The Most Unlikely Performances of the Year by Daily RAPM Estimate

Almost nightly, basketball fans can run through the evening’s box scores and single out one player who seems to have just then played the game of his life. Likewise, fans are also quick to notice when a player plays much more poorly than expected. Naturally, I was curious which box score line was in fact the most out-of-character performance of the year. To do this, I turned to our one game metric, Daily RAPM Estimate (or if you have forgotten about it during the offseason, DRE.)

I went ahead and found the averages and standard deviations for each player’s DRE scores[1. The Daily DRE, if you will.], and then calculated the corresponding z-score for every game in order to look for the most unlikely performances of the year given a player’s usual performance and consistency. [1. Assuming normal distribution of single game scores, which based on my tests proved accurate.] For the sake of sample size, I decided to limit this exercise to players who appeared is 58 or more games [2. The cutoff to be eligible for a scoring title] so that I felt confident that the year’s sample captured a good idea of each player’s general range of single-game DRE.

The idea is that the higher the absolute value of the z-score, the more unlikely of an event occurred. For example, Russell Westbrook has games with a DRE of 22.1 (2/6 vs New Orleans) and of -17.3 (1/7 vs Sacramento); however, his scores were so wildly variable throughout the year  (i.e. had a high standard deviation) that his z-score for those games aren’t in the overall  top or bottom 5 for the season. Generally, high usage players are more prone to a wide range of performances, so the unlikely performances should belong to role players who took took on a rare high usage game rather than the usual stat-stuffing suspects.

Without further adieu, the most unlikely performances of the year:

The Good Unlikely:

Trevor Booker– 4/11/15 Jazz @ Portland – DRE: 19, Z-score: 4.64 (box)

Jared Dudley – 12/26/14 Milwaukee @ Atlanta – DRE: 18.9, Z-score: 4.20 (box)

Ersan Ilyasova – 3/26/15 Milwaukee vs Indiana – DRE: 20, Z-score: 4.19 (box)

Cody Zeller – 1/31/15 Charlotte @ Denver – DRE: 15.4, Z-score: 4.13 (box)

Robert Sacre – 11/23/14  LA Lakers vs Denver – DRE: 9.8, Z-score: 4.07 (box)

The Bad Unlikely:

Robert Sacre – 12/5/14 LA Lakers @ Boston – DRE:-10.3 ,Z-score: -3.56 (box)

Amar’e Stoudemire – 11/26/14 New York @ Dallas – DRE: -10.5, Z-score: -3.34 (box)

Carlos Boozer – 10/29/14 LA Lakers @ Phoenix – DRE: -12.7, Z-score: -3.27 (box)

Hollis Thompson – 2/9/15 Philadelphia vs Golden State – DRE: -15.3, Z-score: -3.27 (box)

Michael Carter-Williams – 12/27/14 Philadelphia @ Utah – DRE: -21, Z-score: -3.18 (box)

Some thoughts:

• It’s impressive that Sacre made both lists. This indicates how incredibly consistent his performances were outside of these two games. In fact, here is a graph of his games by DRE.

• As expected, the good outliers are mostly role players throwing up high usage games with incredible and unsustainable efficiency.
• Turnovers are bad, while steals are in fact good. The top 5 performances had 1 turnover total between them, while the bottom 5 netted only one steal.
• Ooph, MCW’s game was awful

Again, these results are not meant to be the best or worst game of the seasons but rather the most unlikely given the player’s overall season. So if you want to argue Trevor Booker played the game of his life at the Moda Center in early April 2015, you might not be far off.