## Tuesday, March 05, 2013

Your NBA teammate is taking a jump shot.  Should you crash the basket, or should you retreat back on defense?  If you crash, you gain a better chance at grabbing the rebound if the shot misses.  If you drop back, you can play better defense on the transition, since you're not trapped behind the play.

One of the research papers presented at the 2013 Sloan Conference (.pdf) talks about this trade-off.  I'm not sure I agree with its conclusions, but I was struck by one of the findings that came out of the data.

It turns out that some teams crash the basket more than others.  That's probably not a surprise ... it's part of a team's particular strategy.  Some coaches like to crash more, and some like to crash less.

Eyeballing figure 4 of the paper, it looks like the Houston Rockets crashed (meaning, in this context, that video replays showed more players moved towards the basket than away from it) on more than 40 percent of missed jump shots (taken minimum 15 feet from the basket).  The Golden State Warriors, on the other hand, crashed only 26 percent of the time.

Could the difference be random?  I don't think so.  It looks like there are around 500 missed shots in the database for each team.  Coincidentally, that gives us a perfect baseball analogy: the Warriors hit .260 in 500 AB, while the Rockets hit .400.  Intuitively, we know that's a non-random difference.

Doing the calculations ... the difference is around 4.8 SD.  Even after adjusting for selective sampling -- I chose the highest and lowest of the 12 teams that had enough data to be included in the paper -- it seems like the authors are measuring something real.

This has obvious implications for the rebounding debate.

We now know that some teams get more rebounding opportunities than others, by choice.  Which means some *players* get more rebounding opportunities than others, by choice -- by the role the coach and system are asking them to play.

And that means that you can't necessarily judge a player's rebounding on the basis of his stats alone.  We've talked about that before, in terms of "diminishing returns", players taking rebounds from their teammates.  This is a bit different -- the *coach* taking rebounds from his players, by his decision to have the team challenge for offensive boards less often.

Now, you might argue that the difference is minimal.  Offensive rebounds are, what, 30 percent of the total?  And we see the most extreme difference between teams is 14 percent of that 30 percent.  And there are five players on the court, so, on average, a player's stats will fall by 20 percent of 14 percent, of 30 percent ... which is less than one percent of the opponent's missed shots.

But ... even that small effect could be significant when ranking players.  And, it could be one particular player taking most of the brunt, if it's always the same guy that the Warriors send back.  And, each offensive rebound not snagged means one more defensive rebound for the other team -- which, again, could be some players more than others.

In any case, in the past, we've had circumstantial evidence about whether rebounding numbers are affected by style of play ... but now, I think, we have evidence that's much more direct.

What I find even more interesting is that now we have evidence that rebounding numbers aren't even accurate for TEAMS.  The Warriors totals are low by design -- the team is trading rebounds for defense.  Which means, you can't just look at team offensive numbers in isolation.  Offense and defense really are intertwined.  We knew that already, in theory, but ... well, for me, personally, I often just pay it lip service, and forget about it.  But, now, this kinds of throws it in my face.  It's the first time I've seen this well-defined a statistical footprint of the tradeoff between O and D.

I won't be looking at NBA team stats quite the same way again.  From now on, any time I see a team with poor offense, I'll be thinking, well, how much of that is because they decided to sell some of it off in exchange for defense?

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