4year Peaks Study using nbarapm.com

[Doctor MJ]

Hey y'all,

So, earlier in the summer I shared a project, Doc's RAPM VORP Career Leaderboards, which focused on longevity.

Recently I've made something of a counterpart spreadsheet based on players best 4-year RAPM numbers on nbarapm.com, which you can find here:

Doc's nbaprapm 4year Peaks Study

In this first post I'm going to mostly focus on pointing out some things to keep in mind when going through the day, but I will list those topping the leaderboard in spoilers for the time being. (Not trying to make you click into the spreadsheet, but also don't want the results to drive the first impression.)

So, things to keep in mind:

1. My prior study used Englemann's Career RAPM, rather than nbarapm.com's Career RAPM, yet here I"m using nbarapm.com. Why? Because Englemann's Career RAPM was easier to access, but nbarapm.com is the place that had the shorter increments. Don't take either source as a holy grail, and be careful about "crediting" one guy over another as "more impactful" based on a lead that may not be bigger than the potential differences between quality models.

2. RAPM on its own doesn't factor in minutes played, so keep that in mind when you see a lower minute guy doing well by this study, and you might want to click over to the VORP to have a sense for what the Peaks data does and does not add up to.

3. Why the 4 year study? Honestly, that's what it defaulted me to on the site. I'd be curious to see other studies done based on 2, 3, or 5 years. I don't believe those other durations are "better" than the 4-year generally, but where we see differences in how a player stacks up between these studies, it definitely tells a story.

4. I will say in general that when we go beyond a 1-year RAPM model, I like the idea specifically of going up to 3-year, so I'm generally less interested in 2-year models...but using the criteria I used here, doing the 2-year approach would mean we'd get Jordan in the study.

5. While Jordan technically has 4-year RAPM numbers here, it's only based on 2 years of play, and generally, if you allow players who only played a fraction of the total span you're regressing over, that's a recipe for noisy outliers.

6. What got me on this kick was specifically the fact that they had regressions for their 6Factors (think Dean Oliver's 4 factors, which are actually 8 when you factor in defense, but nbarapm is combining eFG & FTr into one TS factor.

7. The overall RAPM data goes back to '96-97, and so the earliest 4 year epoch is '96-97 to '99-00.

8. The 6Factor data only goes back to '99-00 for whatever reason, and so the earliest 4 year epoch is '99-00 to '02-03.

9. The 6Factor data only goes through '23-24 to this point, so if you see a player that peaked through '24-25, expect that an updated 6Factor study would probably help the player in those metrics.

10. Included in the spreadsheet are over 400 players, which includes all all-stars back to the 1984 draft regardless of whether they qualified by the full-4-year requirements, and beyond that every other player who played relatively long careers that I could think of and who had a Peak 4-year RAPM at least as big as +1.0

11. The Raw data was a manual process , and so expect if you find errors, please let me know - or by all means, automate the process.

12. Always keep in mind that different RAPM studies might end up with different scaling, which is why I used so to have a spreadsheet that normalized the data across studies to give us more of an apples-to-apples set of data.

I have not made a normalization adjustment here, and that might prove to be a problem. However, the fact that these are 4-year studies should make scaling differences smaller, and the fact that all the studies came from the same place also helps. Just having eyeballed the data, I didn't see any glaring red flags of data being on drastically different scales, but if folks see something, they should say something.

In the spreadsheet, I think the Ranks tab is the one people will probably be most interested in first, and in spoilers here, I'll put the player(s) who lead each category:

Spoiler:

Offensive TS Value: Steve Nash
Offensive TOV Value: Chris Paul
Offensive Reb Value: Steven Adams

Offensive RAPM: Steve Nash

Defensive TS Value: Shawn Bradley
Defensive TOV Value: Alex Caruso
Defensive Reb Value: (tie) Nikola Jokic & Nene

Defensive RAPM: Kevin Garnett

Overall RAPM: Kevin Garnett

Just to put in on record, Garnett's 4year Peak here doesn't include his '03-04 MVP season which most of us consider his actual peak, which is amazing, but does also encourage us to remember that there's more to a player's situational impact than pure goodness.

[Tim Lehrbach]

there's more to a player's situational impact than pure goodness

I am glad you included this but wish it wasn't hidden by a spoiler tag. I guess I am left wondering: what do you think these data mean or tell us?

[Djoker]

Good stuff as usual from you Doc.

Just wondering... why 4-year and not 3-year or 5-year?!? Edit: Nevermind just saw your explanation.

[Doctor MJ]

there's more to a player's situational impact than pure goodness

I am glad you included this but wish it wasn't hidden by a spoiler tag. I guess I am left wondering: what do you think these data mean or tell us?

Well, I don't mind you bringing this part out of the spoilers. It just happened to cross my mind when I posted the leaders in the spoiler.

I would say broadly that impact data gives us an estimate for how effective - and thus valuable - a player was within a given role and the scheme it exists in. A player effectiveness in this regard will vary based on context, and his most capable vintage might not be where he was actually most valuable.

Additionally, when we're talking about guys playing considerably less minutes than a normal starter, those low minutes might be essential for the player to have that impact. So maybe a Caruso just burns out if you play him 30 MPG each night, or maybe a Collison-style change-up only works really well if he plays few enough minutes that opponents don't prioritize scheming to exploit him.

Of course with all of this I'm not swearing that the values in question are perfectly precise and accurate measures of the player's impact within that context - noise is certainly a thing - but in principle, value-in-context is what I'd hope to get from these sorts of measures rather than, say, some kind of known ceiling for what a player could ever have done.

Thoughts?

[Doctor MJ]

So, realizing that this might all feel pretty opaque to people, I'm going to give some observations from the data. I want to be clear that I'm less interested in sharing my opinion of specific data than I am just having this as a tool to use, but realistically I shouldn't expect others to get the conversation going without me.

I'll start with some discussion of the stuff I spoiler'd in the first post, because now it just seems to me like the fact I didn't make it un-spoilered up front was annoyingly coy.

I want to start off by emphasizing my excitement of having this kind of data with this degree of coverage for 4-Factor type regression analysis drove my curiosity here. While the actual score on the scoreboard - which is gets regressed in APM-style analysis - is the most important thing overall, from there we should drill down to try to get as specific as we can, and we should also be looking to be able to sum up the specifics in a way that attempts to match the overall RAPM.

What nbarapm.com has done here isn't drilling super-far down of course, but it's the first time I've seen something like this done to such scale, and frankly not only would I not want to skip this intermediate step of granularity, I really like that they replaced Oliver's separate eFG and FTr categories with a combined TS category. I'd still like to see those regressions done on their own, but the reality is that TS has really overtaken eFG in significance since Oliver wrote about this stuff 20 years ago, and so for anyone who is more likely to use TS than eFG - most of us I think - this is the more meaningful slice.

So then each side of the ball gets only 3 factors to regress, and each of those factors is pretty easy explain without stats:

Off TS Val: Impact by improving your team's shots.
Off TOV Val: Impact by reducing your team's turnover rate.
Off Reb Val: Impact by increasing your team's offensive rebounding rate.

Def TS Val: Impact by worsening the opposing team's shots.
Def TOV Val: Impact by increasing the opposing team's turnover rate.
Def Reb Val: Impact by increasing your team's defensive rebounding rate.

I think this is a reasonable way to divide the two sides of the game (offense & defense), into 3 sub-categories in a way that includes everything on the court.

(Let me really emphasize what the "Val" means here, and why I phrased these categories like I did. This data doesn't represent, for example, the literal impact on the TS%, but rather a holistic impact on the scoreboard estimated to be caused by that literal impact. I don't know the details of how they did it, and I'm sure they made some decisions that we would nitpick, but I applaud their intention here and their competence is on a level that I think it unlikely that the best course of action is to ignore the data.)

I'd expect that the distinctions between Offense & Defense for TS & TOV are pretty intuitive to folks, but in Rebounding it's murkier. There's clearly one set of guys in the Ranks who show up for both Rebounding leaderboards and nothing else (posterboy: Steven Adams), and so it's not unreasonable to think that perhaps it's more meaningful to separate the game between Offense, Defense & Rebounding, but in this area where +/- is the spearhead stat, this would lead to some pretty weird stuff I think.

But what should we expect in Offensive Rebounding impact vs Defensive Rebounding impact?

The way I've always thought about it is this:

Getting a defensive rebound is like a team "holding serve", in the sense that that's what's supposed to happen - the defense the literal inside track, and most missed shots don't bounce off the rim to the perimeter. It's thus more about the defense claiming the territory everyone knows the ball is most likely to end up, which can be done most effectively with effective, cooperative boxing out.

By contrast, getting an offensive rebound is like a team "breaking serve", in the sense that that's not what's supposed to happen. While some offensive rebounds are about dumb luck - the guy getting the ball didn't do anything to pursue the rebound until it bounced to him - the guys who get the most are those who are either guys who a) were already in the interior, or b) crash the glass.

In both cases you'd love to have a guy be a strong, athletic big, but I'd argue that traditionally offensive rebounding is thought to be more about physical talent, while defensive rebounding is thought to be more about team play and general savvy.

Okay, actually I think that's enough for one post. Let me start another one before I start zooming in to actual players.

[Doctor MJ]

So, let me do it like this, in this post I want to focus on Off TS & Off TOV, because I think the similarities and differences on the leaderboards definitely help us think in terms of particular archetypes.

The top 10 Off TS Val guys are:

1. Steve Nash 7.8
2. Steph Curry 7.5
3. LeBron James 7.2
4. Joel Embiid 6.4
5. James Harden 6.2
6. Kevin Durant 5.8
(tie) Nikola Jokic 5.8
8. Damian Lillard 5.6
9. Dwyane Wade 5.2
10. Manu Ginobili 5.1

And top 10 Off TOV Val guys are:

1. Chris Paul 2.8
2. Mike Conley 2.5
3. Tracy McGrady 2.4
4. Kobe Bryant 2.2
(tie) DeMar DeRozan 2.2
6. Baron Davis 2.1
(tie) CJ McCollum 2.1
(tie) Gary Payton 2.1
(tie) Kemba Walker 2.1
10. Stephon Marbury 2.0
(tie) Tayshaun Prince 2.0
(tie) Nick Van Exel 2.0

First thing to note here is the dramatic disparity between how heavily Off TS is weighted compared to Off TOV. Even the king of turnover reduction (Chris Paul) is - in this metric - adding 50% more vale by Off TS than Off TOV.

So the question should be asked: What if that weighting is wrong?
Or maybe even better: How much uncertainty is there in their process, and how big a deal might that be?

Mostly here though I want to focus on the difference in ranks rather than the ratings.

Immediate thing there, there's literally no overlap between the two leaderboards listed. Not that we don't have guys who are great at both (and make the Top 100 in both), but no Top 10 overlap.

Next thing I'd note is that there are bigs in the Off TS Val, but not in the Off TOV Val. As with anything I notice, maybe it won't hold up to more detailed study, but this makes sense to me NOT because bigs themselves are turnover prone, but that passing to traditional bigs on the interior is a tricky business.

Looking further into the TOV group, something that's interesting is that while the top 2 guys short, smart pass-first point guards, the next three guys are iso wings, followed by a cohort that's mostly point guards who aren't known for passing (along with the oddball Prince).

So, while I think Paul & Conley represent one archetype which likely directly reduces turnovers by playing a shrewd cautious game, there doesn't really seem to be a ton of guys like them.

By contrast, most of the guys in that top 10 are guys who seem to be avoiding turnovers indirectly by not passing when an elite facilitator would pass simply because they're looking for their own shot. But to be clear, this doesn't change the fact that this approach reduced team turnovers, and this approach is generally more in line with crunch time trends where offenses tend to fear passing against the most intense defenses.

Now, back to the TS group, actually, I may have overstated how clear the archetypes are. While the #1 guy (Nash) was initially a bit influence on the #2 (Curry), Curry's peak span is taking place entirely in the Kerr years, when I would argue his style of play is closer to Reggie/Ray/Klay, none of whom are in the Top 10. (Ray's 16th, Klay's 28th, and post-prime Reggie ranks 64th.)

Trying to come up with a recurring theme for the elites of the TS group, what I just see is a bunch of great scorers who aren't trapped in the interior, but I should note that Shaq's coming in at #11, and he'd surely be way higher if he could just hit his damn free throws. So in the end, it really just seems like great scoring of any stripe is the main thing you need here, and then from there having a supreme facilitation IQ really helps.

Next thing I think I'll make a point to look for: What are the highest non-all-stars in these lists?

For Off TS:

22. Channing Frye 4.0
30. Jamal Murray 3.5
33. Lou Williams 3.4
39. JJ Redick 3.3
48. Kelly Olynyk 3.0

For Off TOV:

6. CJ McCollum 2.1
10. Tayshaun Prince 2.0
13. Matt Bonner 1.9
26. Tim Hardaway Jr. 1.6
(tie) Jason Terry 1.6

So, harder to make it high on the Off TS list without being an all-star level guy, though that is what we should probably expect given the weighting of the factors.

I will note that Frye topping the non-all-star Off TS list makes some sense given how good he was at stretching the floor at a time when that was still considered weird.

What else?

Well, I always think it's fun to look at guys in NBA families, and we get something cute here:

Both Steph (2) and Seth (94) make the Off TS list.
Both Tim Jr. (26) and post-prime Tim Sr. (38) make the Off TOV list.
Top 2nd generation guy by Off TOV? Kobe.

Okay, I'll end it by doing a quick combination I didn't do in the spreadsheet just to get a Top 10 Off TS+TOV Value - and keep in mind that this basically assumes that a player's peak in the two categories occurred simultaneously, which is not necessarily true. Anyway, let's see what we get:

1. Steve Nash 9.7
2. LeBron James 9.1
3. Steph Curry 8.3
4. Kevin Durant 7.2
5. Damian Lillard 7.1
6. Chris Paul 7.0
7. James Harden 6.9
8. Dirk Nowitzki 6.8
9. Dwyane Wade 6.7
10. Joel Embiid 6.5

[FrodoBaggins]

IIRC, Shaq was top three for regularized four factors offensive eFG% in the 28-year JE career age curve-adjusted RAPM sample that was on nbarapm.com. I think, but I may be wrong.

[Doctor MJ]

IIRC, Shaq was top three for regularized four factors offensive eFG% in the 28-year JE career age curve-adjusted RAPM sample that was on nbarapm.com. I think, but I may be wrong.

Interesting. Are you saying it may still be on there, or that it was taken off? I haven't seen it, but I may just not know where to look.

[FrodoBaggins]

IIRC, Shaq was top three for regularized four factors offensive eFG% in the 28-year JE career age curve-adjusted RAPM sample that was on nbarapm.com. I think, but I may be wrong.

Interesting. Are you saying it may still be on there, or that it was taken off? I haven't seen it, but I may just not know where to look.

It was taken off nbarapm.com for some reason. The 4Factors were included on the same page as the ORAPM, DRAPM, & RAPM. JE updated his career RAPM, and it shifted some numbers; I'm not sure what the changes made were outside of adding the 2024-25 season. Stockton and MJ dropped a little, while Jokic went up.

[FrodoBaggins]

Here it is:

https://web.archive.org/web/20250509224828/https://www.nbarapm.com/datasets/LifetimeRAPM

Shaq with the highest offensive-eFG at +4.8

[trelos6]

Where can I see which 4 years were chosen for each player?

[Doctor MJ]

Here it is:

https://web.archive.org/web/20250509224828/https://www.nbarapm.com/datasets/LifetimeRAPM

Shaq with the highest offensive-eFG at +4.8

Interesting that they removed it. Makes sense that Shaq looks so strong just on the eFG side.

Now, I think that number was based on career rather than peak 4-year RAPM, but I expect he'd do very well by either.

[Doctor MJ]

Where can I see which 4 years were chosen for each player?

I'm afraid I didn't jot that down so I can only give you my process and refer you to the site.

One thing to keep in mind that I'm not using a players "peak 4-year span" across the board. It's the best number I can find for a guy in a given category where he played all 4 seasons, and so in different categories there will be different 4-season epochs.

Just to give a sense using Garnett, who probably varies more than most.

RAPM: 05-09 (10.6)
ORAPM: 02-06 (5.5)
DRAPM: 05-09 (6.8)

Off TS: 02-06 (4.3)
Off TOV: 02-06 (1.3)
Off Reb: 99-03 (1.0)

Def TS: 05-09 (4.7)
Def TOV: 08-12 (1.5)
Def Reb: 01-05 (1.0)

So we see a favoring of offense & rebounding in his Minnesota years, while defense favors his Boston years.

Incidentally Garnett's peak 4-year RAPM in Minnesota-only years is that 02-06 run, and he's at 9.0 there, and that would place him below peak LeBron (08-12), Jokic (21-25), Curry (14-18) & Paul (14-18).

[DraymondGold]

So, let me do it like this, in this post I want to focus on Off TS & Off TOV, because I think the similarities and differences on the leaderboards definitely help us think in terms of particular archetypes.

The top 10 Off TS Val guys are:

1. Steve Nash 7.8
2. Steph Curry 7.5
3. LeBron James 7.2
4. Joel Embiid 6.4
5. James Harden 6.2
6. Kevin Durant 5.8
(tie) Nikola Jokic 5.8
8. Damian Lillard 5.6
9. Dwyane Wade 5.2
10. Manu Ginobili 5.1

And top 10 Off TOV Val guys are:

1. Chris Paul 2.8
2. Mike Conley 2.5
3. Tracy McGrady 2.4
4. Kobe Bryant 2.2
(tie) DeMar DeRozan 2.2
6. Baron Davis 2.1
(tie) CJ McCollum 2.1
(tie) Gary Payton 2.1
(tie) Kemba Walker 2.1
10. Stephon Marbury 2.0
(tie) Tayshaun Prince 2.0
(tie) Nick Van Exel 2.0

First thing to note here is the dramatic disparity between how heavily Off TS is weighted compared to Off TOV. Even the king of turnover reduction (Chris Paul) is - in this metric - adding 50% more vale by Off TS than Off TOV.

So the question should be asked: What if that weighting is wrong?
Or maybe even better: How much uncertainty is there in their process, and how big a deal might that be?

Cool stuff Doc! Just to complete this analysis of offensive 6 factors, here's...

the top 10 Off Reb Val guys:
1. Steven Adams 4.1
2. Enes Kanter 3.5
3. Mitchell Robinson 2.9
4. Kevon Looney 2.7
(tie) Zach Randolph 2.7
(tie) Andre Drummond 2.7
7. Jonas Valanciunas 2.6
8. Kevin Love 2.4
(tie) Clint Capela 2.4
10. Greg Ostertag 2.3

So if the splits are accurate (haven't read up in too much detail on the accuracy of these yet), that would suggest
top players' effect on offensive True Shooting >> top players' effect on offensive rebounding > top players effect on offensive turnovers.

Mostly here though I want to focus on the difference in ranks rather than the ratings.

Immediate thing there, there's literally no overlap between the two leaderboards listed. Not that we don't have guys who are great at both (and make the Top 100 in both), but no Top 10 overlap.

Next thing I'd note is that there are bigs in the Off TS Val, but not in the Off TOV Val. As with anything I notice, maybe it won't hold up to more detailed study, but this makes sense to me NOT because bigs themselves are turnover prone, but that passing to traditional bigs on the interior is a tricky business.

Looking further into the TOV group, something that's interesting is that while the top 2 guys short, smart pass-first point guards, the next three guys are iso wings, followed by a cohort that's mostly point guards who aren't known for passing (along with the oddball Prince).

So, while I think Paul & Conley represent one archetype which likely directly reduces turnovers by playing a shrewd cautious game, there doesn't really seem to be a ton of guys like them.

By contrast, most of the guys in that top 10 are guys who seem to be avoiding turnovers indirectly by not passing when an elite facilitator would pass simply because they're looking for their own shot. But to be clear, this doesn't change the fact that this approach reduced team turnovers, and this approach is generally more in line with crunch time trends where offenses tend to fear passing against the most intense defenses.

We see a similar thing with rebounding. The top TOV value guys all seem neutral or negative in Reb value, while the top Reb guys all seem neutral or negative in TOV value.

Bigs are of course the biggest movers in rebounding value, with Steven Adams in particular way out in front. He's definitely in contention for the greatest rebounder of the pace and space era, both as a great individual rebounder himself, but also as someone with relatively good positioning and a willingness to use his strength to box out for his guards.

If your hypothesis is that the bigs generate turnovers because interior passes are tricky (and potentially because some of them are turnover prone themselves, although this isn't a requirement), it makes sense that these best rebounders don't generate great TOV value.

Any insights as to why the best TOV value guys don't generate good offensive value? Perhaps the short, pass-first guards aren't great individually at rebounding or boxing out, while something about the iso wings' attack (its predictability or the emphasis on midrange shots rathe than long distance shots) makes them easier for opponents to rebound?

...

Okay, I'll end it by doing a quick combination I didn't do in the spreadsheet just to get a Top 10 Off TS+TOV Value - and keep in mind that this basically assumes that a player's peak in the two categories occurred simultaneously, which is not necessarily true. Anyway, let's see what we get:

1. Steve Nash 9.7
2. LeBron James 9.1
3. Steph Curry 8.3
4. Kevin Durant 7.2
5. Damian Lillard 7.1
6. Chris Paul 7.0
7. James Harden 6.9
8. Dirk Nowitzki 6.8
9. Dwyane Wade 6.7
10. Joel Embiid 6.5

Just to complement this with the Top 10 Off TS+TOV Value guys (in simultaneous stretches, so no combining peaks in TS and peaks in TOV in different stretches), we get:

(Rank. Player TS Val + TOV Val = TS+TOV Val (ORAPM peak in parentheses) )
1. 10 Steve Nash 7.8 + 1.1 = 8.9 (7.9 ORAPM)
2. 19 LeBron James 7.2 + 1.0 = 8.2 (7.7 ORAPM)
3. 19 Steph Curry 7.5 + 0.2 = 7.7 (8.8 ORAPM)
4. 22 Trae Young 5.6 + 1.3 = 6.9 (6.9 ORAPM) [Not on above list; maybe a typo?]
5. 20 Chris Paul 4.2 + 2.6 = 6.8 (6.0 ORAPM, 6.2 ORAPM in 11)
6. 18 James Harden 6.2 + 0.4 = 6.6 (7.4 ORAPM)
7. 24 Damian Lillard 5.6 + 1.1 = 6.6 (7.0 ORAPM, 7.2 ORAPM in 21)
8. 24 Joel Embiid 6.4 + 0.1 = 6.5 (4.8 ORAPM)
9. 10 Dwyane Wade 5.2 + 1.0 = 6.2 (6.0 ORAPM)
10.14 Dirk Nowitzki 4.9 + 1.3 = 6.2 (5.1 ORAPM)
11 09 Kobe Bryant 3.8 + 2.2 = 6.0 (6.6 ORAPM)
12. 21 Kevin Durant 5.5 + 0.2 = 5.7 (5.1 ORAPM, 5.2 ORAPM in 16)
13. 23 Devin Booker 4.7 + 0.8 = 5.5 (6.1 ORAPM, 6.5 ORAPM in 24)
14. 24 Nikola Jokic 5.8 -0.3 = 5.5 (5.6 ORAPM)
15. 06 Kevin Garnett 4.3 + 1.3 = 5.5 (5.1 ORAPM, 5.2 ORAPM in 05)

New players: Kobe and Trae Young sneak into the list based on the use of single-stretches (I think Trae Young should have been in the original). I included Kevin Garnett, Devin Booker, and Nikola Jokic at the end to round out the top 15 in TS+TOV value.

Trends going to best single-stretch:
-Nash, LeBron, and Curry remain the clear top three in both versions in that order, and are often considered the clear top 3 offensive players of the play by play era (or the clear top 4 along with Jokic, who's surprisingly low in 21-24). It's neat that this data supports that impression.
It's possible Jokic will sneak up in 22-25, or it's possible we've finally found a plus minus stat that's low on peak Jokic

Nash and LeBron seem to have peaked in their skills at different times. Nash peaked in TS when he was older (06-10), but peaked in TOV value when he was slightly younger, including a couple Mavs years (03-06 and 04-07). LeBron peaked in rebounding value in 1st Cavs stint, peaked in TOV value in his 1st Cavs stint and retained some value in Miami, then peaked in TS in his 2nd Cavs stint. This evolution helped lengthen his legendary prime, but also reduced the value of his single-stretch peak compared to if he had combined his best skills at once.
Curry got slightly more turnover prone as his volume and off-ball emphasis increased under Kerr, but was still a positive in TOV value regardless. Curry also looks the best of the three in Reb value (more on that later), and ends up with the top four best overall 4-year ORAPM stretches.

-Lillard, Harden, Paul, and Trae Young make up the next best set across both metrics.
Kevin Durant is in this group if we combine their best TS and TOV stretches, but seems to have a pretty large decline in TOV value and a slight decline in Reb value as he improves in TS and overall RAPM. Durant's decline in TOV and Rebounding really keep him from entering this Tier 2 in single-stretches. Was this decline in TOVs from his increased load as he got older?

I do find it interesting that some of the biggest improvers from TS+TOV (i.e. the guys with the best Reb value) are roughly Steph Curry, Damian Lillard, James Harden, and Devin Booker. Kobe likewise has positive rebounding. The bigs, Dirk and Embiid, are among the worst in Rebounding value during their overall offensive peak. Garnett has slightly negative offensive rebounding value in 03-06 (although slightly positive value in 02-05). The wings, LeBron and Durant, have neutral to negative rebounding value in their best offensive RAPM years.

If this trend continues across a larger sample of players, this would seem to suggest that high volume three point shooting can be as valuable (if not more valuable) to improving team offensive rebounding as strong (but not outlier strong) individual rebounding from a wing or a big. Stretching the floor and pulling bigs out of the paint makes it harder for the defenses to crash the glass.

It's also possible that the inverse (attacking the rim rather than three point shooting) has a negative effect on rebounding. Nash is a pretty fantastic three point shooter, but has negative rebounding value unlike Curry or Trae or Lillard or Harden -- is this in part because he puts such emphasis on attacking the rim with his passing threat, which allows the defense to collapse to the rim to prevent the offensive rebound (in addition to Nash obviously also being small in stature even relative to other point guards)? Giannis is one of the best rim attackers and has neutral to negative offensive rebounding value throughout his career, despite having such athletic gifts, while Ray Allen is a clear positive in Rebounding value and of course is one of the great shooters.

It would be interesting to do a larger study of this, e.g. looking at relative three points made per game vs Rebounding value here.

[Doctor MJ]

Mostly here though I want to focus on the difference in ranks rather than the ratings.

Immediate thing there, there's literally no overlap between the two leaderboards listed. Not that we don't have guys who are great at both (and make the Top 100 in both), but no Top 10 overlap.

Next thing I'd note is that there are bigs in the Off TS Val, but not in the Off TOV Val. As with anything I notice, maybe it won't hold up to more detailed study, but this makes sense to me NOT because bigs themselves are turnover prone, but that passing to traditional bigs on the interior is a tricky business.

Looking further into the TOV group, something that's interesting is that while the top 2 guys short, smart pass-first point guards, the next three guys are iso wings, followed by a cohort that's mostly point guards who aren't known for passing (along with the oddball Prince).

So, while I think Paul & Conley represent one archetype which likely directly reduces turnovers by playing a shrewd cautious game, there doesn't really seem to be a ton of guys like them.

By contrast, most of the guys in that top 10 are guys who seem to be avoiding turnovers indirectly by not passing when an elite facilitator would pass simply because they're looking for their own shot. But to be clear, this doesn't change the fact that this approach reduced team turnovers, and this approach is generally more in line with crunch time trends where offenses tend to fear passing against the most intense defenses.

We see a similar thing with rebounding. The top TOV value guys all seem neutral or negative in Reb value, while the top Reb guys all seem neutral or negative in TOV value.

Bigs are of course the biggest movers in rebounding value, with Steven Adams in particular way out in front. He's definitely in contention for the greatest rebounder of the pace and space era, both as a great individual rebounder himself, but also as someone with relatively good positioning and a willingness to use his strength to box out for his guards.

If your hypothesis is that the bigs generate turnovers because interior passes are tricky (and potentially because some of them are turnover prone themselves, although this isn't a requirement), it makes sense that these best rebounders don't generate great TOV value.

Any insights as to why the best TOV value guys don't generate good offensive value? Perhaps the short, pass-first guards aren't great individually at rebounding or boxing out, while something about the iso wings' attack (its predictability or the emphasis on midrange shots rathe than long distance shots) makes them easier for opponents to rebound?

A lot of great stuff in your post generally DGold, and I'm really glad to see someone applying their attention to it.

I'm just going to respond to this part right now where you put forth a question.

A key thing I'd emphasize is that Chris Paul is the #1 TO guy and by their weighting contributes considerably more value by TS than by TO. Meaning, it's not that being low TO means you can't do great elsewhere, it's just that that factor has a relatively lower weight implying that the primary job for a point guard is really about getting guys good shots more than it is about ball control.

In terms of the meaning of the weighting, how I'd put it is that it implies that in the modern NBA TS impact is where the competitive advantage can be found primarily. Doesn't mean it's always so - pretty sure if you did this analysis on a kids league, TO impact might dominate both sides of the ball - but if everyone has good enough ball control in the league, it makes that it's harder to gain larger competitive advantage that way.

[Doctor MJ]

Cool stuff Doc! Just to complete this analysis of offensive 6 factors, here's...

the top 10 Off Reb Val guys:
1. Steven Adams 4.1
2. Enes Kanter 3.5
3. Mitchell Robinson 2.9
4. Kevon Looney 2.7
(tie) Zach Randolph 2.7
(tie) Andre Drummond 2.7
7. Jonas Valanciunas 2.6
8. Kevin Love 2.4
(tie) Clint Capela 2.4
10. Greg Ostertag 2.3

So if the splits are accurate (haven't read up in too much detail on the accuracy of these yet), that would suggest
top players' effect on offensive True Shooting >> top players' effect on offensive rebounding > top players effect on offensive turnovers.

Awesome! So then doing the same for Def Reb:

1. Nikola Jokic 2.1
(tie) Nene 2.1
3. Ivica Zubac 2.0
4. Jusuf Nurkic 1.9
(tie) Jonas Valanciunas 1.9
(tie) Nikola Vucevic 1.9
7. Robin Lopez 1.7
8. Steven Adams 1.6
(tie) Jason Collins 1.6
(tie) Kevin Love 1.6

We get some overlap (Adams, Jonas, Love) here, and beyond that there's also the matter that a great rebounder who spends his offensive time more toward the perimeter isn't going to be getting offensive rebounds to his capacity.

I do think that the dominance of foreign players particularly on the defensive side is telling us something beyond talent. I kinda feel like if there's any of these categories that is about team fundamentals, this is it.

It's also, of course, weighted quite weak, so that probably tells us something about why fundamentals can wane.

Doing the combined thing again, first as I did it before (add best from each category)

1. Steven Adams 5.7
2. Jonas Valanciunas 4.5
3. Enes Kanter 4.2
4. Kevin Love 4.0
5. Clint Capela 3.8
6. Nikola Jokic 3.7
(tie) Robin Lopez 3.7
(tie) Ivica Zubac 3.7
9. Kevon Looney 3.6
(tie) Zach Randolph 3.6

And then doing it finding the best sum from one 4-year run:

1. Steven Adams 5.5 (2019-23)
2. Enes Kanter 4.1 (2017-21)
(tie) Jonas Valanciunas 4.1 (2018-22)
4. Clint Capela 3.7 (2020-24)
5. Kevon Looney 3.5 (2020-24)
6. Andre Drummond 3.4 (2020-24)
(tie) Kevin Love 3.4 (2008-12)
8. Zach Randolph 3.3 (2009-13)
(tie) Ivica Zubac 3.3 (2017-21)
10. Omer Asik 3.2 (2012-16)
(tie) Nikola Jokic 3.2 (2015-19)
(tie) DeAndre Jordan 3.2 (2016-20)

Adams continues to seem like the top rebounder of the century, which we should note, is not what you'd assert at all from RPG totals.

[Doctor MJ]

And to complete the cycle:

Def TS Val:

1. Shawn Bradley 5.9
2. Tim Duncan 5.4
3. Rudy Gobert 5.3
4. Joel Embiid 5.2
5. Andrew Bogut 5.0
6. Jermaine O'Neal 4.8
7. Kevin Garnett 4.7
(tie) Dikembe Mutombo 4.7
9. Immanuel Quickley 4.6
(tie) Theo Ratliff 4.6

All bigs plus Quickley. Quickley's NY +/- continues to be a very interesting thing that it's really unclear how what it meant.

Def TOV Val:

1. Alex Caruso 3.5
2. Ricky Rubio 2.9
3. Mario Chalmers 2.8
4. Tony Allen 2.7
5. Trevor Ariza 2.5
6. Matisse Thybulle 2.4
7. Kyle Lowry 2.1
(tie) John Stockton 2.1
(tie) Anderson Varejao 2.1
10. Manu Ginobili 2.0
(tie) Chris Paul 2.0
(tie) Ben Wallace 2.0

Caruso really is a potential paradigm shifter of a player. His limited minutes put a cap on his total defensive value, but per minute, there's not another guard like him.

Adding the players bests together:

1. Shawn Bradley 7.2
2. Kevin Garnett 6.2
3. Ben Wallace 5.8
4. Draymond Green 5.5
5. Bo Outlaw 5.3
6. Tony Allen 5.2
(tie) Rudy Gobert 5.2
8. Andrew Bogut 5.1
9. Alex Caruso 5.0
(tie) Tim Duncan 5.0
(tie) Jermaine O'Neal 5.0
(tie) Immanuel Quickley 5.0

And trying to get the performers combining the two categories within the same span:

1. Shawn Bradley 6.2 (1999-03)
2. Kevin Garnett 5.6 (2005-09)
3. Draymond Green 5.5 (2013-17)
4. Bo Outlaw 5.3 (2001-05)
5. Andrew Bogut 5.0 (2008-12)
(tie) Immanuel Quickley 5.0 (2020-24)
7. Alex Caruso 4.9 (2020-24)
8. Ben Wallace 4.8 (2002-06)
9. Tony Allen 4.7 (2011-15)
(tie) Tim Duncan 4.7 (2001-05)

So with the two "pure" defensive metrics, Bradley appears to be the strongest per minute defender we've seen, but when we include Defensive Rebounding, Garnett takes a commanding lead at the top with Bradley falling down to 8.

[Doctor MJ]

Ooh, forgot to do the tops on the rebounding & defense lists who were not all-stars:

Off Reb:
1. Steven Adams 4.1
2. Enes Kanter 3.5
3. Mitchell Robinson 2.9
4. Kevon Looney 2.7
7. Jonas Valanciunas 2.6

Def Reb:

1. Nene 2.1
3. Ivica Zubac 2.0
4. Jusuf Nurkic 1.9
(tie) Jonas Valanciunas 1.9
7. Robin Lopez 1.7

Def TS:

1. Shawn Bradley 5.9
9. Immanuel Quickley 4.6
12. Greg Ostertag 4.3
14. Brendan Haywood 4.2
15. Derrick White 4.0

Def TOV:

1. Alex Caruso 3.5
2. Ricky Rubio 2.9
3. Mario Chalmers 2.8
4. Tony Allen 2.7
5. Trevor Ariza 2.5

Okay so, while Off TS & Off TOV are dominated at the top by stars, the other for Factors appear to be dominated by specialists who don't get celebrated as all-stars.

[FrodoBaggins]

Dean Oliver's historical weighting (2002) of the four factors was:

eFG: 40%
TOV: 25%
ORB: 20%
FTr: 15%

A 2017 analysis by Squared2020 suggested that eFG and TOV are understated & ORB and FTr are overstated per that 2002 mark:

https://squared2020.com/2017/09/05/introduction-to-olivers-four-factors/

So what about these weightings? If we were to average their absolute values for each of the four factors, we gain insight into whether the 40/25/20/15 rule is upheld by the data. In this case we find:

Shooting: 380.52 average
Turnovers: 288.36 average
Rebounding: 97.9235 average
Free Throws: 55.7335 average
This yields a weighting of 46.2617 / 35.0574 / 11.9051 / 6.7758 result. This identifies that rebounding percentages and free throw rates are over-inflated and instead should have more emphasis on effective field goal percentage and turnovers.

[DraymondGold]

1. Steven Adams 5.7
2. Jonas Valanciunas 4.5
3. Enes Kanter 4.2
4. Kevin Love 4.0
5. Clint Capela 3.8
6. Nikola Jokic 3.7
(tie) Robin Lopez 3.7
(tie) Ivica Zubac 3.7
9. Kevon Looney 3.6
(tie) Zach Randolph 3.6

And then doing it finding the best sum from one 4-year run:

1. Steven Adams 5.5 (2019-23)
2. Enes Kanter 4.1 (2017-21)
(tie) Jonas Valanciunas 4.1 (2018-22)
4. Clint Capela 3.7 (2020-24)
5. Kevon Looney 3.5 (2020-24)
6. Andre Drummond 3.4 (2020-24)
(tie) Kevin Love 3.4 (2008-12)
8. Zach Randolph 3.3 (2009-13)
(tie) Ivica Zubac 3.3 (2017-21)
10. Omer Asik 3.2 (2012-16)
(tie) Nikola Jokic 3.2 (2015-19)
(tie) DeAndre Jordan 3.2 (2016-20)

Adams continues to seem like the top rebounder of the century, which we should note, is not what you'd assert at all from RPG totals.

Re: Rebounding, agreed that peak Steven Adams seems like the standout guy.

A lot of the top guys seemed to play with perimeter stars. Steven Adams played with Westbrook earlier and Ja Morant in this stretch. Ones Kanter played with Westbrook and Steven A(dams) for one year in 17 and a young Tatum in 20 and Damian Lillard in 21. Clint Capela played with Harden and Trae Young. Kevon Looney played with Steph Curry. Kevin Love played alongside LeBron. DeAndre Jordan played with Chris Paul and had a short stint with young Luka and a short stint with Kyrie. Is this randomness or is there some trend here? Is this scalability / positive chemistry at work? E.g.
-The star perimeter player takes on an outsized portion of the scoring or playmaking load, leaving the big man more energy and attention to exert on the glass, or
-The star three point threat (Curry, Harden, Trae Young, etc.) space the floor and pull the opposing big away, making it easier for a strong rebounder to maximize their value competing for rebounds against smaller opponents, or
-Strong perimeter rebounders (Westbrook, Harden, LeBron, Luka, etc.) can stand out more if they have a big man who's effective at boxing out, and so both players benefit when the big is on the floor.

Jokic's performance on defensive rebounding is impressive, and a touch surprising. I know Jokic usually has surprising defensive impact, and much of that is attributed to rebounding, but I didn't expect him to be seen as the most valuable defensive rebounder of the century.

Perusing some missing top Rebounds per Game guys, I don't see Ben Wallace, Rudy Gobert, Dwight, Shaq. Shaq is particularly surprising, given his effectiveness on the offensive glass, which is usually seen as more valuable. It could be the fact that this is regular season only (I think) with Shaq being a famous regular season coaster (particularly in 2001 onward) + that we only have data since 2000. So an earlier Shaq stretch could sneak in. But it also provides more circumstantial evidence to my prior hypothesis, that players who attack the rim as their main offensive attack don't add as much rebounding value as you would expect even if they're highly effective individual rebounds -- since attacking the rim allows the defense to collapse, which in turn makes team rebounding more difficult.

...

Looking at both offense and defense from your latest top 10s, it looks like the weighting for top-end value in each area is:

Offensive True Shooting (~ +5 to +8) > defensive true shooting (~ +4.5 to +6) >>
offensive rebounding (~ +2.25 to +4) > defensive turnovers (~ +2 to +3.5) > offensive turnovers (~ +2 to +3) > defensive rebounding (~ +1.5 to +2)

So at least in the play by play era...
-individual offense > individual defense, which is consistent with the public perception (although it's possible casual fans go too far in valuing offense)
-impacting team efficiency > impacting team possessions
-offensive rebounding > defensive rebounding, consistent with people's perception
-defensive rebounding value is quite low, although it's less clear if the same would be true in an earlier era where shots came from closer in and there was a greater strategic emphasis on defensive rebounding

...

And to complete the cycle:

Def TS Val:

1. Shawn Bradley 5.9
2. Tim Duncan 5.4
3. Rudy Gobert 5.3
4. Joel Embiid 5.2
5. Andrew Bogut 5.0
6. Jermaine O'Neal 4.8
7. Kevin Garnett 4.7
(tie) Dikembe Mutombo 4.7
9. Immanuel Quickley 4.6
(tie) Theo Ratliff 4.6

All bigs plus Quickley. Quickley's NY +/- continues to be a very interesting thing that it's really unclear how what it meant.

Def TOV Val:

1. Alex Caruso 3.5
2. Ricky Rubio 2.9
3. Mario Chalmers 2.8
4. Tony Allen 2.7
5. Trevor Ariza 2.5
6. Matisse Thybulle 2.4
7. Kyle Lowry 2.1
(tie) John Stockton 2.1
(tie) Anderson Varejao 2.1
10. Manu Ginobili 2.0
(tie) Chris Paul 2.0
(tie) Ben Wallace 2.0

Caruso really is a potential paradigm shifter of a player. His limited minutes put a cap on his total defensive value, but per minute, there's not another guard like him.

Adding the players bests together:

1. Shawn Bradley 7.2
2. Kevin Garnett 6.2
3. Ben Wallace 5.8
4. Draymond Green 5.5
5. Bo Outlaw 5.3
6. Tony Allen 5.2
(tie) Rudy Gobert 5.2
8. Andrew Bogut 5.1
9. Alex Caruso 5.0
(tie) Tim Duncan 5.0
(tie) Jermaine O'Neal 5.0
(tie) Immanuel Quickley 5.0

And trying to get the performers combining the two categories within the same span:

1. Shawn Bradley 6.2 (1999-03)
2. Kevin Garnett 5.6 (2005-09)
3. Draymond Green 5.5 (2013-17)
4. Bo Outlaw 5.3 (2001-05)
5. Andrew Bogut 5.0 (2008-12)
(tie) Immanuel Quickley 5.0 (2020-24)
7. Alex Caruso 4.9 (2020-24)
8. Ben Wallace 4.8 (2002-06)
9. Tony Allen 4.7 (2011-15)
(tie) Tim Duncan 4.7 (2001-05)

So with the two "pure" defensive metrics, Bradley appears to be the strongest per minute defender we've seen, but when we include Defensive Rebounding, Garnett takes a commanding lead at the top with Bradley falling down to 8.

Caruso's defensive turnover value is crazy high! That said, I would definitely put Toy Allen in the same tier of overall defensive impact per possession as Caruso. The list you have in defensive TS + TOV value have them quite close, and Tony Allen actually speaks ahead in overall defensive RAPM.

Like you say, no one has quite as much TOV value as Caruso. But I do wonder if something about the modern era is juicing the value of defensive TOV. With such emphasis on three point shooting and the resulting perimeter passes that are accompany it, does that.. either give more opportunities to guys like Caruso to jump the passing lanes, or increase the value of those jumped passing lanes (since they're preventing a more valuable shot). I'm not married to this theory, but if there is some era difference at play, that might suggest that Caruso is not quite as singular in terms of raw ability at producing defensive turnovers (although he'd still presumably be in the upper echelon in any ear)-- instead that those turnovers have become more valuable today. Or maybe Caruso really is that good.

One thing that shows up here is the relative value of different archetypes. We see the value of big man defense and rim protection. Older Garnett in a better situation / more defensive role is the clear most valuable defender of this era, at least in the regular season. Most of the usual best defensive bigs are in the general top tier (Draymond, Duncan, Wallace, etc.). Duncan's a bit low relative to his reputation, but he sneaks up to 3rd overall (under older Garnett and Bogut) when we consider overall defensive RAPM (with rebounding).

That said it's interesting to see you can still get a handful of perimeter players sneaking into the Top 10 / 15 group. Andre Roberson sneaks in when we consider overall dRAPM. And more than that, it's the best defensive pests, the point of attack and passing lane menaces, who seem to be preferred over the versatile, rim protecting, communicating guards (e.g. Kidd, Marcus Smart, etc.) and wings (e.g. Iguodala, LeBron, etc.). A bit different from the reputation of these archetypes in more analytical circles. Again, is this changing value in different skills due to the newer era?

Like you say, both Caruso and Allen play a smaller role and had fewer minutes. Give how high energy and high motor they are, this smaller role likely enhances/enables their per possession impact. You'd expect some of their motor to reduce as their role increased, either on defense or on offense. At the same time, their per possession impact is large enough that they still might be ahead of some of the top versatile bigger guards / wings in overall impact, even after accounting for the smaller minutes. While I do think the swinging of the pendulum away from valuing point of attack man defense or disruptive perimeter defense and towards versatility, IQ, and rim protection has definitely improved our accuracy in evaluating individual defenders, it's also possible the pendulum has swung too far... or that certain outliers like these two aren't well characterized by the usual strengths/weaknesses of their defensive archetype.