Top player peaks all-time (loosely based on Owly's model)

[trex_8063]

Have been experimenting with formulas to evaluate player peaks statistically.

Owly had used a method that (iirc) takes the all-time RANK of a player's best WS/48 season, multiplied by the RANK of his best PER season. And peaks ranked according to the resulting product, with the lower the resulting number the better (because being ranked #1 in a category is better than being #2, and so on).

I kinda liked the basic model (as I think utilizing both favors a nice balance of volume and efficiency), but it has it's limitations given only the top 251 single season results for each stat are listed in bbref. This is problematic because, for examples, we can't rank Bill Russell because he doesn't have a single season within the top 251 for PER. We can't rank Allen Iverson because he doesn't have a single season in the top 251 in WS/48, and so on (many noteworthy players can get left out).

I thought about simply multiplying best PER by best WS/48, but ultimately I wanted something that looked a little deeper than that. So I decided to basically combine some aspect of (PER)*(WS/48) with some of the principles of Moonbeam's Score+ ratings (i.e. considering value over the avg player), and also with some consideration of volume---that is: minutes.

So here's the formula I went with:
(bPER-15)*(bWS/48-0.1)*(avg mpg)

...where bPER is their single season (rs numbers) best PER, bWS/48 is their best single season WS/48 [EDIT: well, actually it's using the best single-season (PER-15)*mpg and best (WS/48-0.1)*mpg], and avg mpg is simply their average minutes per game of the two seasons in question (though in some instances it's just one season, as some players had their bests in both categories during the same year).

The principle behind subtracting 15 from the PER value and 0.1 from the WS/48 value is approximating their value over replacement (because league avg PER is 15, league avg WS/48 is .100). I realize those league averages aren't exactly "replacement" values, because they're the average of both replacements as well as stars/starters. Replacements would probably be marginally lower in both; but I feel it's close enough for our purposes here.
So the formula estimates how much more over replacement/league avg they give you, multiplied by how many minutes per game they're giving you that value over replacement.
Make sense?

Anyway, just thought I'd share the top 75 (or so) player peaks of all-time based on this formula, just fyi, discussion, whatever. Short-comings of the two base stats (they under-rep the value of certain player types, overrate others) obviously apply. I made no distinction between eras. If the peak occurred in the ABA, ABA seasons/ABA numbers were at 86% value (this was based on a previous estimate I'd made for a different project.....year-to-year it actually ranged from 82.9% up to 87%, iirc; but I just went with a flat 86% valuation for this formula). For one player (Dan Issel), I used one ABA season and one NBA season to estimate his peak; so his score was rated at 93% value (he doesn't crack the top 75, though: is #77, though). Anyway, here they are (current 2014-15 season not considered):

1. Wilt Chamberlain
2. Kareem Abdul-Jabbar
3. Michael Jordan
4. Lebron James
5. David Robinson
6. Shaquille O’Neal
7. Kevin Durant
8. Chris Paul
9. Oscar Robertson
*10. Rick Barry (*admittedly, I used his '69 season here, in which he only played 35 games; so it's a touch sketchy)
11. Kevin Garnett
12. Tracy McGrady
13. Connie Hawkins
14. Charles Barkley
15. Dirk Nowitzki
16. Karl Malone
17. George Mikan
18. Neil Johnston
19. Dwyane Wade
20. Bob Pettit
21. Paul Arizin
22. Magic Johnson
23. Julius Erving
24. Tim Duncan
25. Elgin Baylor
26. Larry Bird
27. Moses Malone
28. Artis Gilmore
29. Amar’e Stoudemire
30. Jerry West
31. Kobe Bryant
32. Bob McAdoo
33. Hakeem Olajuwon
34. Dolph Schayes
35. Walt Bellamy
36. Kevin Love
37. Spencer Haywood
38. Elton Brand
39. Ed Macauley
40. Dwight Howard
41. Grant Hill
42. Adrian Dantley
43. Jimmy Jones
44. Terrell Brandon
45. Kevin McHale
46. Larry Foust
47. Alonzo Mourning
48. Yao Ming
49. Bob Lanier
50. John Stockton
51. Patrick Ewing
52. Anfernee Hardaway
53. Chauncey Billups
54. Bill Russell
55. Pau Gasol
56. Bernard King
57. Vince Carter
58. Harry Gallatin
59. Allen Iverson
60. Stephen Curry
61. Vern Mikkelsen
62. Brandon Roy
63. Clyde Drexler
64. Tiny Archibald
65. Shawn Marion
66. Manu Ginobili
67. James Harden
68. Steve Nash
69. Bill Walton
70. Chris Webber
71. Chet Walker
72. Kevin Johnson
73. Brad Daugherty
74. Robert Parish
75. John Drew
76. Chris Bosh
77. Sidney Moncrief
(and Dan Issel is 78th)

Thoughts?

[CaliBullsFan]

Interesting. The list kind of goes off the deep end at 35 though

[Laimbeer]

I always suspected Elton Brand's peak was higher than Hakeem's.

[trex_8063]

I always suspected Elton Brand's peak was higher than Hakeem's.

Green font?

Obv you have to view these results within context of what they're based on: PER and WS/48 both tend to inadequately credit defense.

[NO-KG-AI]

To be fair, I bet hakeem goes a lot higher if you do it for post season or championship runs.

[trex_8063]

I always suspected Elton Brand's peak was higher than Hakeem's.

To be fair, I bet hakeem goes a lot higher if you do it for post season or championship runs.

I wrote the list out based on my spreadsheet results, noted Hakeem's spot as somewhat unexpected, but did not investigate. After your post, though, I was inspired to double-check.....turns out there was a simple typo when I entered his data. It has been corrected: Hakeem is actually #33 (five spots ahead of Brand).

[Hornet Mania]

Cool idea, and I appreciate the explanation of your methodology.

This sort of illustrates the challenges that come with exclusively crunching numbers to determine value. Neil Johnston over Wade, Kobe over Hakeem and Kevin Love topping Ewing are just a few of the head-scratchers that jumped out at first glance.

The very top of the list looks plausible, so I don't think you're too far off from a good metric.

[Moonbeam]

I like it, and I also quite like the use of MPG. I wonder whether it might be worth looking at some weighted average of the top 3 consecutive seasons or something combined across both PER and WS/48. If you want, I've downloaded all of the player data from BBREF and can send it to you to play around.

[D Nice]

As we say at work "Garbage in, Garbage out"

And if he's trying to pinpoint individual peak seasons why use inputs that [X]% of the time aren't even doing to come from the same data-point (year)?

New metrics are only useful if they tell us something not readily gleaned from data we already have. Arbitrarily weighted composite metrics (in any data project, not just here talking about PER/WS) tend to be trash.

[JeepCSC]

I agree that you can't call something a "peak" if it involves multiple years.

[Joao Saraiva]

What season did you use for James? Was it 09? And if it was 09, what would be his position in the list?

[trex_8063]

What season did you use for James? Was it 09? And if it was 09, what would be his position in the list?

'09 and '13.

btw--I'd forgotten to run Penny Hardaway thru; he comes in at #52 (edited above).

[trex_8063]

Cool idea, and I appreciate the explanation of your methodology.

This sort of illustrates the challenges that come with exclusively crunching numbers to determine value. Neil Johnston over Wade, Kobe over Hakeem and Kevin Love topping Ewing are just a few of the head-scratchers that jumped out at first glance.

The very top of the list looks plausible, so I don't think you're too far off from a good metric.

Well yeah; and I implied to take into consideration the basic flaws of the root metrics (and stated something a touch more specific in a later reply). Era considerations also apply. But widely varied opinions exist on how to weight the different eras of pro basketball; it wasn't my intent to debate that here.

And just so I'm totally clear: this is not my personal ordered list of player peaks. I'm only sharing the results given by this formula.

idk, maybe that is clear, but there's some wording in your post that got me worried that it wasn't. Specifically, it was the "head-scratchers" comment. Head-scratcher: implying confusion or lack of understanding (e.g. I simply cannot understand how he arrived at these conclusions).

Except these are not my conclusions. I laid bare the formula, along with some reasoning as to its construct, and the results simply are what they are (no subjectivity to it, it's purely a numbers game). So there shouldn't be any room for confusion or mystery; I've made it transparent.

[trex_8063]

As we say at work "Garbage in, Garbage out"

And if he's trying to pinpoint individual peak seasons why use inputs that [X]% of the time aren't even doing to come from the same data-point (year)?

Obviously if I was trying to pinpoint a peak season (singular), I wouldn't sample from multiple seasons.

My aim here was highest (peak) performance attained. Many players have such a distinct single season peak (e.g. Shaq, TMac, Penny, KG, Brand, etc) that all inputs came from the same year. But if---due to slightly different circumstances while still playing a same-ish level---a player happened to have two separate seasons which are rated best by two different metrics, I don't really see an issue with sampling from both. It's still illustrative of their peak potential (as measured by the two separate variables). And particular for players like Lebron James, for instance, for whom no one can even agree as to which season was his best/peak season.....I don't feel restricting to a single season is entirely fair; it feels like it's penalizing him (among others) for having a more extended peak.

Further, even if we did restrict to a single season's sampling, it would only marginally change the above order anyway. Generally the two seasons---for those players who actually DID have two seasons sampled---are pretty close in one or both of PER and WS/48; so it's not changing their score by any large degree.

New metrics are only useful if they tell us something not readily gleaned from data we already have. Arbitrarily weighted composite metrics (in any data project, not just here talking about PER/WS) tend to be trash.

I'm not sure what you're referring to as arbitrarily weighted. The only arbitration was wrt the valuation of ABA numbers, which I do think some manner of modifier is necessary and I didn't think mine was too unreasonable (but you're welcome to suggest something else). At any rate, that only effects precisely 7 players out of the 77 listed.
Or if you're referring to PER and WS/48 as "arbitrary", then.....whatev I guess.

[Hornet Mania]

Cool idea, and I appreciate the explanation of your methodology.

This sort of illustrates the challenges that come with exclusively crunching numbers to determine value. Neil Johnston over Wade, Kobe over Hakeem and Kevin Love topping Ewing are just a few of the head-scratchers that jumped out at first glance.

The very top of the list looks plausible, so I don't think you're too far off from a good metric.

Well yeah; and I implied to take into consideration the basic flaws of the root metrics (and stated something a touch more specific in a later reply). Era considerations also apply. But widely varied opinions exist on how to weight the different eras of pro basketball; it wasn't my intent to debate that here.

And just so I'm totally clear: this is not my personal ordered list of player peaks. I'm only sharing the results given by this formula.

idk, maybe that is clear, but there's some wording in your post that got me worried that it wasn't. Specifically, it was the "head-scratchers" comment. Head-scratcher: implying confusion or lack of understanding (e.g. I simply cannot understand how he arrived at these conclusions).

Except these are not my conclusions. I laid bare the formula, along with some reasoning as to its construct, and the results simply are what they are (no subjectivity to it, it's purely a numbers game). So there shouldn't be any room for confusion or mystery; I've made it transparent.

No, you were clear. It was late in the evening when I posted that so I didn't word it all that great. It was meant to be supportive of the general concept, but also hesitant to proclaim complete success. The head-scratchers part was just me pointing out bits where the formula spit out very unexpected results, not to suggest that was your personal opinion.

Should have said something more like. "Cool post, very interesting concept. It does illustrate some of the problems you come across when trying to nail down a good formula. It's hard to avoid ending up with strange results, like Johnston over Wade or Love over Ewing." Sorry for the confusion dude.

[ThunderDan9]

I always suspected Elton Brand's peak was higher than Hakeem's.

And Amare is better than Kobe and Hakeem... and almost as good as Larry Bird.

[Owly]

Because minutes are thrown in I like that the baseline has been moved up (not that it would have huge effect in a single season, but reflecting the principle that playing 48 minutes at slightly below league average doesn't add the same value as playing at nearly twice the league average level of productivity for 24 minutes).

Obviously it's easy to point out the odd looking results but people know what the input metrics are. Amar'e has an amazing stats peak. Now obviously that doesn't reflect how bad on D he was or whether that system/Nash helped him and that's where we bring our own brains and perspective to it. Ditto (regarding context) for Hakeem, excellent player but better in the playoff than RS, and this RS metric will reflect this. Jimmy Jones looks very odd where he is but he was (boxscore wise) dominant in the ABA, if we were perfecting it maybe we'd tweak ABA to yearly weights, but again, nobody's claiming a holy grail here, just something interesting. Neil Johnston was numerically dominant in the mid 50s, and whether or not you believe those numbers overstate his value, his presence might at least make people take a second look at what he did rather than just laugh this off. Walter Bellamy has great peak numbers and this will reflect that, we know we need to factor in context and other factors mentally. John Drew's (numbers wise, again this is a poor defender) peak might surprise people too, I'm not sure I'd heard of him until I started looking at numbers (have since read up a lot more on my NBA history). One other thing to note is, it is about one year peaks. Brand or Brandon didn't maintain their peaks so don't have star name recognition value, but that doesn't mean they weren't special at their very best. If you take it for what it is (not great for covering D, one year peak, reflection of the metrics input) it's certainly something interesting to look at, start a debate etc.

I'll throw in the results of my PPRN rank (including beyond the top 100, right down to the lowest qualifiers - obviously at the bottom end it's a bit arbitrary if you met the minimum baseline for each metric, if you narrowly missed one, you can't make it in) just for comparison.
Those who follow the top 100 project, may recall the methodology, I may post again or link to it if/when I have time. The short version is it's WS/48 ranking (1 season per player) squared plus PER ranking squared (then square rooted to give a smaller number). Not absolutely up to date. As noted in orignial threads, a ranking of rankings doesn't know the size of metric gaps, obviously again far from perfect.

2.236067977 1 Wilt Chamberlain
4.242640687 2 LeBron James
4.472135955 3 Michael Jordan
6.403124237 4 David Robinson
9.055385138 5 Kareem Abdul-Jabbar
9.433981132 6 Shaquille O'Neal
10 7 Chris Paul
15.62049935 8 Kevin Garnett
15.65247584 9 Kevin Durant
18.60107524 10 Charles Barkley
20.24845673 11 Dirk Nowitzki
21.40093456 12 George Mikan
21.63330765 13 Karl Malone
22.36067977 14 Oscar Robertson
23.08679276 15 Tracy McGrady
27.29468813 16 Earvin "Magic" Johnson
29.69848481 17 Amare Stoudemire
32.80243893 18 Neil Johnston
34 19 Bob Pettit
34.525353 20 Dwyane Wade
34.71310992 21 Tim Duncan
37.21558813 22 Larry Bird
38.28837944 23 Moses Malone
42.48529157 24 Dolph Schayes
43.56604182 25 Paul Arizin
47.38143096 26 Bob McAdoo
48.3011387 27 Hakeem Olajuwon
50 28 Dwight Howard
52.77309921 29 Jerry West
54.3783045 30 Walt Bellamy
55.90169944 31 Terrell Brandon
61.40032573 32 Julius Erving
63.07138812 33 Elton Brand
63.78871374 34 Elgin Baylor
65.30696747 35 Ed Macauley
67.53517602 36 Emanuel Ginobili
68.01470429 37 Arvydas Sabonis
68.60029154 38 Adrian Dantley
69.37578828 39 Kobe Bryant
73.00684899 40 Robert Parish
73.8241153 41 Alonzo Mourning
76.53103945 42 Larry Foust
77.46612163 43 Bob Lanier
78.71467462 44 Grant Hill
79.25906888 45 Kevin Love
79.64923101 46 Harry Gallatin
81.05553652 47 Pau Gasol
81.32035416 48 Anfernee Hardaway
81.39410298 49 John Stockton
83.81527307 50 Yao Ming
84.62860037 51 Kevin McHale
86.68333173 52 Chauncey Billups
94.81033699 53 Bernard King
94.84724561 54 John Drew
97.62171889 55 Brandon Roy
97.67292358 56 Clyde Drexler
99.15644205 57 Steve Nash
100.2397127 58 Bill Walton
103.8123307 59 Rick Barry
104.3551628 60 Patrick Ewing
108.8944443 61 Kevin Johnson
111.6288493 62 Bill Russell
112.3788236 63 James Harden
113.7409337 64 Andrew Bynum
114.8651383 65 Clyde Lovellette
115.5508546 66 Vince Carter
116.211015 67 Brad Daugherty
118.1270502 68 Kenny Sears
119.5533354 69 Shawn Kemp
119.6202324 70 Marques Johnson
120.5072612 71 Shawn Marion
123.6931688 72 Sidney Moncrief
129.0736224 73 Derrick Rose
133.2216199 74 Cliff Hagan
133.7348122 75 Vern Mikkelsen
134.0335779 76 Paul Pierce
134.3167897 77 Artis Gilmore
134.8517705 78 George Gervin
135.67977 79 Chris Bosh
137.2333779 80 Charlie (Chuck) Share
138.0326048 81 Scottie Pippen
138.9460327 82 George Yardley
139.8463442 83 Chris Webber
139.917833 84 Chet Walker
140.121376 85 Dan Issel
142.2743828 86 Tony Parker
142.3516772 87 Andrei Kirilenko
142.8425707 88 Ray Allen
151.7135459 89 Dominique Wilkins
152.8005236 90 David Thompson
152.8823077 91 Terry Porter
154.3826415 92 Sam Cassell
154.8418548 93 Bob Houbregs
159.81239 94 Mark Price
160.5521722 95 Russell Westbrook
160.8011194 96 Walt Frazier
161.0124219 97 Kenneth Faried
161.9012044 98 Sam Jones
166.291912 99 Darrell Armstrong
166.964068 100 Gary Payton
167.0568765 101 Blake Griffin
167.2871782 102 Brook Lopez
167.3140759 103 Bailey Howell
167.4305826 104 Gilbert Arenas
169 105 Larry Nance
169.0562037 106 Allen Iverson
173.104015 107 Willis Reed
175.6018223 108 Nate Archibald
180.3357979 109 Paul Westphal
189.2141644 110 Ryan Anderson
189.9078724 111 Marcus Camby
191.4497323 112 Bobby Jones
192.3174459 113 Carlos Boozer
192.8989373 114 Reggie Miller
193.1450232 115 Predrag Stojakovic
198.4363878 116 Terry Cummings
199.4016048 117 David Lee
200.8780725 118 Jack Twyman
203.1181922 119 Walter Davis
204.2155724 120 Carmelo Anthony
205.3606584 121 Horace Grant
210.5089072 122 Jason Kidd
215.4065923 123 Jameer Nelson
216.2059204 124 Zydrunas Ilgauskas
216.208233 125 Zach Randolph
217.6074447 126 Ricky Pierce
222.7128196 127 Cedric Ceballos
225.5593048 128 Toni Kukoc
226.0088494 129 Tim Hardaway
227.5280203 130 Kiki Vandeweghe
229.0938672 131 Antonio McDyess
229.6170725 132 Gus Williams
230.670761 133 Brad Miller
235.6374334 134 Calvin Natt
237.2867464 135 Dave Bing
239.9208203 136 Jack Sikma
242.8929805 137 Detlef Schrempf
244.1003892 138 Terry Dischinger
245.7580111 139 Nene Hilario
247.9697562 140 Jose Calderon
250.7369139 141 Tiago Splitter
252.6202684 142 Steve Francis
253.1600284 143 Jerry Lucas
255.1803284 144 "Mookie" Blaylock
257.241132 145 Rudy Tomjanovich
264.0700665 146 Alvan Adams
265.1377001 147 Paul Millsap
265.4091182 148 Kevin Martin
267.9178979 149 Deron Williams
269.6312296 150 Jermaine O'Neal
270.8006647 151 Glenn "Doc" Rivers
271.7425252 152 Antawn Jamison
272.6554602 153 Rod Strickland
277.0433179 154 Dana Barros
278.6000718 155 Stephen Curry
278.9587783 156 Ersan Illyasova
282.9699631 157 Al Horford
282.973497 158 Bob Cousy
285.5678553 159 Gail Goodrich
285.6028711 160 James Worthy
287.3604009 161 Rasheed Wallace
295.9358038 162 Calvin Murphy
300.3747659 163 Gerald Wallace
303.3562262 164 Tom Boerwinkle
304.1742921 165 Archie Clark
307.2474573 166 Tom Heinsohn
317.2380809 167 David West
323.8826948 168 Matt Geiger
335.1715978 169 Jim Paxson
335.8943286 170 Erick Dampier
340.8111647 171 Rik Smits
353.2085078 172 Derek Harper

For both lists I'd also add the qualifier about comparing metrics across eras being imperfect, and z-scores might at least offer an interesting counterpoint metric (plus, stating the obvious here, but metrics measure dominance within era, this does not mean Mikan would be great if whizzed to the modern day in a time machine).

[D Nice]

As we say at work "Garbage in, Garbage out"

And if he's trying to pinpoint individual peak seasons why use inputs that [X]% of the time aren't even doing to come from the same data-point (year)?

Obviously if I was trying to pinpoint a peak season (singular), I wouldn't sample from multiple seasons.

My aim here was highest (peak) performance attained. Many players have such a distinct single season peak (e.g. Shaq, TMac, Penny, KG, Brand, etc) that all inputs came from the same year. But if---due to slightly different circumstances while still playing a same-ish level---a player happened to have two separate seasons which are rated best by two different metrics, I don't really see an issue with sampling from both. It's still illustrative of their peak potential (as measured by the two separate variables). And particular for players like Lebron James, for instance, for whom no one can even agree as to which season was his best/peak season.....I don't feel restricting to a single season is entirely fair; it feels like it's penalizing him (among others) for having a more extended peak.

It’s misleading to call it a peak measure when it 1, isn’t consistent across all objects (players), and 2, in many cases is combining data from different windows. If you wanted to make a thread/metric based on the hypothetical value of “combine the best RS and best PS from each player to create a ’synthetic’ season” then do that. But don’t call it a peak metric when we have a well-established definition for peak here that differs from what you’re measuring. I mean you can do whatever you want, but if you are trying to estimate magnitudes of what actually happened you cannot pull one reading from the training period and one reading from outside the training period and act like they both happened in the training period to artificially enhance the results. It defeats the purpose of trying to identify a “peak” at all.

Further, even if we did restrict to a single season's sampling, it would only marginally change the above order anyway. Generally the two seasons---for those players who actually DID have two seasons sampled---are pretty close in one or both of PER and WS/48; so it's not changing their score by any large degree.

This is even more reason to only pull data from 1 year per-player.

I'm not sure what you're referring to as arbitrarily weighted. The only arbitration was wrt the valuation of ABA numbers, which I do think some manner of modifier is necessary and I didn't think mine was too unreasonable (but you're welcome to suggest something else). At any rate, that only effects precisely 7 players out of the 77 listed.
Or if you're referring to PER and WS/48 as "arbitrary", then.....whatev I guess.

Garbage in Garbage out is a saying in statistical modeling circles that refers to the phenomenon of “poor predictive independent variables” = “does a poor job forecasting/estimating dependent variable.”

Arbitrarily weighted spoke to PER and WS, not any of your permutations. In this case “garbage in” refers to PER and WS/48 as the “inputs.” And yeah, PER is arbitrarily weighted.