Before we get started in our Statistical Analysis for Sports class, Prof. Jim Lackritz (who you met in our previous post) always asks us to provide some statistical gems from the world of sports that occurred since we last met.
On Monday, Dr. Lackritz shared some quick stats he ran on the improbability that New Mexico guard Kendall Williams would torch Colorado State for a whopping 46 points on Saturday.
Williams entered the game averaging 13.1 points per game, with scoring outputs ranging from 2-24 points in New Mexico’s first 25 games before hitting 12-of-16 shots, including 10-of-13 from three.
Those numbers resulted in a standard deviation of 5.67, which means that Williams’ 46-point outburst is about 5.75 standard deviations above his scoring average. This is a mind-blowing stat because there is a 1 in 224 million chance that an outcome would fall that many standard deviations away from the mean.
Furthermore, this came against a Colorado State defense that now yields 94.0 points per 100 possessions, 6.3 points per 100 better than the D-I average.
What’s even crazier is that Williams had averaged just 1.28 three-point makes a game with a range of 0-4 and a standard deviation of 1.02. In 60 percent of his games, Williams canned either zero or one from distance.
That means his 10 three-point hits were over 8.5 standard deviations above the mean, an occurrence so rare it possesses a probability beyond several hundred billion to one. In other words, perhaps anybody who does not believe in the hot hand theory should pop in the tape of Williams. The one mitigating factor is the fact that Williams took so many 3-pointers, so the odds of him nailing 10 when taking 13 threes are significantly better but still pretty long.
As fate would have it, Williams’ next game comes tonight against this program’s very own San Diego State Aztecs, who boast the 19th-best defense in all of D-I by yielding 88.6 points per 100.
I wouldn’t exactly bet my tuition check on Williams coming close to matching his career game this time around.
UPDATE: Williams regresses to the mean vs. SDSU
A game after knocking down 10-of-13 treys, Williams regressed to the mean by missing all four of his long balls … and scoring a mere eight points on 1-for-6 shooting Wednesday against the Aztecs.
This should come as no surprise as such an outcome is well within the usual output the Lobos get out of Williams, and it provides further evidence that Saturday’s outburst was quite the statistical anomaly.