Monday, January 10, 2011

The Greatness Equation

For the last few years, as I've watched the great players that I grew up idolizing (basically the original Dream Team) retire and give way to a new generation of superstars (basically the Redeem Team, with maybe a dozen other guys who didn't make the cut), I really began to wonder how these players stacked up against each other. And I don't mean just the biggest iconic names of their generations like LeBron vs. Kobe vs. Jordan. I'm talking even Barkley vs. Garnett. Or Nowitzki vs. Pippen. Or Reggie Miller vs. Ray Allen. How do those guys stack up against one another? Sure you can look at stats and see how many points or rebounds or assists someone averaged and compare them, but what about across different positions, who, by definition, are going to have wildly different averages in different categories? How could I compare Jordan or Magic to Shaq or Duncan? Hell, how could I really even compare any of them to Wilt or Russell or Kareem who played in completely different eras?

To solve this problem, I decided I needed an equation that would give a certain value to certain accomplishments and achievements that would remain relatively the same across all eras of basketball. It sounds like a ridiculous prospect, but keep in mind, this equation is not intended to say which player would win in a game of one on one, or even which player you'd rather have on your team in their prime. This equation simply sets out to answer the question: "Which player had the better career?"

Here's the formula, and I'll explain why it's set up the way it is and the two caveats with it afterward:

Win Shares + MVP Award Shares*25 + All-NBA 1st Team Selections*15 + All-NBA 2nd Team Selections*10 + All-Star Selections*5 + Playoff Win Shares for a Championship Team*10 + Playoff Win Shares for a Finals Losing Team*5 + Playoff Win Shares for a Conference Finals Losing Team*2.5

I decided early on that I wanted to count only accomplishments/achievements that had been awarded or tracked for the entire history of the NBA (or as close to it as I could get.) All-NBA 1st and 2nd Teams have been awarded since the league's first year so that was perfect. The first All-Star game was in 1951, so that works well, too. The MVP was first awarded in 1956, nine years after the league's first year, which is a bit later than I would've liked, but the NBA MVP is probably the most significant award in all of sports so I definitely needed to incorporate it, and that's still relatively early compared to all the other awards. I considered including the Rookie of the Year Award, but I ultimately decided against it because I didn't want to include an award that only a small percentage of players were eligible to win each year.

Win shares are fairly complicated to try and explain, if you want the full breakdown, click here. But the goal of win shares is to measure how many of a team's wins an individual player was responsible for. This, to me, is the essence of basketball: individual points don't necessarily matter, neither do individual rebounds or assists, team wins matter. And since basketball-reference has win share data back to 1952, this became my baseline stat for my formula. Every win share is worth one point.

Here's where the awards come into play, where individual greatness is recognized. It's hard to compare different positions based on statistics because who's to say how much a point guard's assist is worth compared to a center's rebound? But since everyone is eligible for every award, it gives us a baseline measure. MVP Award Shares are added in at a rate of 1 Award Share = 25 points. I chose Award Shares, which are the percentage of votes a player received in a given year (a unanimous MVP would be worth 1 Award Share) because I wanted to count MVP caliber seasons, rather than just MVP's won. Plus, this means that a unanimous MVP is worth more than a very contentious MVP, and the player who gets 2nd in the contentious MVP race gets more credit than the player who gets second to a unanimous MVP.

All-NBA 1st Team selections are worth 15 points each. All-NBA 2nd Team selections are worth 10 points each. And All-Star selections are worth 5 points each. (I considered using All-NBA 3rd Team selections and All-Defensive selections at around 2 points each, but since they're relatively recently established awards, they skew the rankings too much towards modern players.)

Now, the final component in the equation is championships - the ultimate goal for every player. But how to measure those? Michael Jordan's 6 titles should certainly be worth more than Jim Loscutoff's 6 titles. Hell, Jordan's 6 titles should probably be worth more than Pippen's 6 titles, even though Pippen's 6 titles are worth much much more than Loscutoff's. And Jordan's 6 are worth more than Horry's 7. But are Horry's 7 worth more than Horace Grant's 4? That's where things get tricky.

What I ultimately decided to do was use win shares again, but this time, playoff win shares. For example, let's look at the '95 Rockets: Clyde Drexler had 3.0 playoff win shares. Olajuwon had 2.8. Horry had 2.5. Mario Elie 1.5, Sam Cassell 1.5, Kenny Smith 1.4, etc. So, I took these playoff win shares and multiplied by ten, so that championship is worth an extra 3o points for Drexler, 28 for Olajuwon, 25 for Horry, 15 for Elie, 15 for Cassell, 14 for Smith, and so on for the rest of the roster.

I also wanted to give players credit for making the finals or conference finals even if they did get crushed by Jordan's Bulls or Russell's Celtics or any other number of great teams. There's no shame in that, but of course, its not nearly as good as winning. So finals losing teams get they're playoff win shares multiplied by 5 and conference finals losing teams multiplied by 2.5.

So, now that I've laid all that out, let's take a look at Michael Jordan for an example:
214 Win Shares = 214 points
8.138 MVP Award Shares = 203.45 points
10 All-NBA 1st Team Selections = 150 points
1 All-NBA 2nd Team Selection = 10 points
14 All-Star Selections = 70 points
26.7 Championship Win Shares = 267 points
0 Finals Losses Win Shares = 0 points
8 Conference Finals Losses Win Shares = 20 points
Which gives us a grand total of 934.5 points

And here's how the top 50 shake out as of the end of the 2010 season:
1. Michael Jordan - 934.5
2. Kareem Abdul-Jabbar - 932.0
3. Bill Russell - 739.6
4. Magic Johnson - 714.0
5. Wilt Chamberlain - 712.6
6. Shaquille O'Neal - 681.9
7. Tim Duncan - 665.3
8. Larry Bird - 654.9
9. Karl Malone - 651.8
10. Kobe Bryant - 630.0
11. Jerry West - 584.6
12. Oscar Robertson - 511.2
13. Hakeem Olajuwon - 511.2
14. John Havlicek - 479.1
15. Bob Pettit - 468.2
16. Moses Malone - 457.2
17. David Robinson - 450.0
18. Charles Barkley - 449.9
19. Kevin Garnett - 449.4
20. Julius Erving - 437.6
21. Elgin Baylor - 416.2
22. Scottie Pippen - 411.5
23. Bob Cousy - 402.3
24. John Stockton - 392.3
25. Dolph Schayes - 388.2
26. Dirk Nowitzki - 366.4
27. Gary Payton - 324.1
28. Elvin Hayes - 322.1
29. Walt Frazier - 321.8
30. LeBron James - 320.7
31. Patrick Ewing - 320.3
32. Rick Barry - 309.9
33. Clyde Drexler - 307.3
34. Jason Kidd - 306.8
35. Steve Nash - 293.4
36. Isiah Thomas - 284.1
37. Sam Jones - 283.0
38. Allen Iverson - 281.7
39. Robert Parish - 278.9
40. George Gervin - 277.5
41. Bill Sharman - 276.2
42. Kevin McHale - 267.7
43. Hal Greer - 251.9
44. Reggie Miller - 244.7
45. Paul Arizin - 244.5
46. Chauncey Billups - 244.1 (I know, this surprised me, too.)
47. Dave Cowens - 239.8
48. Dominique Wilkins - 238.7
49. Willis Reed - 234.5
50. George Mikan - 232.2

Keep in mind, this isn't to say that David Robinson was definitively better than Charles Barkley or that Allen Iverson was definitively better than Robert Parish, but it gives us a really good idea of the ballpark area players should fit in the hierarchy of greatness, and the closer a player's total is the more interchangeable they could potentially be. (Robinson and Barkley are separated by a tenth of a point - they're virtually equal.)

A few final caveats to the equation. The first one is fairly simple - ABA stats and accomplishments are included, but they're worth 25% of NBA stats. The second one is a bit more complicated. I was initially calling it the "Robert Horry Rule", but it actually affects Horace Grant the most, because without it, Grant ranks as the 47th best player of all-time. Basically I implemented it to prevent "right place, right time" guys who piled up tons of championship and playoff win shares by being lucky enough to be on several great teams in their career. Not to disparage Grant, who was a really good player, but he wasn't that good.

What I eventually decided to do was make players reach certain individual benchmarks in order to receive full credit for their scores. If a player won an MVP, or was named to an All-NBA 1st or 2nd Team, they automatically get full credit. If they made 1 All-Star team, they get two-thirds credit, if they made 2 All-Star teams, they get three-fourths credit, and if they made 3 All-Star teams, they get full credit.

So there you have it: "The Greatness Equation." I'll be using it for my next series of posts about improving the Hall of Fame after my Tournament wraps up next week. And I'd always appreciate any thoughts/comments/feedback on the equation itself if anyone has any ideas on how to make it even better.


  1. I am really surprised about how this equation fit really well with how I would rank players on my own...

    The top 10 shakes out to about where I would put it, except that I would slide Kareem down to behind Wilt at the 5 spot, put Bird ahead of Duncan, and swithc Malone and Oscar, putting Oscar at the 9 spot.

    Havlicek, Cousy and Sam Jones all seemed to have benefitted a little too much from being on the Celtics. And I would have KG jump Barkley and Robinson.

    The biggest flaw, however, I see in this formula is human error when it comes to MVP voting.

    Voters tend not to vote players who assist and steal the ball a lot, meaning Points Guards, which I consider the most important position on the court offensively, do not get their fair share of MVP votes.

    This may be why Stockton is at number 24, but I believe he should be at 10 and just slightly edge Kobe (Kobe will probably surpass him and another of other players before it's all said and done) out of the top 10.

    What do you think?

  2. Well, there's no doubt Havlicek, Cousy, and Sam Jones all benefitted greatly from being on the Celtics dynasty. (Everyone else on those teams did, too. Heinsohn comes in at #57, which is almost certainly too high.)

    And I thought about it a little, but I really don't think it's necessarily geared against point guards. Or, at the very least, the MVP voting tends to fall in line with what actually ends up happening historically. What really hurts the point guards is that very few of them are the focal points of dynasties. Winning championships is, by far, the easiest way to move up these rankings, and if you think about it, very few teams are built around point guards without having at least one transcendent big man. Magic probably being the only exception here while Kareem was on his way out.

    Robertson never won when he was the main guy. Neither did Payton, Frazier, Kidd, or Nash. And Stockton and Cousy were never the main guy.

    And as far as specific rankings go, when I look at the list, I'm more concerned with "Charles Barkley is about 18th." He could realistically be a few spots either way, and the closer his number is to another guy, the more reasonable it is to say they could be switched. It works a little better, at least in my mind, if you look at it as a bubble or tiered system and that the surrounding names are very close to one another in greatness (depending on the difference in their ratings) and not a hard and fast definitive "#1 Greatest, #2 Greatest, #3 Greatest, etc." list.