[Analysis] There is a 0.000003% chance that the discrepancy between Jaren Jackson Jr.'s Blocks/Steals is solely due to random distribution

There is much debate right now about JJJ and the Memphis Grizzlies' scorekeeper boosting his stats. I am not skilled enough in the rulebook to analyze each play individually, but I can look at the numbers to see what the likelihood would be.

Fortunately, we can use a Normal Distribution (or Gaussian Distribution) to do this analysis. Here is a study showing Normal Distribution in NBA games..

A normal distribution lets us analyze the "bell curve" of a statistic. Once we know the mean (average) and standard deviation (how spread out it is), we can determine the probability falling in a certain range. As a rule of thumb, 68% of values will fall within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations. Here is a link with more reading if anyone is curious.

So now onto the analysis. I downloaded the game logs from Basketball Reference, and split them up into home and away. I calculated the Mean and Standard Deviation for his home and road games, and used a Z-Test to compare the two. A Z-Test tells you the probability that a randomly generated sample (of the same size as the data) has a mean value greater than a specified number based on the original data set. Since the number of home and away games is essentially identical, this works out.

The results of the Z-Test show that there is only a 0.000003% chance that the difference between his road and home splits is due to random chance. This is 1 in 3 million chance. I am more likely to get struck by lightning than JJJ to have gotten these stats due to random chance.

Important:

It’s important to note that statistically significant doesn’t describe the cause behind it. It could be he’s playing much better at home, or he’s getting better scorekeeping. All it says is that “something is different here”

Edit: for those saying that you can’t do this analysis because home and road splits are different- see this comment from u/Fofodrip . The difference is 4.8 vs 4.7 blocks per game. It’s totally possible JJJ just plays better at home but thats not really the norm.

Link to my spreadsheet with analysis here: https://docs.google.com/spreadsheets/d/1Q8mgET8hyUOtn8XSchWZL-Jip9kPrwoF8eWS_7KOwwI/edit?usp=sharing