1. 1991 Jordan (Honorable mention years: 1b. 1990 Jordan, 1c. 1989 Jordan)
2. 2013 LeBron(Honorable mention years: 2b. 2012 LeBron, 2c. 2016 LeBron, 2009 2d. LeBron).
3. 1967 Wilt(Honorable mention opponents: 2017 Curry, 2000 Shaq).
To me, Jordan and LeBron have some separation as the clear greatest peaks of all time.
Jordan's year choice: Jordan's best years were 89-91, with the earlier years having greater athleticism (so better driving on offense and motor on defense), while the later years having more greater skill, control, and scalability (so better midrange shooting / touch, better passing, better off-ball ability to pair with teammates). In 92 and on, his lost athleticism and motor pulls down his value. Of 89-91, I prefer the older one of the three.
Why 91 > 90, 89? Qualitatively, I tend to be higher on creation and scalability with teammates over raw defensive motor. Quantitatively, you can see the impact of Jordan's greater scalability / teammate fit on the performance of the Bulls. The Bulls clearly improved from 89 to 91 (
https://projects.fivethirtyeight.com/complete-history-of-the-nba/#bulls). Some of this is attributable to Jordan's improved teammates of course, but I credit some of it to Jordan's increased familiarity and effectiveness within the Triangle system. It's also noteworthy that 91 is likely his best playoffs of the three -- I credit his increased experience as the cause for his resilience here.
LeBron's year choice: LeBron is probably the hardest player to choose a single peak year for. There's at least 3 clear local peaks: in 2009, in 2012 playoffs / 2013 regular season, and in 2016 (with smaller secondary peaks in 2017 or 2018 playoffs if people are
very low on the regular season and on defense). I favor 2012/2013 > 2009 and 2016?
Why 2013 > 2009? I can see arguments for each. 2009 may be his best floor-raising year, and the regular season impact metrics may peak here with his all-time motor. However, I have concerns about his lack of scalability and resilience. I think 2009 would have had the same playoff resilience struggles that 2010/2011 LeBron facing the more drop/zone centric Celtics/Mavs/Spurs defensive schemes. This came from a lack of offensive versatility, particularly with his lack of shooting, post game, off-ball ability, and without reaching his peak yet with passing, BBIQ, or controlling the pace of the game. That same lack of versatility also hampers his value in a ceiling-raising ability alongside high-volume all star teammates (again, see 2011 LeBron's fit with Wade vs 2012/13's fit with Wade).
Why 2013 ? 2016? I could see arguments for either, and there certainly have been some compelling arguments for 2016 in this thread already. The 2013 regular season certainly surpasses the 2016 regular season (e.g. in AuPM, Backpacks Box Plus Minus, and Corp Plus Minus). 2016 does have some superior metrics in the playoffs (AuPM, Backpicks BPM, Goldstein RAPM/PIPM), and visibly improved on defense vs regular season 2016 LeBron, and improved in his passing / control of the game vs 2013 LeBron. But 2016 also had some favorable context in the playoffs: he coasted in the regular season and so had more energy, he had healthy teammates (vs Wade who was injured), and he had injured/suspended opponents. If 2013 LeBron had this kind of favorable context, perhaps we'd be talking about 2013 as his best playoffs. The fact that he had one of his best playoffs immediately before in 2012 gives credence to this idea. When I also consider that 2013 LeBron had a higher motor for more consistent defensive effort, and had a better off-ball game and post-game, I end up siding with 2013 over 2016 (though it's understandable if you disagree).
Jordan vs LeBron:Let's consider impact stats. I'm using the closest years I can find for Jordan, and showing their rank among the top ~20 peaks of all time in parentheses (only 1 year per player).
Ai. Regular Season Augmented Plus Minus per game:
+6.6 2013 LeBron (4th all time) > +6.5 1991-1993/1996 Jordan (5th all time). [+7.8 2009 LeBron (would be 1st all time), +5.7 2016 LeBron (would be 7th all time)]
Aii. Postseason Augmented Plus Minus per game:
+6.1 1997 Jordan (4th all time) > +5.8 2013 LeBron (6th all time) [+6.9 2012 LeBron (would be 3rd all time), +8.7 2009 LeBron (would be 1st all time), +7.3 2016 Lebron (would be 3rd all time)].
Bi. Regular Season Backpicks Box Plus Minus:
+9 1991 Jordan (1st all time) > +8.8 2013 LeBron (3rd all time) [+8.5 2009 LeBron (would be 5th all time), +6 2016 LeBron (not top 20)]
Bii. Postseason Season Backpicks Box Plus Minus:
+12.1 1991 Jordan (1st all time) > +8.3 2013 LeBron (8th all time) [+12 2009 LeBron (would be 2nd all time), +9.5 2016 LeBron (would be 2nd all time)]
C. Goldstein RAPM / Historical RAPM:
+6.82 1991 Jordan (12th al time) > +6.4 2013 LeBron (13th all time) [+7.47 1988 Jordan (would be 7th all time), +9.5 2012 LeBron (would be 2nd all time), +8.84 2009 LeBron (would be 3rd all time), +8.62 2016 LeBron (would be 3rd all time)]
D. Backpicks Championship Over Replacement Player percentage:
31.1% 1991 Jordan (1st all time) > 28.7% 2013 LeBron (3rd all time) [31.2% 1989 Jordan (would be 1st all time), 31.1% 1990 Jordan (would be 1st all time), 27.1% 2009 LeBron (would be 3rd all time), 26.5% 2016 LeBron (4th all time)]
Jordan and LeBron both have numerous years that we could say are their peaks, and whichever we pick, advanced metrics would have them near the top. Ultimately, I side with Jordan. With many metrics, we only have small samples or off-peak years for Jordan, yet he still compares favorably.
A. For Regular season AuPM, his years from 1991-1993/1996 are 1 rank below 2013 LeBron; for postseason RAPM, 1997 Jordan is 1 rank below LeBron. I think it's fair to say in his peak, we would expect 1991 Jordan to improve over 2013 LeBron in AuPM.
B. For both regular season and post season Backpicks BPM, 1991 ranks first all time over 2013 LeBron.
C. In our (very limited) RAPM sample, 1991 Jordan is just over LeBron. The Bulls actually underperformed vs their season average in this sample, so it's possible Jordan would rank higher for a full season RAPM, though of course small-sample noise is an issue.
D. In Backpicks CORP%, 1991 Jordan ranks first all time over 2013 LeBron.
Of course, you could take another year for LeBron. 2016 LeBron performs worse in regular season AuPM, better in postseason AuPM, much worse in regular season BPM, better in postseason BPM, better in RAPM (though worse vs 2012's RAPM), and worse in CORP%. If we were to combine the better qualities of LeBron's various peaks (e.g. 2013's regular season motor and defense with 2016's postseason performance), it would absolutely beat 1991 Jordan. But... that's not what happened. This is what ultimately puts Jordan's peak for me.
Jordan put together all his best qualities into a single season. LeBron's best qualities are spread across numerous seasons 7+ years apart, giving him clearly better longevity, but a worse one-year peak. *** 2 Down, 1 to go
After a small gap, we reach the next peak of players. To me, some possible candidates are: Shaq, Wilt, Hakeem, Curry, Duncan, Kareem.
Here are their peak years ranked by the advanced stats I discussed above.
First, the modern stats:
Ai. Regular Season AuPM: [2016 Curry...], 2017 Curry, 2000 Shaq, 2001 Shaq, 2003 Duncan... 1994 Hakeem (missing: Wilt, Kareem -- too old)
Aii. Postseason AuPM: 2017 Curry, 2003 Duncan, 2001 Shaq, 2000 Shaq... (missing: Hakeem, Wilt, Kareem)
C. GoldsteinRAPM: ... 2003 Duncan... 2000 Shaq, 2017 Curry... 2001 Shaq, 91 Hakeem (missing: Wilt, Kareem, peak Hakeem)
Next, the historical stats:
Bi. Regular Season Backpicks BPM: [2016 Curry]... 1967 Wilt... [1972 Kareem]... 00 Shaq... 2017 Curry... 93 Hakeem... 03 Duncan... 01 Shaq... 94 Hakeem... 77 Kareem.
Bii. Postseason Backpicks BPM: ... 2017 Curry/2003 Duncan... 1977 Kareem... 1967 Wilt, 1994 Hakeem... 2001 Shaq... 1993 Hakeem... 2000 Shaq
D. CORP%: ... 2000 Shaq... 1993 Hakeem /[ 2016 Healthy Curry], 2001 Shaq, 1977 Kareem... 1967 Wilt, 2017 Curry, 2003 Duncan, ... 1994 Hakeem
Looking at each player's actual plus minus value (e.g. taking the average), we find a
clear top 3 of: 1967 Wilt, 2000 Shaq, and 2017 Curry. We find the same top 3 if we look at each player's rank. All three gain small separation over Duncan and clearer separation over Hakeem and Kareem.
Does this make sense? I think so. 2001 Shaq might have been slightly better than 2000 Shaq in the postseason, but he suffers from a noticeably worse regular season (and this coasting may have enabled his improved performance in the post season). 1977 Kareem also suffers from a poorer regular season relative to competition. Like LeBron, if we combined their better regular seasons with their better postseason, we might get someone clearly better than the competition. Without this, they gain longevity but fall back in 1 year peaks. Hakeem also falls back. Duncan has the best argument, and I wouldn't be upset if other data supported Duncan. Basketball reference's BPM favors him, and WS/48 says he's in the mix, though WOWY, on/off, ESPN's RPM, and scalability seem to favor the current top 3. Like Kareem, it seems Duncan gains when we consider longevity, and falls slightly for 1 year peak.
So who do we take between 1967 Wilt, 2000 Shaq, and 2017 Curry?
Curry vs Shaq: AuPM certainly favors 2017 Curry > 2000 Shaq in both the regular season and post season (and it favors healthy 2016 Curry by even more). Box Plus Minus also favors Curry > 2000 Shaq (by a lot in the 2017 postseason in 2016 regular season, though 2017 Curry falls just behind in the regular season). 2000 Shaq does beat 2017 Curry in RAPM by a touch and in CORP% (though healthy 2016 Curry wins in RAPM and closes some of the gap in CORP%). TBH I'm surprised

... I thought Shaq would be the clear better peak.
Maybe more stats would help Shaq come out? Curry still comes out on top in ESPN's RPM and raw on/off (by a lot, though I've never been a fan of raw on/off). My back-of-the-napkin calculation of WOWY has them similar, while WS/48 and BR's BPM aren't conclusive either (Shaq takes the regular season, while Curry takes the postseason).
... I knew I had a Curry bias, but I was sure I'd take Shaq over Curry. Despite all that... I think I'm convincing myself of 2017 Curry over 2000 Shaq. Certainly the data seems to support it.
The main counters I can think of are: 1. if you're lower on health risks (I'm not for 1 year peaks, though I am for longevity), 2. if you think all the data is underrating Shaq's defense (... eh), 3. if you think the resilience disparity is wayyy in Shaq's favor (I don't think it's enough if we give Curry health), 4. if you think Curry's fit improves his data more than Shaq's fit (maybe?), or 5. if you use a backward Time Machine argument (while ignoring a forward time machine argument).
You know what? Screw it. I'm doing it. I'm saying it.
2017 Curry > 2000 Shaq. Come at me haters

(seriously, please do... I'd love to hear if there's data to prove this wrong).
Wilt vs Curry: This is much harder comparison, given our lack of data. Backpicks Box Plus Minus is mixed: 1967 Wilt beats 2017 Curry in the regular season, though he loses in the playoffs (and loses to 2016 healthy Curry). There's a similar pattern with CORP: 1967 Wilt beats 2017 Curry, though he loses to healthy 2016 Curry. For what it's worth, WS/48 and and WOWY favor Wilt. We now get to the same questions Curry faced with Shaq:
1. Health risks (which favor Wilt > Curry)
2. measuring defense with limited data (the data is certainly sparser and noisier in the 60s, but there's no doubt Wilt > Curry on defense)
3. resilience (both were seen by media as playoff strugglers. Wilt suffered from GOAT-level defensive opponents, while Curry suffered from health. With favorable context, I see them equally resilient)
4. Fit (both had favorable fit in their peak year)
5. Time machine argument (the 60s certainly favor Wilt over Curry. In future eras, Wilt gains value with data / coaching / strategy / medicine, while losing value with the 3 point line and increased perimeter focus).
Certainly, 1967 Wilt has greater uncertainty vs 2017 Curry. But it seems to me like he's slightly favored in the data, and remains favored when we consider the 5 contextual factors. Phew, I was worried everyone would see me as a biased Curry fan!
1967 Wilt > 2017 Curry.Sources:
Backpicks source:
https://backpicks.com/metrics/player-seasons/ and
https://backpicks.com/metrics/historical/corp-valuations/.
AuPM source:
https://docs.google.com/spreadsheets/d/1A-vid8kuilwdyjKNLDKu6Qvc-6pARwQGjAXMf-2ku4k/edit#gid=0RAPM source:
https://docs.google.com/spreadsheets/d/1eK0i6L0q2Brih5nKOKZLGHVofY0JWKOlnnEaSMu1LTM/edit#gid=0)
Historical RAPM pre-1997:
https://squared2020.com/2021/09/11/1990-1991-nba-rapm/