The Value of Rebounding

ESPN will release this week a proposal for a new passer rating, called the Total QBR, or Total Quarterback Rating. It has been developed by several quarterbackmeisters at the network — most notably Trent Dilfer — and by some stat heads in the network’s production analytics department. The point: Passer rating, developed in 1973 to measure a passer’s efficiency, does that, but it doesn’t necessarily measure what makes a quarterback great.

So the analysts at ESPN have taken every game played in the NFL since 2008 and measured the quarterback’s contribution to the result on every play except handoffs. They say they’ve divined a system to rate quarterback performance in every game, and for full seasons, on a scale of 1 to 100 (no more 158.3 rating).

via Nnamdi Asomugha, Johnathan Joseph among cornerbacks making out well in free agency – Peter King –

Let the games begin – the “play around with numbers and see if anything meaningful happens” game, that is.

I’m a self-professed stat/basketball hybrid-nerd. Part of that indentity is looking at data like it’s a video game, manipulating different variables like they’re the moving pieces in a Legend of Zelda dungeon puzzle. My computer is full of spreadsheets and text documents spelling out random ideas and convoluted equations. It’s just the way that my mind works, for better or for worse. And when I see a comment like this one, it causes my brain to spin into motion:

Harsh words about Brook Lopez’s ability to rebound the basketball. As the conversation continued on twitter, one clear line of thinking developed among several people – Marcin Gortat’s rebounding prowess makes him a better overall player than Lopez. It’s an interesting argument, indicative of what I see as a larger problem.

On some level, we have data to compare the two. There are offensive numbers and rebound rates, defensive ratings and PERs. The intrinsic difficulty in comparing contemporary players, even at the same position, is in weighing their different strengths and weaknesses appropriately. In this discussion, the issue becomes determining how important rebounding is to the success of a team. As King points out several paragraphs later in his article, many of these statistical measures across various sports do not accurately reflect what creates wins (though I take issue with his phrasing of “what makes a [player] great”). That’s what we’re looking for, after all – the value of players’ actions on the court and the way in which they impact the scoreboard. Our best measure of the that impact is points per possession and, with a little finagling, we can convert a player’s rebounding rate into the number of points per possession those rebounds either create or deny.

…wait, what?

Well, when a player corrals a rebound, one of two things is happening:

1.) On offense, he’s affording his team a continued opportunity to score. Given that we don’t have access to the Offensive Efficiency ratings of teams after offensive rebounds, we’ll make the (admittedly incorrect) assumption that they score at their average efficiency after such a rebound. By grabbing offensive rebounds, then, a player is creating points equal to the rate at which he grabs said rebounds times the number of rebounding opportunities, times the points per possession his team scores.

.5 x [Offensive Rebound Rate x (ORebound Opportunities*/100 Possessions) x Off Points Per Possession]

2.) Defensive rebounds, on the other hand, are an extension of the defensive possession; securing a defensive rebound is analogous to forcing a turnover, ending the opponent’s chance to score. Therefore, these rebounds have value insomuch as a point denied is just as good as a point scored. The points “created” by defensive rebounds, then, is:

.5 x [DRR x (DReb Opp/100) x D PPP]

*Rebounding opportunities have to encompass both missed field goal and those free throws which end with a mass of bodies in the lane like it’s Black Friday at the one Target in a town of 10,000. It’s standard practice to multiply free throw attempts by .44 to determine the number of possessions (and therefore potential rebounds) taken up by trips to the line:

Reb Opp/100 = (Missed FG% x FGA/100) + .44(Missed FT% x FTA/100)

With these basic equations, we can determine a very rough, very inaccurate picture of the difference in value between the rebounding rates of the two players.

Gortat’s DRB% with Phoenix was 28.5%, and he averaged 49.52 rebounding opportunities/100 possessions for a team that allowed 1.104 points per possession. In essence, he ended 14.11% of opponents’ possessions – with a little help from bad or unlucky shooting, of course. By grabbing those rebounds and preventing the Suns from allowing any more points on each possession at their usual rate, Gortat arguably took 7.79 points/100 possessions off the board. On offense, he added 2.07 points/100 with his rebounding.

Lopez? He only erased 3.36 points/100 on the defensive glass and contributed 2.25 points/100 on offense.

The glaring difference, obviously, is on the defensive end. Both players posted 7.8% ORB%, but New Jersey’s higher rate of rebound opportunities, owing to their worse field goal percentage, afforded Lopez a slight advantage in points generated from rebounding on that end. Because the Suns’ defensive rating is actually worse than the Nets’, Gortat’s outstanding rebounding on defense is even more important than Lopez’s would be in New Jersey. That fine line, related to team performance, is something that comes into focus when viewing rebounding (and other aspects of the game) through the prism of points per possession.

There are many flaws with my numbers. Some of the assumptions are faulty or not completely thought out. Much of the data is either incorrect or incomplete. Beyond that, this is merely one aspect of the games of two of the league’s best centers – and likely a minute one at that. It may say little about the difference between the two. It may say nothing at all.

The key, however, is the line of thinking. I’m usually against comparing players for the sake of argument, but in this case, I appreciate the spark it provided. The more we think outside of the box, the closer we’ll come to precisely measuring the value of on-court decisions. This is just the first step. With the advent of motion capture technology in arenas and more and more precise statistical evaluation, I envision a future where we can pinpoint the value of, well, everything. Tony Allen moves two feet laterally in .4 seconds less than Shawn Marion? Figure out how many points per possession that’s worth on defense. Compare it to the differences in their rebounding rates, assist rates, turnover rates – the sum of the parts, ultimately.

Until then, I have some numbers to tackle that are starting to look an awful lot like the Water Temple.

Andrew Lynch

When God Shammgod created the basketball universe, Andrew Lynch was there. His belief in the superiority of advanced statistics and the eventual triumph of expected value-based analytics stems from the fact that he’s roughly as old as the concept of counting. With that said, he still loves the beauty of basketball played at the highest level — it reminds him of the splendor of the first Olympics — and the stories that spring forth from the games, since he once beat Homer in a game of rock-paper-scissors over a cup of hemlock. Dude’s old.