Posted by Neil Paine on June 21, 2010
For those who missed the epic Kobe-LeBron thread over the weekend, here's a recap of a good back-and-forth between myself and a commenter named "Anon" (a far different Anon from the user who usually posts under that moniker, apparently)...
First off, I stated that if LeBron's teammates played as well vs. Boston as Kobe's did against the Celts, Cleveland would have advanced. In retrospect, I should have said "Cleveland would probably have advanced," since obviously there are no certainties, in life and least of all in sports, but the general point stands -- Cleveland's probability of beating Boston would have been higher had James' teammates given him a performance like Kobe's did against the same opponent. The justification for that statement is this:
"LeBron's SPM in the Cleveland-Boston series was +7.47. His team's efficiency differential was -5.8.
Kobe's SPM in the L.A.-Boston series was +7.45. His team's efficiency differential was +4.0.
Remember, 5 * the minute-weighted average of the SPMs of the individuals on a team must equal the team's efficiency differential.
This is what I mean when I say, 'if LeBron had gotten a Gasol-like performance from one of his teammates, Cleveland would have won.' Kobe and LeBron played at identical levels in their respective series vs. Boston. The only possible reason for their teams' disparate efficiency differentials must be the performances of their teammates."
I went on to show the cumulative stats for both teams during their respective series vs. Boston:
However, as Anon pointed out, it's not necessarily quite that open-and-shut. On average, LeBron and Kobe did perform at essentially equal levels vs. the C's, but the game-by-game distributions of their performances were radically different. Here are Kobe's game-by-game SPM scores vs. Boston:
That's a standard deviation of 5.41... Meanwhile, here are LBJ's game-by-game SPMs vs. Boston:
That's a standard deviation of 10.58... This means that LeBron was more likely to have a monster game, but he was also more likely to have a poor game that damaged his team's chances. Linking this back to team performance, Dean Oliver found in Basketball on Paper that, among two teams with equally positive point differentials, the one that was more consistent was likely to win more ballgames. Now Kobe suddenly has a case for contributing more wins vs. Boston than LeBron, given equal teammates.
This is an interesting development. I'm not saying Kobe is always more consistent than LeBron, mind you, or that they're always equal performers. This is based on a very specific, very miniscule sample size, and we all know the dangers of drawing conclusions from this kind of short-term data. So please keep that in mind going forward.
Nonetheless, let's set up a simple Monte Carlo experiment to test this: say for a second that these numbers do represent the true ability levels of LeBron James, Kobe Bryant, and their teammates against the Boston Celtics in May and June of 2010. So Kobe and LeBron are two players with equal contributions to victory on average (+7.5), but Kobe's per-game distribution is much narrower -- let's give him a standard deviation of 5.5 SPM each game, and give LeBron a standard deviation of 10.5. And they both play 42 MPG.
Of course, we also need to establish the production of their teammates. Remember that the team's efficiency differential will always equal
(5 * (m1s1 + m2s2)) / (m1 + m2)
where m1 is the player's minutes, s1 is the player's SPM, m2 is his teammates' total minutes, and s2 is those teammates' minute-weighted SPM.
During their Boston series, Kobe's teammates averaged a -0.56 score with a per-game standard deviation of 2.6; LeBron's teammates averaged a -2.87 score with a standard deviation of 3.8. Combined, the two superstars' teammates averaged -1.63 with a 3.3 standard deviation.
So for the purposes of this simulation, let's say that the star can be on either Cleveland, where he'll get -3 support with a stdev of 4; L.A., where he'll get -0.5 support with a 2.5 stdev; or "Clevangeles", where he'll get -1.5 support with a 3.5 stdev. In each situation, which player contributes a higher cumulative winning percentage, the Kobe-esque one or the LeBron-esque one?
10,000 simulated games later, here's your answer:
|Team Wins/10,000 G|
As you can see, the players were actually well-suited to their real-life situations -- a player with James' all-or-nothing variance would win more on a team like Cleveland than he would if he had Kobe's steadier approach. Likewise, Bryant's consistency would buy the Lakers more wins than LBJ's boom-and-bust tendencies. And on the bizarre amalgam of the Cavs and Lakers, Kobe has a very slim edge in total wins.
Another major thing we can derive from this sim? More often than not, neither Kobe nor LeBron would have been enough to put Cleveland over the top vs. Boston, given the way the rest of the team played. Also, the Lakers win the NBA championship more often than not no matter whether James or Bryant is leading the way. Proving again that, whoever you are, you always need help from your friends.