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Droppin' grilled cheese science: rebounds

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I've said it before.  Odds favor me saying it again:  It's rare for players to see substantial improvement in his rebounding over the course of his career.  Here's a preliminary look showing exactly that.

So here's a series of box plots.  They aren't very pretty unless you're a stats-fiend like myself.  But what they lack in aesthetic beauty they make up for in information.



These plots are a product of a dataset including every player who began his career after 1981 until the present.  To generate these plots I took every player's per-minute rebounding stats. Since we're interested in how a player improves or declines over time, the figures are based on each player's yearly fraction vs. their best season.  For example, if a player had his best season in year 4 of his career, getting a rebound every 3.6 minutes (10 per 36, roughly the average for an NBA center), year 4 would receive a value of 1 and all other years would be expressed as their fraction of his year 4 rebound rate.  This provides a way of comparing players of differing initial abilities across time and across positions.  The closer to 1 any other year is, the less change there's been in the player's rebounding rate. 

Follow?  Maybe?  (Maybe not?) 

I looked at three groups: all players, players who started their NBA careers after turning 22 and players who entered the league prior to their 22nd birthday.  For each group, I looked at the average and spread of the Max_rate fraction for every season of the player's career. Only the first 10 seasons are charted as ridiculously few players play that long.

In all three cases, what you should see is that the average fraction (marked by the thickest black line in the middle of each box) in year 1 is the highest.  This is in very large part a product of players who only play one season, including the 10 day call-ups you'll never hear from again.  Similarly, players who only play 2 years must have their highest rate (the "1" fraction) in either year one or year two.  But as time goes on, the average levels off and stabilizes. This suggests that even among those players who play 3, 4, 5, 6 or more seasons, there's not much change, and, as a group, not a noticeable improvement in rebounding over time.  Were more players improving, more would find their "1" fraction later in their careers.  And while this happens (the stats savvy out there should note the standard error does reach the maximum value across the board, the lack of an upward trend in the average after the initial 'short career' bias suggests that it isn't long into a player's career that what you see is what you get.

Of course there's a degree of variation and the particular cases don't have to follow the general rule.  But overall, the trend suggests that rebounding isn't something that you can expect to change much for a player over the course of his career.  And it doesn't seem to matter much if you came into the league early or played 4 years of college ball. If you can board, you do.  If you can't, you don't and you won't.

This is still preliminary data.  I churned it out while watching a baseball game and burning a couple of grilled cheese sandwiches. I repeat: this is preliminary data, and anyone with some advanced statistical training should see that this "study" is woefully incomplete in the way it deals with small sample sizes in particular year and short careers among other things. (It very likely ignores the rising cost of gasoline for the summer driving season.)   But it's certainly something to think about. 


More to come...