Posted by Justin Kubatko on April 6, 2010
The other day I decided to check out the Most Improved Player (MIP) list on ESPN.com's NBA Awards Watch. Before visiting the page I figured that Kevin Durant would be at the top of the list, as Durant has made a stratospheric leap this season, going from at best an average player to one of the top five players in the NBA. Imagine my surprise when I saw Durant in the second spot on this list, behind Aaron Brooks of the Houston Rockets. In my mind I knew that this had to be wrong, that Durant's improvement was the most improbable performance of the season, but I needed a way to quantify it. The question is: How? Let's go to the data...
I started by determining which players would make up the pool of MIP candidates. I decided to use cutoffs of 70 games played or 1400 minutes played. Why those figures? Because in the last ten years, 104 of the 105 players who finished in the top ten of the MIP voting reached at least one of those minimums (the exception was Von Wafer in 2009). Then, using all players from 1985-86 through 2008-09 who met the criteria, I did the following:
- Computed the player's Win Shares per 48 minutes (WS/48).
- Using the Simple Projection System (SPS), computed a baseline WS/48 expectation for the player going into the given season. In short, the SPS will produce a projection for the player that takes into account the player's age and recent performance, with some regression to the mean factored in for good measure.
- Computed the difference between the player's actual and expected WS/48.
Let me go through an example using Boris Diaw in 2005-06:
- Diaw averaged 0.1490 WS/48.
- Based on his previous seasons, a reasonable expectation for Diaw would have been an average of 0.0192 WS/48.
- Diaw's actual average was 0.1490 - 0.0192 = 0.1298 WS/48 better than expected.
I did this for all 4645 players in the player pool and examined the distribution of the differences. Here is a histogram of the results:
As you can see, the data are approximately Normal with mean 0 and standard deviation 0.04. We can then use this information to answer the following question: "What is the probability than a randomly selected player will beat his expectation by at least x WS/48?" Let's return to the Boris Diaw example. In 2005-06 Diaw beat his expectation by 0.1298 WS/48. We want to find:
P(X ≥ 0.1298)
where X is the difference between the player's actual and projected WS/48. Since the data are approximately Normal, this calculation is straightforward:
P(X ≥ 0.1298) = P(X / 0.04 ≥ 0.1298 / 0.04) = P(Z ≥ 3.245)
Now, Z is a standard Normal random variable, so:
P(Z ≥ 3.245) = 0.0006
In other words, the difference between Diaw's actual performance and his expected performance was highly improbable: only about 6 out of every 10,000 players will beat their expectation by at least 0.1298 WS/48. Now, 2005-06 happens to be the only season where the player with the most improbable performance was also the MIP. Here are the ten most improbable performances of that season:
Rk Player WS/48 Proj Diff Prob 1 Boris Diaw* 0.1490 0.0192 0.1298 0.0006 2 Gerald Wallace 0.1630 0.0576 0.1054 0.0042 3 Kevin Martin 0.1375 0.0384 0.0991 0.0066 4 DeSagana Diop 0.1299 0.0336 0.0963 0.0080 5 Dwyane Wade 0.2388 0.1536 0.0852 0.0166 6 Andres Nocioni 0.1437 0.0624 0.0813 0.0211 7 LeBron James 0.2322 0.1536 0.0786 0.0247 8 Smush Parker 0.1005 0.0240 0.0765 0.0279 9 Chris Kaman 0.1139 0.0432 0.0707 0.0386 10 Elton Brand 0.2294 0.1632 0.0662 0.0490 * = MIP Award Winner WS/48 = Actual WS/48 Proj = Projected WS/48 Diff = Actual WS/48 - Projected WS/48 Prob = Probability
OK, now let's get back to the 2009-10 MIP race. What have been the most improbable performances so far this season?
Rk Player WS/48 Proj Diff Prob 1 Kevin Durant 0.2328 0.1008 0.1320 0.0005 2 Luke Ridnour 0.1651 0.0720 0.0931 0.0100 3 Quentin Richardson 0.1278 0.0480 0.0798 0.0230 4 Jermaine O'Neal 0.1418 0.0624 0.0794 0.0236 5 Donte Greene 0.0400 -0.0384 0.0784 0.0250 6 Zach Randolph 0.1594 0.0816 0.0778 0.0259 7 Russell Westbrook 0.1157 0.0384 0.0773 0.0266 8 J.J. Redick 0.1699 0.0960 0.0739 0.0323 9 Josh Smith 0.1614 0.0912 0.0702 0.0396 10 Channing Frye 0.1389 0.0720 0.0669 0.0472
Rk Player WS/48 Proj Diff Prob 106 Aaron Brooks 0.0898 0.0912 -0.0014 0.5140
Believe it or not, Brooks has actually played a bit below his expectation. Now, I know the argument: Brooks has managed to maintain his efficiency while increasing his minutes by about 10 per game. That's true, but that does not mean that Brooks has actually improved. There are two possibilities:
- Brooks should have seen a decrease in efficiency given an increase in his minutes, and the fact that he has been able to maintain that efficiency is evidence of improvement.
- Brooks has not improved beyond what we would expect from a player his age, and his per game numbers are up simply because of an increase in minutes played.
Quite frankly, there is no way to prove whether (1) or (2) is correct. I tend to believe that the answer is a combination of the two, but more (2) than (1). Regardless, the fact that we can argue this point should make it clear that Durant should be the winner, as we are certain that Durant has shown remarkable improvement.
Before I go, let me make it perfectly clear that I am not suggesting that the NBA actually use a formula to determine the MIP. I can think of quite a few reasons why a player who is, say, 5th using this method should be voted the MIP. However, I do think this is a good way to whittle down the list of candidates, and to separate players who have obviously improved from players whose improvement is questionable.