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Numberwang! Vote your rebounding stat conscience.

Kevin Love and Brook Lopez came into the NBA together in the 08-09 season, Love having been drafted 5th overall and Lopez 10th.

The two players were basically the same age. Lopez had prototypical size and decent athleticism (or "agility" if you prefer) for an NBA center; Love as a physical prospect was inferior to the bigger man. The two players worked out against each other prior to that draft, and both garnered basically favorable scouting reports about their rebounding. For example, Draftexpress said these things at the time:

"(Lopez) also has improved his rebounding this year, showing a good pursuit of the ball and a consistent tendency to box out his man strongly."

 

"(Love's) strength allows him to pull rebounds away from the opposition, and he does a great job sealing out his man."

 

We've seen two years of performance by both these players now. What's the most accurate (and complete) way to describe Kevin Love and Brook Lopez as rebounders? Let's decide what you believe, shall we?

Per Game

Love has averaged 9.9 rebounds per game so far over his two-year career. Lopez has averaged 8.4 boards. Those simple numbers provide us with a descriptive comparison:

 

Reb/G
Love 9.9
Lopez 8.4

(All the stats used here are derived directly or indirectly from basketball-reference.com.)

Both pretty good rebounders, right? In fact they've collected an almost identical total number of boards over two years:

Career rebounds: Love 1392, Lopez 1374. 

Based on those per-game stats and the total number, one would give Love a modest edge – a rebound-and-a-half more per night, which is pretty good. Nice to have an extra board and a half each time around. And then, of course, today's box scores, in an innovation, break out offensive vs. defensive rebounds too. Again, one can see Love with a an edge over Lopez across the categories:

 

Off Def Tot/G
Love 3.6 + 6.3 = 9.9
Lopez 3.0 + 5.4 = 8.4

 

But wait a second. About those career counts, which seem so nearly equal. They're rather deceptive. And how misleading you think they are comes down to whether you understand and accept so-called "advanced" rebounding stats.

Rate

Another extremely simple set of numbers – straight career counts:

Minutes Reb
Love 3762 1392
Lopez 5528 1374

 

That minutes column is significantly different, yes? Love has collected more overall rebounds while playing less than 70% as much as Brook Lopez. Figuring by the game, Brook has pulled down 85% (8.4/9.9=.848) as many rebounds as Love – but he's been out there for 7 more minutes a night.

If we're trying to describe these two players as rebounders – just describe them, specifically as rebounders – don't we need to take that into account? Wouldn't our description be badly inadequate, otherwise? Would you describe your car's mileage in terms of "gallons per commute"? Or might you, instead, be wiser to ask how many miles it gets per gallon? That's the sort of distinction we're talking about.

You're smart enough to see that figuring out the rate at which each of these two players gets rebounds, by time instead of varying "commutes" or "games," is another useful way to look at them. Surely you're patient enough to follow the quite simple math involved, anyway.

Reb Minutes Reb/Min
Love 1392 / 3762 = 0.37
Lopez 1374 / 5528 = 0.25

 

Oh my word, we've just performed straightforward division! Like when people divide miles driven by gallons consumed to arrive at an arcane and not directly observable new idea called "mileage"! Only with rebounds! That is just.... so.... WRONG. 

Hello, and welcome to Numberwang!

"Advanced statistics," unlike Mitchell and Webb's skit there, aren't arbitrary and silly. They're ways of asking questions about, and describing, what happens on the basketball court. The easy majority of the supposedly arcane stats certain people object to are, fundamentally, no more complicated than "basic" stats. Just like the offensive and defensive rebound categories that were introduced when data collection made them possible, "advanced" rebounding stats help to more fully describe what a player does on the court. No more. 

 

Per-Minute ---> Per-Whatever Rates

Those 0.37 and 0.25 rebounds/minute rates – which we got by dividing rebounds by time on the court above – don't fit our familiar per-game sense of how many rebounds is a decent number. The only reason anyone quotes a "per-36" or (occasionally) "per-48" number is to get the numbers into the ballpark we're used to seeing.

The idea is to ask the question:

"For every 'starter's game worth' this guy has played, how many rebounds did he pull down?"

(or with per-48 numbers, it's a bit more like "If we had people like this player filling every available minute of a given game, what kind of performance would we get?")

 

One could easily calculate per-(whatever period of time) rates directly from the original data. All you'd have to do is cut up the pool of minutes into blocks of 36 or whatever, and then do your division, same as before. The results, though, are the same when you multiply the per-minute rate by the unit you're using. (If you'd like to prove the essential properties of multiplication and division to yourself at this point, feel free to flash back to algebra class. I spent much of that class pining for a girl who happened to be in my little square of desks, so if I tried you'd mostly be reading about her winsome smile, braces or no.) Results:

Reb/Min *36 *48 *500
Love 0.37 13.3 17.8 185
Lopez 0.25 9 12 125

 

It's worth emphasizing, here, that each of these numbers is literally true. For every 36 minutes Kevin Love has spent on an NBA court, he has on average recorded 13.3 rebounds. That's not a "made up" number, it's not hypothetical. For every 500 minutes he's played, he's gotten those 185 boards, on average. We don't choose to use a per-500 number because we're not used to looking at players that way, but it's every bit as true. It's as true as the per-gallon mileage rate of a car driving around; the fact that we usually don't take trips that use one exact gallon of fuel doesn't somehow invalidate the usefulness of that figure.

But what about muddles to do with team context??

But, but, but players' stats are embedded in their complicated teams, you say. The world is horribly complex! (I drive in the city and on the highway!) The Timberwolves are justly famed for their "United We Run" slogan and purported Showtime ways. They've also boasted a passel of fairly awful shooters during Love's tenure. Maybe Love gets rebounds because Corey Brewer is jacking up off-balance threes over his shoulder early in the clock. Maybe he gets less when Jonny Flynn is pounding the ball. If we describe rebounding adjusted only for time, we aren't saying anything about that stuff! (So go the sincere objections of people who, mysteriously, are perfectly willing to accept "rebounds per game" despite its vulnerability to things like games-where-you-played-only-four-minutes-due-to-a-first-quarter-hangnail.)

The most obvious and accessible board stat that addresses those problems is "rebounding percentage." Remember shooting percentage? "Shots Made / Shots Taken = Shooting %"? Rebounding percentages are the same thing. The calculation is, in its essence:

Rebpercentage_medium

That "rebounds (of this type) he could have gotten" category isn't too hard to figure out. For long-past seasons back to 1971, one can do an easy estimate with old data. Now things like how many rebounds each team got while a player was on the court are available, too. Want to see how many Offensive Boards were possible for Love out there? "The Wolves' offensive rebounds + the other team's defensive rebounds" gets you that number for his playing stints. No mystery. 

Across the three basic rebounding categories, Love and Lopez compare this way:

ORB% DRB% TRB%
Love 14.8% 27.9% 21.2%
Lopez 10.2% 19.2% 14.6%

 

And no, nobody says these percentages somehow perfectly describe a player's rebounding – not any more than they would say "shooting percentage" was a complete and perfect description of Ray Allen as a scorer. What they show, though, is that Kevin Love actually grabbed a significantly higher percentage of available rebounds than Brook Lopez, when either of them was on the floor. They let us compare players in a way that no scouting report can, too.


To most of you, this entire post seems ridiculously basic, I am pretty sure. None of these numbers is in any way the product of the secret cabal of Numberwang experts who developed that terrifying robot, which subsequently attempted to take over the world. We're talking about math like straightforward division, basically, and about collecting better data for things like what happened when a player was on the court. We're talking about asking questions and looking for their answers.

What percentages and other "advanced" stats do is let us get a handle on a whole bunch of potential confounding factors, seeing players in different ways, so that we can get closer to our (poll) question from just before the break up there:

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