# The Rebound, The Intersection Of Self-Containing Half Spaces

Mar 9, 2014
Originally published on March 9, 2014 12:00 pm
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RACHEL MARTIN, HOST:

Did you forget again? You did, didn't you? You tried your best, but you missed The 2014 MIT Sloan Sports Analytics Conference. I can barely say it. It happened last weekend.

Good news, though. Mike Pesca of Slate.com has combed through all the results and is ready to talk about a whole new level of understanding when it comes to basketball and rebounds.

Right? Right? That's what you want to do.

MIKE PESCA, BYLINE: Yeah. Yeah. And if you me and what I look like, combing through results is what I comb through most often.

(LAUGHTER)

PESCA: Yeah.

MARTIN: ...from a new study on the mathematics of rebounds.

PESCA: Right.

MARTIN: So here I go. This is the definition of a Voronoi cell. Here it is: For any point, it is the intersection of the self-containing half-spaces defined by hyper-planes equidistant from that point to all other points.

PESCA: Yeah.

MARTIN: What does that mean?

PESCA: Now you know how to get a rebound, Rachel?

MARTIN: Yeah. Totally.

PESCA: Voronoi tessellations. Well, there's something about the language that I love. I mean Harold Ramis died just recently and I was thinking of "Ghostbusters" when the key master came in one of the pre-chosen forms and during the last of the McKetrick supplicants. I'm like voranoid tessellations. That sounds like that. But what it really is, is a mapping technique that kind of shows how close you are to something. And I was thinking about this the other day. I'm not like where have I heard that phrase? Recently, I was with my kids in the Museum of Math in New York City, and they have these magnets like that, are shaped like squiggly little monkeys or rabbits and you try to put the magnets on a board and you kind of understand positioning. I think it's really cool that kids' magnets and NBA players are somewhat similar. The idea - the big, bold, let's back up a step back idea - behind this study is kind of to ask what is rebounding? Because when we think about sports statistics, it usually answers a question. Bill James, the noted baseball guru says that there's a question. Like should we bunt more than we not bunt? Should we walk a batter or pitch to him? But with this, it's more like the question is what is a rebound? They're really asking what is a rebound? And it seems simple, right, it's like...

MARTIN: It's where the guy gets a ball and - yeah.

PESCA: That's right. It's where one player misses a shot. But they're breaking it down. They're saying actually, a rebound isn't just a guy grabbing a ball. That's the stat we had up to this point. But now that we have cameras and now that we have intricate ways of looking at it, a rebound is some component parts. So, think about it. Part one: positioning - and this is where the voranoid tessellations come in. Before the ball's even up, where does this player go? Where does his teammate go to try to get the rebound? Then there's crashing. You know, how much do you go for, how much do you run towards the basket or maybe away from the basket when the ball's in the air? And then there's hustle. So, when you talk about the component parts, you begin to understand what really makes up a rebound.

MARTIN: How does this change how we understand basketball?

PESCA: This is one of those preliminary studies where right now there's a couple of things - certain players that maybe we didn't know were great - Lance Stephenson of Pacers, he turns out to be a much better rebound. But they're laying the groundwork. And the authors of the study say the second or third iteration of this will be able to do something like saying, you know, positioning has been so far underrated before. Like, maybe they'll be able to say 80 percent of your job before the shot's even up. Or maybe they'll be able to say actually it's where you go when the shot's in the air and there are spots on the court that we haven't even considered. So, we don't exactly know. But just to think about this very basic action a little differently, it's one of the interesting things about sports statistics.

MARTIN: Oh, I'm thinking, I'm thinking about it. OK. Curveball.

PESCA: Uh-huh. Yeah. So, talk about interesting. NBA players are sometimes wearing short-sleeve shirts instead of the tank tops, basically so Adidas can sell some extra jerseys. Well, LeBron James went 6-18 in a game on Thursday wearing the short sleeves. And he said something like I'm not making excuses but - and in the history of that sentence you know an excuse is coming. He had shot extremely poorly with the short-sleeve jersey. Others have complained mightily about it. They probably will eliminate the short sleeves, although statistically in the league, shooting is up with short sleeves.

MARTIN: All right. Good to know. Mike Pesca. He appears on Slate's sports podcast, Hang Up and Listen. Thanks, Mike.

PESCA: You're welcome. Transcript provided by NPR, Copyright NPR.