Projecting Jimmy Butler’s Regression

During the preseason, optimism runs high. Improvements can be seen in nearly every player on a roster if one looks hard enough. In particular, fans nearly inevitably expect further improvements from young players coming off a breakout season. This expectation is often unwarranted, wit’s the lack of further progress foiling most generous predictions for a team.

Entering this season, one such recently-emerged player is Chicago’s Jimmy Butler. With Derrick Rose seemingly always hampered by some injury or another, in 2014/15 Butler became an unquestioned two-way star on the wing. Butler posted career highs across the board while continuing to play excellent defense. More impressively, his increased statistical production wasn’t the result of a big minutes increase – he simply did much more in the time[1. 38.7 minutes per game in both 2013/14 and 2014/15.] he was allotted, jumping from +2.4 to + 4.7 in Basketball-Reference’s Box Plus Minus. After such a big jump, what sort of progressional is reasonable to expect from him this coming season.

To investigate, I took a sample of players of Butler’s age range (23-25) who also completed 3 consecutive seasons with at least 500 minutes. Rather than using a holistic measure like Real Plus Minus[3. Which we don’t have much public data for, especially historical.] I opted for a huge dataset – all of Basketball-Reference.com‘s Box Plus Minus[3. Probably the best box-score statistical estimate of player contributions per 100 possessions.] historical data.

Here’s what I found:

Quick couple notes: For comparison, the left side of the graph is a player dropping in per-100 contributions. (Whatever the opposite of a breakout season is.) Also the first player season is “Year A”, second player season is “Year B” (i.e. Butler last year), and third player season is “Year C.”

Using the regression line here[4. The equation is Season_3_Minus_Season_2_BPM~ -0.326*Season_2_Minus_Season_1_BPM + 0.2196], we see that a player with Butler-level jumps in BPM tend to fall by about half point per 100 possessions. So by this method, Butler’s box plus minus would regress from 4.7 to 4.2 in 2016.

Diving a little deeper, we can find even closer comparisons. Not just players who got better but players who started out in Butler’s range (+2.4 in 2014), and jumped like Butler did (to +4.7 in 2015). There were just a handful of qualifying players – whose BPM was between 2 and 3 at age 24, and whose BPM was between 4 and 6 at age 25. Did they regress differently? Here’s how their seasons went:

Other than Horace Grant and Joakim Noah, there was a rather constant regression towards the mean. The highest comp (Grant) jumped all the way to +7.3. The lowest comp (Steve Francis) dropped to +2.5. To quickly project Butler, we can take the average of all the players in this sample at age 26: +4.2 per 100. Same answer! Plus 4.2 per 100 would drop him about 2 spots in BPM rankings if we just look at last year, from #17 to still-great #19.

So just by measuring his prior two seasons, we can see that historically, a player like Butler would not project to regress by a huge margin. However, a slight decline from last year’s peak is perhaps more likely than another big leap forward, and expecting such improvement and building it into predictions for the Bulls as a team is likely a recipe for disappointment.