Perhaps not in a metaphysical sense. But in basketball the informational value of 'minutes played' seems to be best described by a logarithmic curve.
As part of my NBA draft model project I had to look at the relationship between minutes played and efficiency as measured by my box score metric Alternative Win Score (AWS) in order to pick an independent variable.
One of the simplest ways to explore that relationship is a nice scatter plot graph, and almost inevitably a fit line or two to help explore the relationship. Below is that scatter plot using every NBA player in my training data set drafted from 2002 on, with each individual season for that player treated as a case.
The two interesting things we see here is both how noisy the metric is with only a few minutes indicated by the large spread of scores on the left side of the chart and how relatively quickly the measure begins to tighten up. Second is that there is a definite upward drift in efficiency as measured by AWS, but one that becomes very gradual after the first 200 or so minutes a player is allowed on the court.
By the way, this is very much what the shooting charts by shot zones looked like when I charted them, very noisy at first though with a definite upward drift in efficiency that was best fit be a logarithmic curve.
In any case this is why I have opted for using a statistical prior in of a replacement level player in forming my independent variable for the Draft model.
It also avoids the Sebastain Telfair Fallacy: In his fourth year in the league Telfair played 1,932 minutes on the court and produced at a very sub-par 2.92 AWS (league median is generally around 4.5). Meanwhile, the player picked after him, future reality TV star and Boston Celtic, Kris Humphries played on 924 minutes in his fourth year, but produced an 5.5 above average AWS.
Time on the court matters, a player can't produce if they don't play. Other studies have shown an independent value captured in RAPM scores to being on the court. No matter how many minutes you put Telfair on the floor you couldn't make him an NBA level player.
Also, if you look at the dot highlighted on the lower right, that's poor Adam Morrison playing 2,300 minutes and producing only a 1.04 AWS in his rookie year.
Comments