NBA HD: Inching For A Rebound

In last week’s post, I looked at the relationship between team height and rebounding.  It’s a good jumping off point to investigate the value of height in today’s game.  Building from that, I’d like to tighten my focus and hone in on the play-by-play data.  Aaron Barzilai graciously publishes play-by-play lineup data on his website and I’ll be playing around in that sandbox today.

Looking at the lineups, how much did a height advantage affect rebounding?

This approach improves upon last week’s analysis in a couple ways.  To start, we’re looking at play-by-play lineup data as opposed to overall rebounding numbers on a season-level.  This allows us to look into detailed matchups and focus on units rather than full rosters.  Secondly, I’m solely looking at the 3, 4, and 5 positions to better reflect those who affect rebounding the most.  In last week’s study, a few people pointed out that Derek Fisher’s smallness skewed the Lakers height numbers even though he doesn’t really matter on the boards.  (Perhaps the best solution is to weight the effective height by position).

The way the data is presented in the basketballvalue format is as follows:

Which ten players were on the floor? How many possessions were they on the court for?  How many offensive and defensive rebounds did each unit have?

Before I dove headfirst, I made some qualifications.  The units would have to have at least 30 possessions on the floor together.  Thirty possessions isn’t a whole lot (a little more than a quarter’s worth of a basketball game) but with the players held constant, it seemed like a fair line in the sand.  This qualifier eliminates about 63,000 lineup units and leaves a remaining sample of 326.

From there, I calculated the average height of the 3,4, and 5 players on each team and compared them to their opponent.  The widest margin of average height between two lineups was 10 inches or 3.3 inches per player (Grizzlies vs. Rockets). We’ll take a closer look at that matchup later.

For each lineup, I gathered their offensive, defensive, and total rebounding percentages during that time period. So, for example, a dataset may read as follows:

Westbrook, Sefolosha, Durant, Green, Krstic
Frontcourt avg height (Durant, Green, Krstic): 82.0 inches
ORR,DRR,TRR: 30.4%, 87.5%, 53.8%
D.Williams, Miles, Matthews, Millsap, Boozer
Frontcourt avg height: 79.3 inches
Margin: 2.7 inches
Possessions: 48

So, here we see that this particular Thunder unit made the most of their height against this specific lineup of the Jazz, grabbing 53.8 percent of all rebounds and locking up the defensive boards in partifular (87.5 pct).    Boozer and Millsap are known as talented board cleaners but against the Thunder height,they couldn’t make up the difference.  But not all matchups work in the taller team’s favor.  Digest:

Conley, Mayo, Gay, Randolph, Thabeet
Frontcourt avg height (Gay, Randolph, Thabeet): 83.0 inches
ORR, DRR, TRR: 10.5%, 72.2%, 40.5%
Brooks, Martin, Ariza, Scola, Hayes
Frontcourt avg height: 79.7 inches
Margin: 3.3 inches
Possessions: 36

Here, we see that the far superior team (in terms of height) got worked on the boards by their smaller foes.  In this matchup, the Grizzlies missed 19 shots but only recovered 2 of those missed shots.  That’s quite an accomplishment for a team giving up 10 inches underneath.  Once again, we bow down to Chuck Hayes’ rebounding prowess.

But these are just two of the 326 matchup pairings that lasted 30 possessions.  What does it look like when we look at all observations in the sample?

Here, we have all 362 lineups and their total rebounding percentages.  As you can see by the positive trendline, the taller the frontcourt, the more rebounds collected (p<.0001).  Earth-shattering stff, I know.  But how much does an inch help? We can use that handy regression equation:

Total Rebounding Percentage = 0.0165*(Height Advantage) + 0.4983

So, for every inch gained in Height Advantage, meaning each frontcourt player has an inch on average on their opponent, we would predict the total rebounding percentage to increase by 1.65 percent.  What’s 1.65 percent? For reference, the Thunder are the sixth best rebounding team in the NBA according to TRR and they are 1.69 percent better than average.   All else equal, having an inch on your opponent matters, but it won’t guarantee a rebound.  In case you were wondering, the lone blue dot on the bottom right represents the Memphis Grizzlies lineup mentioned above.

How about strictly looking at offensive rebounding? Does height more critical on the offensive boards?

It doesn’t appear that height margin matters more on the offensive boards than overall, given that they have nearly identical coefficients (0.01645222 vs. 0.01645211 to be exact).  Like overall rebounding, an inch in average height advantage tends to lead to 1.65 percent more offensive boards.  Any interesting matchups? As you can see on the graph, some units failed to get a single offensive rebound (0.0% ORR).  Who were they? For fun, let’s take a gander:

Curry, Ellis, Maggette, Hunter, Tolliver (-1.7")
Nash, Richardson, Hill, Stoudemire, Lopez
11 rebounds
31 possessions
Rondo, Allen, Pierce, Garnett, Perkins (-1.3")
B.Davis, Butler, Thornton, Camby, Kaman
13 rebounds
35 possessions
Udrih, Greene, Casspi, Thompson, Hawes (+0.3")
Fisher, Bryant, Odom, Gasol, Bynum
12 rebounds
31 possessions
Fisher, Bryant, Artest, Gasol, Bynum (+1.0")
Foye, Miller, Butler, Jamison, Haywood
9 rebounds
32 possessions

You got the obvious Warriors Nellieball lineup but you also have the Lakers on both ends of the deal.   I’m not surprised that the Odom, Gasol, Bynum lineup grabbed all 12 available rebounds even with Donte Green at the 2.  That’s a ridiculously tall lineup.  However, I didn’t expect the Lakers to be on the losing end of the deal against the pre-trade Wizards.  Interesting stuff, I say.

On the offensive end, it still holds that the taller your frontcourt, the more offensive boards you will tend to collect.  Let’s finish up with the defensive side of the boards.

Again we see a positive relationship with height advantage and rebounding rates but the coefficient here is greater (0.0175).  This means that an inch advantage on the defensive end tends to increase defensive rebounding percentage by 1.75 percent.  This contradicts my finding in last week’s exercised that showed that team minutes-adjusted height had almost a completely random correlation with defensive rebounding rate.

In the end, conventional theory holds true that it helps to be taller in order to grab rebounds. However, it’s not as strong of a correlation as I expected.  Of course, height doesn’t explain all the variation in rebounding rates because there are other factors that contribute to rebounding: wingspan, vertical jump, horizontal jump, reaction time, positioning, etc.  I like that this study holds the lineup personnel constant but I would always like to get a larger sample size. But that has it’s drawbacks too.  When we increase the requirement threshold, we lose reliability.

How do we reconcile this study with last week’s that said height mattered more to offensive rebounding?  Last week’s looked at the forest rather than the trees.  I only had 30 teams in the sample size and the height effects could have been clouded in the aggregate numbers.  Additionally,  in this post, I tried to improve the validity of the measure by only looking at the frontcourt height rather than the whole five.  Perhaps a weighted height would be the best option, giving more weight to the bigger position and less weight to the point guard position.  For another time.

Again, have to thank Aaron for providing such a helpful resource.  Assist point to you, sir.

Seth Carstens