A few years ago I developed a method for identifying the leading candidates for the Most Improved Player (MIP) award. Since the winner of the award for the 2013-14 season will be announced soon, I thought it might be interesting to revisit this topic. I’ve made some minor tweaks to the method since it was first conceived, so let me outline the process 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 2012-13 who met the following criteria:
- Played at least 1,500 minutes in the given season.*
- Played at least 1,500 minutes (cumulatively) in the three previous seasons.
* Cutoffs of 915 minutes and 1,208 minutes were used for the lockout-shortened 1998-99 and 2011-12 seasons, respectively.
This gave me a sample of 4,978 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 value 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 receiving a weight of one.*
- Computed the difference between the player’s actual WS/48 and his baseline WS/48.
* Seasons in which the player has missing data are zeroed out.
Let me go through an example using Kevin Durant in 2009-10:
- Durant averaged .2386 WS/48 in 2009-10.
- The previous season, his second in the NBA, Durant finished with 7.897 Win Shares in 2,885 minutes. In in his rookie season, Durant had 2.286 Win Shares in 2,768 minutes. Thus, Durant’s baseline value was 48 * ((6 * 7.897) + (3 * 2.286)) / ((6 * 2885) + (3 * 2768)) = .1016.
- Durant’s actual average was .1370 WS/48 above his baseline.
I did this for all 4,978 qualifying 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 0.036. 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 .1370 WS/48. We want to find:
P(X ≥ .1370)
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 ≥ .1370) = P(X / .036 ≥ .1370 / .036) = P(Z ≥ 3.806)
Now, Z is a standard Normal random variable, so:
P(Z ≥ 3.806) = .0001
In other words, the difference between Durant’s actual performance and his baseline performance was highly improbable: about one out of every 10,000 players will beat their baseline by at least .1370 WS/48.
How did that performance compare to others that season? Here are the five most improbable performances of the 2009-10 season, plus the MIP winner:
|91||Aaron Brooks (MIP)||2919||.0908||.0897||.0011||.4878|
My opinion back in 2010 — an opinion that I still hold — is 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 2013-14 MIP race. Which players have shown the most improvement this season?
From a statistical standpoint, Markieff Morris improvement is the most impressive of the season, as about one out of every 250 players will beat their baseline by at least .0956 WS/48.
This method also highlights why the Phoenix Suns surprised so many people this season. In addition to Markieff Morris and Dragic, two other Suns — Gerald Green (ninth) and Marcus Morris (12th) — finished in the top 12 on the list of most improbable performances, while P.J. Tucker finished 22nd.*
* Two other Suns who showed great improvement — Eric Bledsoe and Miles Plumlee — did not qualify for the list, Bledsoe because he did not play enough minutes this season and Plumlee because he did hot have enough minutes played coming into the season.
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 isn’t in the top five based on 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.