Measuring defensive efficiency, or defensive points per possession, using the standard deviations of various defensive statistics provided rather simple results. Lineup data was used and standard deviation variables were created for personal fouls, steals, blocks, and defensive rebounds based on the percentage in each category that each of the five players in a lineup accounted for.
Defensive efficiency was predicted using lineup per possession statistics in personal fouls, steals, and blocks as well as defensive rebounding %. Each of these categories increased with a more even distribution or lower standard deviation. As a result, for the positive statistics of rebounding percentage, steals and blocks, as the standard deviation decreased giving us a more even distribution, defensive points per possession also decreased, as much as 4, 9 and 1 point(s) per 100 possessions, respectively. In the case of personal fouls, a negative statistic, the reverse was true; as the standard deviation of personal fouls increases, personal fouls per possession and defensive points per possession decrease.
So what do these results mean and why do I refer to these results as simple? They are simple because they essentially mean that we want everyone in a lineup playing defense. We want everyone rebounding, everyone playing strong defense on the ball and getting steals, and everyone contesting shots and getting blocks.
Obviously when players are getting steals and blocks successfully, they aren't fouling, and ideally, players are getting those steals and blocks efficiently without fouling, so why is a wider distribution of personal fouls beneficial for a defense? Perhaps this means we want a player or two in a lineup getting fouls when a steal or a block isn't a realistic possibility. These fouls are likely skewed towards players in the paint, lending itself to a higher standard deviation, where fouling is preferred to allowing easy buckets on dunks and layups.
