26-year RAPM and updates to the aging curve

[J.E.]

With publicly available PlayByPlay data now reaching back to '97, I was able to run '97-'22 RAPM
Results are here https://docs.google.com/spreadsheets/d/ ... sp=sharing

With that analysis came updates to the (offensive, defensive) aging curves

[Crow]

Thanks for sharing this curiosity.

What I see:

9 of top 15 active.

Morant and Doncic not in top 100. Dillon Brooks slightly ahead of Morant.

Jordan 7th, with J Tatum, Jokic and C Paul ahead of him.

LeBron and KG 1, 2. Stockton 5th.

Draymond slightly ahead of Steph Curry.

Giannis 13th. Durant 28th. Tony Allen 27th.

Alex Caruso 50th, essentially tied with Yao Ming. Andre Roberson right on tail and tied with Kidd and Barkley and Schrempf.

Kobe Bryant, 73rd and tied with Royce O'Neale.

Karl Malone 88th.

Jamario Moon slightly ahead of Al Horford and Kyrie Irving.

Nick Collison, 169.

Olajuwon tied with Matt Barnes and Anunoby.

Gary Payton (I assume Sr.?) at 218.

SGA at 352 and tied with Rodman.

Shawn Kemp, 561 and tied with TJ Leaf, Zhaire Smith, DeClerq, Webber and John Wall. All slightly negative.

Andrew Wiggins tied with Stackhouse, Lucious Harris and Tarik Black.

Maledon and Sean Marks in bottom 1%.

8 Sonics / Thunder in bottom 5%. About double the average representation.

Tom Chambers in bottom 20% and tied with Naz Reid.

Antoine Walker, modestly below median.

Deni Avdija and Michael Beasley about median.

Tyler Herro and Pokusevski tied at a bit below 1000th.
Derrick Coleman at 951. DeRozan at 795. Trae Young at 245.

Westbrook at 166 but tied with D Wade.

Kidd-Gilchrist, out of league fairly young but ranked 41st best and just slightly behind Steve Nash and Zo Mourning.

Shaq slightly ahead of Mutumbo and David Robinson.

T Duncan 8th, Ginobli 15th, Tony Parker 559th.

Pretty serious initial doubts about giving weight to this list as presented... Then I remember to consider estimate errors. What average error do you calculate, if any? Could make rank differences in the hundreds to many hundreds or many many hundreds. That eases some concerns but obviously makes things more vague. Minutes played will affect the size of the estimate error.

I know the selected lambda value will affect things but I don't have a good idea of the sensitivity.

[Crow]

Age curve from rookie season to peak has about twice the rise on offense (net move of 3 pts) as defense (about 1.5).

[Crow]

Is is technically possible for this exercise or for a single year to minimize error for the top 100 by minutes or BPM or by the RAPM values from the standard / first run? I assume it would be but interested in your thoughts.

[J.E.]

Is is technically possible for this exercise or for a single year to minimize error for the top 100 by minutes or BPM or by the RAPM values from the standard / first run?

I don't think I quite understand what you have in mind. Generally, errors are anything but minimized when running this for a single season. 2-3 seasons are usually the sweet spot

Morant and Doncic not in top 100. Dillon Brooks slightly ahead of Morant.
..
T Duncan 8th, Ginobli 15th, Tony Parker 559th

As little fun as it is arguing about these things with no 100% factual data to back up opinions..
I was nodding along with almost all of these notes, then was surprised by the final remark. Obviously, I have looked at these types of numbers every once in a while, for all different time frames, so there were little surprises there. That's not the say that they're accurate only because I'm used to seeing players ranked like this
Almost all of your - if I may call them so - 'disagreements' disappear if you looked at offense only, something very common with APM numbers

Some comments
- The Grizzlies went 19-4 in Morant's absence last season (+one L when the standings were decided)
- Draymond known to kick it up a notch in the playoffs, which this includes
- Caruso probably still(?) one of the most underrated players in the league. The Lakers' implosion, I would argue, is tied to his and Green's departure
- Jordan/Kemp/Malone/Olajuwon. Obviously this '97-onwards data isn't covering their entire careers. Kemp, certainly, wasn't great anywhere but in Seattle. Jordan wasn't quite as good with the Wizards, etc
- Players that didn't play much, or looked 'OK' in relatively limited minutes, will mostly appear near the median. Obviously there's less certainty around their estimate

[Crow]

Instead of a function that minimizes error for all players without favoritism, could a function minimize error for the top 100 (alone or 80-90% on the top 100 and 10-20% on the rest)?

That is as simple as I can say it.


The case I mentioned are curiosities. Some I agree with, some I don't, but I gave no opinions in the above and am not interested in debating. Some I am just pointing out.
Data presented and looked at as a whole, not just offense.


"97-onwards data isn't covering their entire careers". Good point.

[J.E.]

Instead of a function that minimizes error for all players without favoritism, could a function minimize error for the top 100 (alone or 80-90% on the top 100 and 10-20% on the rest)?

Because of variable coefficients usually being dependent on each other, I would assume that whatever metric comes up with the most accurate player ratings automatically would have the most accurate ratings for random subsets of players

Of course, a prior informed version of this would very likely be more accurate

[DarkStar48]

A lot of the results on the top and bottom end confirm much of my previous priors, for post-1997 draft players that is

James, Curry and Jordan (even at a later stage) as the best overall offensive players of that era. Honorable mention for Harden. I already had Jokic as one of the top offensive players in NBA history, but the positioning of Towns on that list was honestly surprising.

Gobert as the most impactful defensive player this side of Bill Russell is obvious to anyone who actually pays attention to the NBA. Young as LITERALLY one of the worst defenders to step on an NBA court (or at least since 1997 ).

Confirms to me that Garnett wasted too many years in Minnesota, as well as Paul and Stockton both being massively underrated historically.

Plus, Stockton (not Malone) was the real driving force for the 90’s Jazz success.

For the younger players, Tatum’s two-ability and consistent availability makes him more valuable to me than Dončić.

[Mike G]

The Aging Curves are most interesting!
Is the sample size (indicated by size of blue dot) based on the number of players in the league at each age?
Or is it the number who played at age x and (x+1) both?

Question is because, for example, the defensive RPM seems to increase for players between age 32 to 35 -- AND the sample size drops significantly.
Could this be a selection bias that is due to the fact that retired/waived players aren't included in the formula? What if they were included with a poor rating like -3 or -5 ? Assuming they Could play but they've gotten too weak/slow due to aging.

Also, pardon my innumeracy, but what does 3e-04 mean?

p.s. -- Why not run Michael Jordan's age 33-39 numbers backward thru the age curve? Sling a guess at his peak and career rates?
Other players too. Arvydis Sabonis ?

[J.E.]

Is the sample size (indicated by size of blue dot) based on the number of players in the league at each age?
Or is it the number who played at age x and (x+1) both?

It's the former, and yes, there's undoubtedly selection bias going on.
As such, we can't use it to make statements about players we expect to play some time in the future. We can only say things like "IF this player gets minutes, then his impact is likely to change by x amount", while also assuming that the process ,which teams use to deem someone fit to play, doesn't change

Also, pardon my innumeracy, but what does 3e-04 mean?

3*10^(-4) = 0.0003

p.s. -- Why not run Michael Jordan's age 33-39 numbers backward thru the age curve? Sling a guess at his peak and career rates?

This is already doing what you're suggesting, unless I understood you wrong
These numbers are supposed to be interpreted as 'career impact', while also trying to 'guess' everyone's impact, relatively to each other, if everyone was the same age

[xkonk]

Also, pardon my innumeracy, but what does 3e-04 mean?

It's scientific notation https://en.wikipedia.org/wiki/Scientific_notation . As a shortcut, you can think of the e as meaning slide the decimal to the left (if a negative number) or the right (positive). 3e-04 takes 3.0 and makes it .0003. 3e4 would be 30000.

[Mike G]

Obviously this '97-onwards data isn't covering their entire careers.

This is already doing what you're suggesting,

Thanks for clarifying that! I did not see that in the OP; and the upper quote here doesn't mention it either.
So you extrapolated an extra 2-3 pts on offense and maybe 0.5 on D to Jordan's pre-1997 minutes to arrive at his career impact?

3e-04 takes 3.0 and makes it .0003

Indeed, and in this case at least, I find .0003 a lot easier to grasp and less apt to be mis-translated.

[v-zero]

ndeed, and in this case at least, I find .0003 a lot easier to grasp and less apt to be mis-translated.

Indeed you might, but I don't know a scientist or engineer who would agree. A string of zeros is easy to miscount, and what's more important is that the standard notation lends itself well to extension to very large and small numbers.

[permaximum]

- Jordan/Kemp/Malone/Olajuwon. Obviously this '97-onwards data isn't covering their entire careers. Kemp, certainly, wasn't great anywhere but in Seattle. Jordan wasn't quite as good with the Wizards, etc

These arguments are null since it's obvious you didn't factor everyone's age back in after adjusting for it in the regression.

To make it simple for others to understand, this RAPM shows how everyone would look if they were the same age. So Jordan, Kemp etc. got huge boosts because of this.

So this doesn't show their performance in the timeframe of 1997-2022. It makes an estimate of everyone who played in that timeperiod's "career" performances.

[DSMok1]

- Jordan/Kemp/Malone/Olajuwon. Obviously this '97-onwards data isn't covering their entire careers. Kemp, certainly, wasn't great anywhere but in Seattle. Jordan wasn't quite as good with the Wizards, etc

These arguments are null since it's obvious you didn't factor everyone's age back in after adjusting for it in the regression.

To make it simple for others to understand, this RAPM shows how everyone would look if they were the same age. So Jordan, Kemp etc. got huge boosts because of this.

So this doesn't show their performance in the timeframe of 1997-2022. It makes an estimate of everyone who played in that timeperiod's "career" performances.

That is true, but it'is only looking at a player's performance in the window evaluated. So if Kemp was not good from 1997 onward for his age, he won't look good here for his "career number". I know you understand this, but just wanted to make it clear.

Players who played very well for their advanced age will show up very high here, if their pre-prime and early prime years are not included in the sample.

The same goes for players doing very well at a young age that don't have their prime years in-sample yet. Since everyone gets the same aging curve, if a player has an early peak (say from 20-24) in this sample, and they're only 25 now, the regression will boost them given anticipated future improvement, no matter if that is realistic or not.