Posted by Justin Kubatko on April 1, 2011
About this time last year, I developed a method for identifying the leading candidates for the Most Improved Player (MIP) award. Since we are nearing the end of the 2010-11 season, I thought it might be interesting to revisit this topic. I made some minor tweaks to last year's method, so let me outline the process once again before reporting this season's results.
The first step, of course, is to select the players to include in the study. The player pool consisted of all players from 1980-81 through 2009-10 who met the following criteria:
- Played at least 1000 minutes in the given season (610 for the lockout-shortened 1998-99 season).
- Played at least 1000 minutes (cumulatively) in the three previous seasons.
That gave me a sample of 5905 player seasons, and for each of those seasons I did the following:
- Computed the player's Win Shares per 48 minutes (WS/48) in the given season.
- Computed a baseline value of WS/48 for the player going into the given season. The baseline vaue is a weighted average of the player's last three seasons, with last season receiving a weight of six, two seasons ago receiving a weight of three, and three seasons ago receving a weight of one. (Seasons in which the player has missing data are zeroed out.)
- Computed the difference between the player's actual and baseline WS/48.
Let me go through an example using Kevin Durant in 2009-10:
- Durant averaged 0.2384 WS/48 in 2009-10.
- The previous season, his second in the NBA, Durant finished with 7.9 Win Shares in 2885 minutes. In in his rookie season, Durant had 2.3 Win Shares in 2768 minutes. Thus, Durant's baseline value was 48 * (6 * 7.9 + 3 * 2.3) / (6 * 2885 + 3 * 2768) = 0.1018.
- Durant's actual average was 0.2384 - 0.1018 = 0.1366 WS/48 above his baseline.
I did this for all 5905 player seasons in the time period 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 0.037. 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 Durant example. In 2009-10, Durant beat his expectation by 0.1366 WS/48. We want to find:
P(X ≥ 0.1366)
where X is the difference between the player's actual and baseline WS/48. Since the data are approximately Normal, this calculation is straightforward:
P(X ≥ 0.1366) = P(X / 0.037 ≥ 0.1366 / 0.037) = P(Z ≥ 3.692)
Now, Z is a standard Normal random variable, so:
P(Z ≥ 3.692) = 0.0001
In other words, the difference between Durant's actual performance and his baseline performance was highly improbable: only about 1 out of every 10,000 players will beat their baseline by at least 0.1366 WS/48.
Here are the ten most improbable performances of the 2009-10 season, plus the MIP winner:
Rk Player WS/48 Base Diff Prob 1 Kevin Durant 0.2384 0.1018 0.1366 0.0001 2 Luke Ridnour 0.1679 0.0683 0.0996 0.0036 3 Quentin Richardson 0.1328 0.0448 0.0880 0.0087 4 Jermaine O'Neal 0.1345 0.0595 0.0750 0.0213 5 Jamal Crawford 0.1425 0.0689 0.0736 0.0233 6 Zach Randolph 0.1526 0.0797 0.0729 0.0244 7 J.J. Redick 0.1728 0.0999 0.0729 0.0244 8 Beno Udrih 0.1069 0.0361 0.0708 0.0278 9 Russell Westbrook 0.1047 0.0348 0.0699 0.0294 10 Channing Frye 0.1411 0.0717 0.0694 0.0303 105 Aaron Brooks* 0.0909 0.0897 0.0012 0.4871 WS/48 = Actual WS/48 Base = Baseline WS/48 Diff = Actual WS/48 - Projected WS/48 Prob = Probability * = MIP Award Winner
My opinion last year — an opinion I stil hold — was that Durant should have been the runaway winner of the award, but in reality he finished a distant second to Aaron Brooks.
OK, now let's take a look at the 2010-11 MIP race. Which players have shown the most improvement so far this season?
Rk Player WS/48 Base Diff Prob 1 Derrick Rose 0.2022 0.0925 0.1097 0.0015 2 Tyson Chandler 0.2153 0.1283 0.0870 0.0094 3 Elton Brand 0.1548 0.0688 0.0860 0.0101 4 Kevin Love 0.2148 0.1328 0.0820 0.0133 5 Ryan Anderson 0.2078 0.1315 0.0763 0.0196 6 Russell Westbrook 0.1576 0.0822 0.0754 0.0208 7 Darrell Arthur 0.1205 0.0454 0.0751 0.0212 8 DeShawn Stevenson 0.0720 -0.0006 0.0726 0.0249 9 Thaddeus Young 0.1396 0.0729 0.0667 0.0357 10 Jrue Holiday 0.0968 0.0325 0.0643 0.0411
Derrick Rose is at the center of every MVP discussion, but I have yet to see him mentioned as the leading candidate for the MIP award. This represents, in my opinion, a fatal flaw with the award. That is, players who are expected to become stars (e.g., Durant and Rose) are almost always passed over in favor of players whose performance "surprised" the voters. But the award is supposed to go to the most improved player, not the most surprising player, so voter expectations for the players should not be a factor.
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, fifth 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.