Who's the Most Improved Player?
Who's the Most Improved Player?
M-I-P, easy as 1-2-3.
Many years ago (13, to be exact), I developed a method for identifying the leading candidates for the Most Improved Player Award. Since the winner of the award for the 2022-23 season will be announced soon, I thought it might be interesting to dust off this topic and revisit it. 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 the 1980-81 through 2021-22 seasons who met the following criteria:
Played at least 40% of all possible minutes in the given season.
Played at least as many minutes (cumulatively) in the three previous seasons as they did in the given season.
Had not recorded a Player Efficiency Rating (PER) of 25 or higher in any previous season.
The third step is necessary to eliminate established stars who are having otherworldly seasons. For example, Nikola Jokic posted the highest PER in NBA history in 2021-22, a season in which he won his second consecutive MVP Award. As far as I know, Jokic received zero consideration for the Most Improved Player Award last season, even though his improvement was statistically notable.
The criteria above gave me a sample of 5,073 player-seasons. For each of those seasons, I did the following:
Computed the player’s PER* in the given season.
Computed a baseline PER for the player going into the given season. The player’s baseline PER is a weighted average of his three previous 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. I also threw in 1,000 minutes of league-average play (PER = 15).
Computed the difference between the player’s actual PER and his baseline PER.
* Is PER the best metric to use? Probably not, but this method can easily be adapted for any measure you wish to use.
Let me go through an example using Ja Morant in 2021-22:
Morant recorded a PER of 24.4 in 1,889 minutes.
The previous season, his second in the NBA, Morant had a PER of 16.7 in 2,053 minutes. In his rookie season, Morant had a PER of 17.4 in in 2,074 minutes. Thus, Morant’s baseline value is ((6 * 16.7 * 2053) + (3 * 17.4 * 2074) + (15 * 1000)) / ((6 * 2053) + (3 * 2074) + 1000) = 16.8.
Morant’s actual PER was 7.6 above his baseline (24.4 – 16.8).
I did this for all qualifying player-seasons in the time period and examined the distribution of the differences. Here’s a histogram of the results:
As you can see, the data are approximately Normal, with mean 0.042 and standard deviation 2.109. We can then use this information to answer the following question: “What is the probability that a randomly selected player will beat his baseline PER by at least x?”
Let’s return to the Morant example. In 2021-22, Morant beat his baseline PER by 7.6. We want to find:
where X is the difference between the player’s actual PER and baseline PER. Since the data are approximately Normal, this calculation is straightforward. First, calculate the player’s Z-score:
We know that Z is a standard Normal random variable, so:
In other words, the difference between Morant’s actual performance and his baseline performance was highly improbable: about one out of every 5,000 players will beat their baseline PER by at least 7.6 (it’s one out of 5,717 players when all decimals are carried).
How did that performance compare to others last season? Here are the six most improbable performances of the 2021-22 season:
Ja Morant (1 in 5,717)
Darius Garland (1 in 990)
Dejounte Murray (1 in 382)
Josh Hart (1 in 40)
Miles Bridges (1 in 37)
Anfernee Simons (1 in 31)
In the actual voting for the Most Improved Player Award, Morant finished first, Garland third, Murray second, Bridges seventh, and Simons eighth. Hart did not receive any votes.
Now let's take a look at the 2022-23 Most Improved Player race. Which players have shown the most statistical improvement this season?
Lauri Markkanen (1 in 3,374)
Shai Gilgeous-Alexander (1 in 1,688)
Tyrese Haliburton (1 in 410)
Jaren Jackson Jr. (1 in 79)
Aaron Gordon (1 in 49)
Jalen Brunson (1 in 45)
From a statistical standpoint, Lauri Markkanen’s improvement is the most impressive of the season, as about one out of every 3,374 players will beat their baseline PER by at least 7.3 (Markkanen’s actual PER was 22.1 and his baseline PER was 14.8).
The three finalists for the award — who were announced last Friday — are Markannen, Shai Gilgeous-Alexander, and Jalen Brunson. Those players rank first, second, and sixth, respectively, using this method.
Now, let me make something perfectly clear: I’m not suggesting the NBA actually use a formula to determine who should win the Most Improved Player Award. I can think of quite a few reasons why a player who isn’t in the top five based on this method should win the honor. 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 those whose improvement is statistically questionable.
That said, I would agree with the math and cast my (fake) vote for Markkanen. Markkanen averaged a career-high 25.6 PPG — good for 12th in the NBA — with a career-best true shooting percentage of 64.0%. Markkanen’s ability to increase his scoring efficiency with a significant increase in his usage rate was particularly impressive (26.5% this season compared to 20.2% over his three previous seasons). Markkanen also improved as a playmaker, registering an assist rate of 8.6%, easily the highest such figure of his career.
The key question is, will this season eventually be seen as a stepping stone to greater things for Markkanen (a la former winners Giannis Antetokounmpo, Jimmy Butler, and Paul George) or will it be considered a fluke (a la former winners Aaron Brooks, Bobby Simmons, and Isaac Austin)?
Love these types of studies. Thanks!