RealGM

As the title suggests, I'm curious about the application of rate of change (differential calculus) to basketball stats. In particular, in tracing the career arc of individual players. Has anyone ever mapped out season-by season data on, say PER, and looked at the fastest-improving players and the fastest-declining players and so on? I suppose you could break it down even further, to 40-game, or 20-game, or 10-game increments, etc. see which players had the most sudden and dramatic increases in production.

Where I'm especially interested in this is in its application to college/high school hoops. From Rob Hennigan's draft picks with the Thunder, along with his most recent two (Andrew Nicholson & Kyle O'Quinn), and comments he made in the introductory press conference of the latter, it seems he values late-bloomers -- and consequently, sudden-bloomers. Russell Westbrook came off the bench for his HS team until his junior year, and James Harden was also a late bloomer in HS. Nicholson and O'Quinn both only started playing basketball as juniors in HS. To quote (1:41): "We feel he's [Nicholson's] unique in that he has a legitimate skill component to his game, but at the same time, has sort of an intriguing development curve and capacity for improvement..."

I'd be curious to see how effective a scouting tool something like this would be.

I'd be interested to see what studies exist on this as well.

The thing that makes it so tricky is that so much of your contribution in basketball has to do with the role assigned to you by your coach. While it's true that some of that factor can be normalized for by using per possession stats, if a player's improvement changes the role that player should be playing while he's on the court, and a coach fails to make such changes, there really isn't going to be any statistical way to tell exactly how much that player has improved.

I will say every year I like to look at guys who've had huge per possession (or minute) improvements. Last year, Pekovic had a jaw dropping 10 point PER improvement which to me both indicated that he had gone through a massive improvement but that also he was able to improve so much because he had some major issues to really address that were getting in his way (look at his foul/min rate). It actually might be more impressive to look at improvements of players that were already quite solid and took that next step (ex: Durant in his breakthrough year).

I'm share interest in the application of rate of change (differential calculus) to basketball stats. I hadn't focus on high school / college development though.