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 2014-15 season will be announced soon, I thought it might be interesting to revisit this topic. I’ve made some 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 1954-55 through 2013-14 who met the following criteria:
- Played at least 40 percent of all possible minutes in the given season.
- Played at least one minute (cumulatively) in the three previous seasons.
This gave me a sample of 7,144 player seasons, and for each of those seasons I did the following:
- Computed the player’s individualized wins per 48 minutes (iW/48) in the given season.
- Computed a baseline value of iW/48 for the player going into the given season. The baseline value is a weighted average of the player’s past 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, plus some regression toward the mean. Note that seasons in which the player has missing data are zeroed out
- Computed the difference between the player’s actual iW/48 and his baseline iW/48.
Let me go through an example using last season’s MIP, Goran Dragic:
- Dragic averaged .2124 iw/48 in 2013-14.
- Dragic’s relevant numbers for the three previous seasons were 6.781 iW in 2,581 minutes (2012-13), 5.593 iW in 1,752 minutes (2011-12), and 1.237 iW in 1,234 minutes (2010-11). Dragic’s weighted totals are 58.702 iW and 21,976 minutes, so his baseline value is: 48 * (58.702 + (1000 * (0.1 / 48))) / (21976 + 1000) = .1270.
- The difference between Dragic’s actual average and his baseline value is: .2124 – .1270 = 0.0854.
I did this for all 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 0.039. 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 iW/48?”
Let’s return to the Dragic example. In 2013-14, Dragic beat his expectation by .0854 iW/48. We want to find:
P(X ≥ .0854)
where X is the difference between the player’s actual iW/48 and baseline iW/48. Since the data are approximately Normal, this calculation is straightforward:
P(X ≥ .0854) = P(X / .039 ≥ .0854 / .039) = P(Z ≥ 2.190)
Now, Z is a standard Normal random variable, so:
P(Z ≥ 2.190) = .0143
In other words, the difference between Dragic’s actual performance and his baseline performance was uncommon: only about one out of every 70 players will beat their baseline by at least .0854 iW/48.
How did that performance compare to others that season? Here are the five most improbable performances of the 2013-14 season:
From a statistical standpoint, Morris’ improvement is the most impressive of the season, as only about one out of every 326 players will beat his baseline by at least .107 iW/48.
This method also highlights why the Phoenix Suns surprised so many people last season. In addition to Morris and Dragic, two other Suns — Gerald Green (seventh) and Marcus Morris (14th) — finished in the top 14 on the list of most improbable performances.*
* Eric Bledsoe was another Sun who showed great improvement, but he did not play enough minutes to qualify for the list.
Enough about last season, though. Let’s move on to this season…
Without further ado, here are the five biggest deviations from baseline in 2014-15:
I’m not surprised to see Gobert at the top of this list. Gobert went from an afterthought who played only 434 minutes last season to a defensive force who averaged over 26 minutes per game (almost 35 minutes per game since the All-Star break).
I suppose it might be surprising to see Davis and Thompson on this list, but both made very difficult leaps this season, Davis from All-Star to MVP candidate and Thompson from slightly above average starter to All-Star.
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.
That said, in this case I agree with the system: I would cast my (fictional) vote for Gobert.