM
Player A wins PI RAPM

The most reasonable conclusion is that it was not a fluke and as a result the NPI RAPM is flat out counterproductive.

Note this doesn't mean I never use NPI, but with regards to this comparison my conclusion is that it is giving us results in the wrong direction.

[colts18]

There was already a PI vs NPI discussion earlier in the thread. It would be fine to go into more debate on it, and I'm happy to explain more my thoughts, but long story short:

The smaller the sample, the more RAPM chops out outlier data on the grounds that it is probably a fluke. If as a result of this you see the following combination repeatedly:

Player A wins APM
Player B wins NPI RAPM
Player A wins PI RAPM

The most reasonable conclusion is that it was not a fluke and as a result the NPI RAPM is flat out counterproductive.

Note this doesn't mean I never use NPI, but with regards to this comparison my conclusion is that it is giving us results in the wrong direction.

You have to remember that the 2002-2006 PI RAPM are incomplete data. Not to mention that it makes no sense at all for KG to lead in PI RAPM if he is trailing in NPI for the 4 years before.

[ElGee]

It does not look substantial to me. I think you are giving the metric too much precision.

I see different tiers -- I would put those 6 guys between 9-11 on the same tier bc of the (lack of) precision of the stat. When you dive into the error in the statistic, the variance in basketball...less than 2 points is pretty much looking like the same "tier" to me. The numbers are per 100 possessions, correct? If we incorporate the possessions per game of a player, the difference is even narrower: At 75 possessions played in a game, the difference between KG and TD is ~1.3 ppt according to the above. I don't believe the RAPM algorithm is precise enough to call those different tiers...

See, I don't think it makes sense to latch on to standard basketball levels of granularity to identify what a substantial difference is here. Forget about RAPM and thoughts on expectations of its precision for a second, if we're seeing results being replicated within a given range, the moment it stops seeming to be luck as the most likely reason for the difference is the moment it becomes substantial to me.

Here's what the comparison between Duncan & Garnett looks like if we break it down comparing best vs best years, 2nd vs 2nd, 3rd vs 3rd, etc:

1st Best: +1.26 Garnett
2nd Best: +2.38 Garnett
3rd Best: +1.59 Garnett
4th Best: +1.46 Garnett
5th Best: +1.38 Garnett
6th Best: +1.35 Garnett
7th Best: +1.59 Garnett

It's really hard for me to look at that as luck.

And of course some might literally think <2 points doesn't matter, but we know different because of analysis such your SRS based championship odds. The 1.5-ish gap we see here if it were the difference between a +6 and a +7.5 SRS would make the second team roughly 50% more likely to win a title.

OK, I agree that I wouldn't call that pattern luck. I'll have to think about this more. Certainly, 2 points is relevant if that's truly the case. Playing with your spreadsheet a bit (this is the first time I've really dived in), we also see the following 3-year chronological peaks by points:

1. LeBron +11.55
2. Shaq +11.06
3. KG +10.31
4. Mourning +9.72
5. Duncan +9.58
6. Dirk +9.13
7. Wade +9.12
8. Ginobili +9.09
9. Robinson +8.19
10. Rasheed +8.16

Thoughts?

[Doctor MJ]

There was already a PI vs NPI discussion earlier in the thread. It would be fine to go into more debate on it, and I'm happy to explain more my thoughts, but long story short:

The smaller the sample, the more RAPM chops out outlier data on the grounds that it is probably a fluke. If as a result of this you see the following combination repeatedly:

Player A wins APM
Player B wins NPI RAPM
Player A wins PI RAPM

The most reasonable conclusion is that it was not a fluke and as a result the NPI RAPM is flat out counterproductive.

Note this doesn't mean I never use NPI, but with regards to this comparison my conclusion is that it is giving us results in the wrong direction.

You have to remember that the 2002-2006 PI RAPM are incomplete data. Not to mention that it makes no sense at all for KG to lead in PI RAPM if he is trailing in NPI for the 4 years before.

Ah, good of view to bring up that point. I had forgotten about it. Feel free to elaborate on it, perhaps in rebuttal to my view.

I never really felt comfortable with the explanation of the PI vs NPI contradiction being based on missing data in the PI. That makes sense in one year, but repeatedly? I never heard any explanation for why we should expect this. And we've got, what, at least 6 years now where there's a disagreement according to sp6r? For me to buy that it's due to incomplete data on the PI I'm going to need some kind of systematic breakdown for what data is missing and why it appears to have a very different opinion from the data we actually have.

To your last thought of it making no sense PI to favor Garnett where NPI of that year and the previous year favor Duncan, after blabla's insight it actually does make sense to me how it's possible.

When RAPM first came out I had issues with it. The stat works by (among other things) adding fake data in with the real data essentially on the grounds that the most extreme outlier data probably represents a fair amount of unbalanced luck which can be "smoothed out" with more average data. It certainly made sense to me that on average that would give you a more accurate picture than APM when you don't have a big sample size, but it really disturbed me the corruption of the data. Over time I largely got over my issues, in part because pure APM largely disappeared from the internet while RAPM became available, but none of that ever made the stat perfect obviously.

Now, the use of priors as well bothers me at times. I've been quite ornery with people using RAPM (and now Real PM) to show LeBron with the edge this year in response to allegations of lesser dominance given that the NPI data agrees with the allegations. To me it's pretty dang clear that if you already have a good sense of what a player has been in the past, it's more important to have NPI data for the current season than PI data.

This doesn't change the fact though that PI is going to give you more reliable data in general.

But in addition to that there's blabla's observation: The degree to which RAPM ought to be forced to smooth out the data is going to decrease as you get more confidence in the data you have. A prior gives you that some of that confidence, and hence a great experiment to run would be this:

What players repeatedly see their NPI data regress them to the mean relative to their APM & PI data? In particular, if such a player is in a situation where their data is likely particularly prone to being smoothed out, then we should simply expect that that player is being underrated by the NPI data.

And of course, Garnett was the king of APM data in the days before RAPM, and as we see with the studies I've consolidated, he's at least one of the "kings" by these PI RAPM methods.

Thoughts?

[Doctor MJ]

OK, I agree that I wouldn't call that pattern luck. I'll have to think about this more. Certainly, 2 points is relevant if that's truly the case. Playing with your spreadsheet a bit (this is the first time I've really dived in), we also see the following 3-year chronological peaks by points:

1. LeBron +11.55
2. Shaq +11.06
3. KG +10.31
4. Mourning +9.72
5. Duncan +9.58
6. Dirk +9.13
7. Wade +9.12
8. Ginobili +9.09
9. Robinson +8.19
10. Rasheed +8.16

Thoughts?

Cool, looking forward to your thoughts.

Interesting list. My immediate thought based on expectations of the 3-year peak method and what I already know of the data is that with +/- more exaggerated response to circumstances than box score data is that I don't really believe that it's enough to look at consecutive years to get a sense of a player's peak.

Now looking at the data though, the top 3 makes a lot of sense to me. That's already basically how I see it. LeBron's last 2 years in Cleveland basically set the standard at this point for how high the metric can go and I've no reason to think those years were a fluke. Shaq on the other hand we're missing some key data for and he did his work on elite teams. In both cases I'd take their peaks over Garnett...but not by a wide margin.

I haven't really discussed Zo much yet but yeah, his data is eye-popping in the '90s data we have. I'll be cautious about using that too far at this point, but I may indeed end up having Zo climb far higher on my list.

The rest makes a lot of sense. Obviously Ginobili takes a big hit for his minutes and Sheed for his crazy.

Robinson, as sp6r pointed out, looks quite good for his "sunset years", and I look forward to really analyzing him along with other '90s era players.

I'll also note while we're at it that Jordan's final season ranks him at +10.44. If this represents his graceful fall from greater years it's incredibly impressive.

[sp6r=underrated]

I have another philosophical point for people who have a strong belief in the value of RAPM. RAPM is considered part of the plus/minus family. Plus/minus stats are really individual point differentials. RAPM, APM and other similar stats are attempt to adjust for external factors and arrive at true individual point differential.

If you really have a strong belief in the value of RAPM and APM I don't know how you cannot heavily rank teams by point differential. Say what you will about a stat such as SRS there is far less adjustments involved in calculating a team's true point differential than there is for an individual's true point differential.

In short, I think if you have a strong believe in individual point differential it is only logical to have an extremely strong belief in the validity of team point differential as the basis for ranking teams. This calls for heavy revisionism as much as RAPM.

I don't know if I really see this as something that will cause heavy revisionism for many people. I'd imagine most people using advanced +/- stats are already pretty well versed in SRS. You're right though it wouldn't make sense to believe in +/- stats and scoff at SRS though.

When I said this calls for revisionism I am primarily referring to posters on this message board rather than the statisticians who make these stats. The later do understand the importance of point differential but IMO many posters who strongly advocate for RAPM downplay team point differential.

Consider the following clubs

1985 Lakers
1987 Lakers
1989 Pistons
1990 Pistons
1994 Rockets
1995 Rockets
2005 Spurs
2007 Spurs
2008 Celtics
2012 Heat
2013 Heat

The Bad Boys Pistons and mid 00s Spurs are routinely disparaged as opportunistic champions who never really reached greatness. By contrast the Showtime lakers, recent Heat and even to a lesser degree 95 Rockets are regarded as truly great teams:

Here are there RS SRS and RS+PS SRS

1985 LAL: 6.48, 7.64
1987 LAL: 8.32, 9.07
1989 DET: 6.24, 7.08
1990 DET: 5.41, 6.18
1994 HOU: 4.19, 4.91
1995 HOU: 2.32, 3.61
2005 SAS: 7.84, 7.86
2007 SAS: 8.35, 8.22
2008 BOS: 9.31, 8.87
2012 MIA: 5.72, 6.82
2013 MIA: 7.03, 7.35




Ranked by RS SRS
2008 BOS: 9.31
2007 SAS: 8.35
1987 LAL: 8.32
2005 SAS: 7.84
2013 MIA: 7.03
1985 LAL: 6.48
1989 DET: 6.24
2012 MIA: 5.72
1990 DET: 5.41
1994 HOU: 4.19
1995 HOU: 2.32



Ranked by RS+PS
1987 LAL: 9.07
2008 BOS: 8.87
2007 SAS: 8.22
2005 SAS: 7.86
1985 LAL: 7.64
2013 MIA: 7.35
1989 DET: 7.08
2012 MIA: 6.82
1990 DET: 6.18
1994 HOU: 4.91
1995 HOU: 3.61

Let’s look at this list carefully.

How can the mid 90s Rockets not be regarded as maybe the worse NBA champion post 1980 if you have a strong belief in point differential?

They’re a total outlier from a point differential perspective. In comparison to these clubs. Only the 88 lakers and 06 Heat have similar SRS.

How can the best single season Showtime lakers clubs be regarded as a massive step up from the best mid 00s Spurs from a point differential perspective?

They are right next to each other.

How can the Heat be considered near GOAT squad from a point differential perspective?

The current Heat do not come close to the top of the list and are far closer to teams such as the Bad Boy Pistons than Jordan’s Bulls.

It is really hard for me to understand how RAPM could hold such influence on people while also believing things such as Showtime Lakers >>> mid 00s Spurs, 95 Rockets great teams, Heat near-GOAT level and other things I haven't touched here. Yet I routinely read posts were that is the case. So no I don’t think team point differential has had nearly the impact on team evaluations that RAPM has on individual evaluations. Well at least in this community.

That is shocking because it is easier to evaluate a team statistically than it is to evaluate an individual statistically. If people really are heavily influenced in RAPM to such a degree that it can cause them to revisit debates that were settled in their mind such as Stockton-Malone** they should be even more influenced by statistical analysis of team point differential.

So far that hasn't really occurred.

.Note: my post-season SRS is a back of the envelope calculation that weighs HCA at 3 points. It doesn’t perfectly match b-r’s results but it is a fair approximation.

** When I say settled debates I am explicitly NOT referring to TD-KG. The great posts by drza, one of the best posters on this board, along with others have really settled that TD only developed this clear margin in the public eye due to the disastrous management of Minnesota.

*** One last totally stray thought, when I say Minnesota had terrible management I am not including Flip. Flip is actually a pretty good coach and is unjustly maligned despite some clear flaws.

[lorak]

On the PC board Hakeem is regarded as a GOAT level player while Robinson is nothing more than a RS warrior/PS choker.

Here is how Robinson ranks in ascreamacrossthecourt's RAPM figures from 98-00:

Code: Select all

                          OFF  DEF TOT LG Rank
1998   David Robinson    0.73   3.64   4.37   23   
1999   David Robinson    1.83   5.18   7.00   3   
2000   David Robinson    1.96   4.53   6.49   4   
2001   David Robinson   -0.10   4.10   4.00   9   NPI
2002   David Robinson   -0.30   2.10   1.80   21   I believe year is incomplete
2003   David Robinson   -0.1    3.4    3.3     9   


Different roles - and comparing players with similar roles is one of the most important rules. When DRob was 1st option KG beats him in RAPM. Robinson has advantage in later seasons (but not in every one!), when more and more he was excellent defensive role player. Using only accrossthecourt’s data:

Code: Select all

PLAYER   YEAR   PI/NPI   RAPM   RAPM RANK
KG   1998   PI   5,6   5
DR   1998   PI   4,4   23
KG   1999   PI   6,3   6
DR   1999   PI   7,0   3
KG   2000   PI   7,7   2
DR   2000   PI   7,0   4



I'll admit, I'm confused and would appreciate a stat guy really going in depth about this.

blabla already explained it on first page.

[colts18]

Different roles - and comparing players with similar roles is one of the most important rules. When DRob was 1st option KG beats him in RAPM. Robinson has advantage in later seasons (but not in every one!), when more and more he was excellent defensive role player. Using only accrossthecourt’s data:

Code: Select all

PLAYER   YEAR   PI/NPI   RAPM   RAPM RANK
KG   1998   PI   5,6   5
DR   1998   PI   4,4   23
KG   1999   PI   6,3   6
DR   1999   PI   7,0   3
KG   2000   PI   7,7   2
DR   2000   PI   7,0   4



Robinson beat KG in Non-PI RAPM every year from 1998-2002. The only reason why his PI RAPM gets ranked higher is because Robinson had an injury year in 1997 which makes his priors 0 even though he was never a 0 player. KG played in 1997 so his PI RAPM gets boosted by that while Robinson's is artificially deflated by that. Same thing Duncan. His PI RAPM gets deflated since he gets the -2 rookie prior while KG's rookie season is never factored into the PI RAPM.

[sp6r=underrated]

We have complete PI RAPM data from Robinson from 98-00. David Robinson looks extremely similar to KG in the same years of KG's career especially when you factor in Colts18's points. You argue that isn't that important because Admiral was more a role player.

Let's check the numbers to verify. Ages 32-34 Robinson averaged 32.5 mpg and KG only averaged 30.7. DR played 6,568 minutes while KG played 6,052.

It is really hard to accept your dismissal of DR's RAPM figures when you factor in that you use it as an absolute bludgeon in Malone-Stockton debates. You act as if the 98-00 RAPM figures basically say QED Stockton> Malone. Let's run the minutes for Malone and Stockton.

Malone from 98-00 averaged 36.8 mpg. Stockton only averaged 29.1 mpg. Malone played 7,809 minutes. Stockton played 5,700.

The gap between Malone's minutes and Stockton is far larger than the gap between Robinson and KG. The gap in minutes played between Stockton and Malone is almost a full season's worth of minutes. Furthermore DR actually played more minutes than KG. You think we can't compare Robinson and KG through RAPM because Robinson was but a role player. How come that doesn't apply to Malone-Stockton?

I'm not a hardcore RAPM man as are many in this thread but it is basically impossible to intellectually square those views if you are are hardcore RAPM man. Perhaps it is time to reassess how much confidence you have in RAPM or reassess David Robinson.

[Dr Positivity]

Is the APBR community confident that the stat can get around:

KG plays with worse teammates than Duncan ------> KG is more important to his team than Duncan

It has always made sense why KG's +/- are intergalactic, because the gap between him and his teammates is the all time example. Yes, it's completely absurd that KG led a team to 47 W pythagorean when their team was -17.5 points worse than their opponent in the minutes he didn't play. (and 57 W pyth with -10.8 with him off the next year) But not sure that necessarily means he's better than Duncan. I haven't seen anything to make me believe that APM/RAPM can "weed out" the effect of KG and Duncan's teammates enough, to get away from the fact that KG on a team way worse than him is likely to be a more polarized +/- situation than Duncan's. I think it's perfectly reasonable to think 03 and 04 KG is better than any Duncan, but +/- stats would only be part of the puzzle for me there. Other factors could also be involved like the TWolves not only having shaky talent, but no plan from a coach or exec perspective of how to have a professional caliber basketball team when KG isn't on the court, while the Spurs are of course, the Spurs in regards like that

[colts18]

Now, relating to LeBron & Shaq, that to me is not a big deal really. Garnett will probably rank ahead of either on my next list, but not because I have confidence in a superior peak for Garnett based on this or anything else, it's the longevity that gives him the edge over those guys.

I'm not sure how you can have KG ahead of Shaq when Shaq has 4 seasons clearly better than any KG season (98, 00-02). Same with LeBron (09, 10, 12, 13).

[Doctor MJ]

Is the APBR community confident that the stat can get around:

KG plays with worse teammates than Duncan ------> KG is more important to his team than Duncan

Because under that it makes all kinds of sense that KG has better +/- stats without us knowing who is better.

So, I'll say a few things:

1. In general APM adjusts for who you play with. There is not a fundamental advantage to playing with weaker teammates or even weaker opponents.

2. However depending on your situation you might be better or worse at thriving in that context in comparison to other contexts. In general I would call this "fit" and a player's tendency to be better at fitting to be more "portable", but no player is immune to redundancy which is the issue at the heart of fit.

3. The specific question here then becomes about Duncan whether he was in a scenario with a relatively redundant fit compared to Garnett.

My answer would be what I mentioned before:

-Duncan's defensive RAPM is already right up there with basically any defender we have on record other than Mutombo.

-Duncan's offensive RAPM probably seems like an underrating to many...but remember that the Spurs remain elite today because they got better on offense as they went to an ensemble approach as Duncan's prime waned. In other words if during Duncan's prime he were averaging less than 20 PPG I doubt anyone would find these ratings to underrate him, and it seems quite likely that if they used Duncan in that way the team wouldn't have actually suffered very much.

-Finally, if we ignore Garnett's rating than Duncan rates as the 3rd most impressive prime we've seen behind only LeBron & Shaq. If you told people in general that something rated Duncan in this way I would say very, very few people would call that underrating Duncan. So it's important to remember then when looking at this comparison is that the unexpected thing is very much the rating of Garnett rather than Duncan and hence any potential explanation for the "discrepancy" that starts by trying to "boost" Duncan is something to be very wary about.

[Doctor MJ]

Now, relating to LeBron & Shaq, that to me is not a big deal really. Garnett will probably rank ahead of either on my next list, but not because I have confidence in a superior peak for Garnett based on this or anything else, it's the longevity that gives him the edge over those guys.

I'm not sure how you can have KG ahead of Shaq when Shaq has 4 seasons clearly better than any KG season (98, 00-02). Same with LeBron (09, 10, 12, 13).

Clearly better based on what? The spreadsheet that I've been quoting from doesn't say anything like that.

https://docs.google.com/spreadsheet/ccc ... _web#gid=3

I'm not saying you have to go by my preferred stat of course, but it sure seems like you're fixating on a mystery stat here to which you incorrectly believe I've given credence.

[Doctor MJ]

Incidentally, it's weird to me that the Robinson vs Olajuwon point ended up turning into a Robinson vs Garnett discussion. My quick thoughts on the latter though:

-Robinson looks very impressive and by no means am I taking it as a given that Garnett has the more impressive prime.

-However, based on the data we have available so far, Garnett's best is outdoing Robinson's best.

-Additionally even in the analogous defensively focused later role Garnett has recorded the best numbers despite the fact that Garnett's time in Boston begins significantly deeper into his longevity than Robinson's time with Duncan occurred.

-To the point that Robinson's prior might underrate him (and the same with Duncan), that's true in 1998, but not in years later. In the end, I look at multiple years here holistically, and with what we see Garnett's peak is well ahead of the other two for the years in question - which admittedly do not encompass Robinson's actual peak.

[lorak]

Robinson beat KG in Non-PI RAPM every year from 1998-2002. The only reason why his PI RAPM gets ranked higher is because Robinson had an injury year in 1997 which makes his priors 0 even though he was never a 0 player.

Are you sure his prior is 0? Because Robinson's NPI RAPM in 1997 is higher than 0.

[lorak]

We have complete PI RAPM data from Robinson from 98-00. David Robinson looks extremely similar to KG in the same years of KG's career especially when you factor in Colts18's points. You argue that isn't that important because Admiral was more a role player.

To be clear: "role player" is bad choice of words on my part. What I meant is that his role after 1998 season was not as important as KGs. And the same with Stockton and Malone. I don't judge it by MPG only, the most important thing is what option on offense and defense player was. Stockton IMO was no 1 option (and "no 1 option" doesn't mean the most FGA or the highest USG%, but who was the most important offensive/defensive player; similar situation with Nash in for example 2005, when he was 5th in MPG, 5th in FGA and 4th in USG% on that Suns team, but not doubt he was no 1 option on offense) on offense and at least as important as Malone on defense. Sure, that probably isn't popular opinion and I'm not 100% sure I'm right here, but that's how I see it right now after analyzing 90s Jazz games.

Going back to KG vs Drob. You've said that Robinson looks extremelly similiar to KG in the same years of KG's career. So lets check it. Doc MJ's work (SD RAPM) would be very helpfull here:

Code: Select all

SEASON   YEAR   SD RAPM
1998   9   2,5
1999   10   2,99
2000   11   2,79
2001   12   ---
2002   13   1,56
2003   14   2,34
      
      
      
SEASON   YEAR   SD RAPM
2004   9   4,26
2005   10   2,26
2006   11   1,99
2007   12   3,05
2008   13   3,62
2009   14   3,31



So we clearly see that KG looks like more valuable player. Among 11 seasons between two of them, 4 best belongs to Garnett.

[colts18]

[
Clearly better based on what? The spreadsheet that I've been quoting from doesn't say anything like that.

Shaq had amazing RAPM numbers those years. But the reason to have him ahead of KG those years is that playoff performance was better than 04 KG. 04 KG declined int he playoffs while 98, 00-02 Shaq increased his level of play. 09-10, 13 LeBron has better RAPm numbers than KG. Plus his playoff performances were better.

Doctor MJ, how many seasons do you think that LeBron and Shaq had better than any of KG's?

[colts18]

Robinson beat KG in Non-PI RAPM every year from 1998-2002. The only reason why his PI RAPM gets ranked higher is because Robinson had an injury year in 1997 which makes his priors 0 even though he was never a 0 player.

Are you sure his prior is 0? Because Robinson's NPI RAPM in 1997 is higher than 0.

I'm pretty sure he gets penalized by RAPM for having really low minutes in 1997 (~100). That lowers his RAPM which is why his 1997 RAPM is really close to 0. Then his prior becomes that low 1997 value.

[Chicago76]

Ah, good of view to bring up that point. I had forgotten about it. Feel free to elaborate on it, perhaps in rebuttal to my view.

I never really felt comfortable with the explanation of the PI vs NPI contradiction being based on missing data in the PI. That makes sense in one year, but repeatedly? I never heard any explanation for why we should expect this. And we've got, what, at least 6 years now where there's a disagreement according to sp6r? For me to buy that it's due to incomplete data on the PI I'm going to need some kind of systematic breakdown for what data is missing and why it appears to have a very different opinion from the data we actually have.

To your last thought of it making no sense PI to favor Garnett where NPI of that year and the previous year favor Duncan, after blabla's insight it actually does make sense to me how it's possible.
Thoughts?

Don't have a lot of time over the next few days, and I want to elaborate on some other things (maybe this weekend), but for now PI vs. NPI RAPM:

I think another possible issue with the NPI vs. PI discrepancy is roster turnover. We discussed RAPM being somewhat tied to team context earlier, and I don't see how anyone could really argue that it isn't. All else equal, we should expect to see more RAPM fluctuation year over year for players changing teams (or staying on a team with major roster changes) than a relatively stable team.

The purpose of the prior is to reduce errors (expected vs. actual net rtg) for noisy lineups. As has been mentioned previously as an example, NPI #s make it difficult to distinguish good players from bad on bad teams. Using the prior typically gives more credit to the player with the highest historical performance. This is generally the correct approach, because it reduces noise and enhances predictive power, but the degree to which it is "correct" will vary across teams.

Why does it vary in its "correctness"? Because team context and noise differ across teams. I don't have the numbers for this, and I would love to see them from someone who does, but I would imagine that the error terms for the NPI lineups of the Wolves are higher than they were for the Spurs. Why? Roster turnover was higher. If a coach needs to experiment with rosters more, he will find some counterintuitive successes and failures, ie, those that perform above and below initial expectations. A halfway decent coach will quickly discard the failures and stick with the lineups that might exceed expectations. Which player is likely to be credited most heavily with the marginal performance? The guy with the highest prior.

Garnett's noise correction factor will therefore be higher than TD's, all else equal. Standard error reduction suggests this is the correct approach, but minimizing standard errors on a team level doesn't necessarily mean beta for a particular player is more accurate. It just means that the particular beta combinations anchored to some extent by the priors provides a better estimate on a team level. Does this approach treat them equitably with respect to their true value? Hell if I know.

[bondom34]

As for the PI/NPI, wouldn't a decent amount of the years KG led be due to Duncan being a rookie/first few years? Very few young players post a positive number until at least 3/4 years into their careers (Drummond I know is still negative last I checked). That would explain the discrepancy in PI/NPI for 3 years prior to the year w/o data. Then after that season, assuming prior is 0 for both, Duncan was rated higher the following year and 4 of the next 6 overall. After that the "noise" chicago is talking about may factor in to the rating issue as well. Just throwing an idea out as for why some of the numbers are what they are.