Wingspan in the Gameplan: A Brief Study With Way Too Many Numbers

Daniel Arellano

Staff Writer

The NBA draft has always been a nebulous matter at best, with scouting rumors flying around haphazardly as teams frantically try to avoid making a decision that will be mocked for years to come (shoutout to Joe Dumars). Teams must examine everything about a prospect, from their mental strength, shooting stroke, and of course, the body that they bring to the league. Around that time of year, one of the most prominent buzzwords that gets tossed around by pundits is the highly valued wingspan. 

As with everything basketball related, offense has already been covered to death. And as prized as those lanky arms may be, outside of the paint, it appears to be a detriment towards a player’s shooting ability. Thanks to redditor /u/mowshowitz, we can see that players with particularly long arms actually appear to be hindered, once they leave the restricted area. Just watch Deandre Jordan for a game and you'll quickly see that he is very effective within his range, which just happens to be the length of his arm.

Defense, however, is a completely different story. Take a look around the league and you’ll find that the top tier defenders almost always have those annoyingly long arms that seem to completely envelop their man. There are few sights as entertaining as Kawhi Leonard flying around the court with his crazy octopus arms, disrupting passing lanes and making his mark appear to effectively disappear. Turn your sights to the shortest rim protector in the game, Draymond Green. After coming into the league as a tweener, Green has overcome his “short” stature thanks to his uncannily long wingspan (85.25 inches). Although he defies all prior thoughts about centers in the NBA, the reasoning seems to be pretty intuitive: a player with longer arms is more easily able to disrupt a shot attempt. Poor Dwight Howard, a victim of no-neck syndrome, knows this better than most. Although he seems to be closer to 6’9” than 6’11”, his standing reach rings in at a towering 9’3.5’’. 

We have to have some measurable way to test this. As revered as the eye test may be, it can favor the players with positive reputations that have taken a step back (think Jimmy Butler) or perhaps never really had it all (think Russell Westbrook). One of the most practical (if crude) ways we can do this is with a simple corollary test. 

At any given time there are around 390 (30 teams with 13 roster spots) players in the NBA. In the interest of time, I eventually settled on the sample size of 60 as it was nearly 15% of this population. To ensure that we weeded out all of the scrubs that never got any burn in the league, I limited the available pool of players to those that had played in 60% of all games in the last three years with at least 15 minutes per game. In a perfect world, this will prevent any statistical outliers, á la 2016 Nikola Jokic. (Side note, Jokic has undoubtedly earned his chance to get big time minutes, and is poised for a year that has real significance outside of a stat geek’s wet dream.)

The NBA has always been a league of tall and lanky guys, but we need some kind of equalizer to compare the defense of Giannis to the defense of JJ Redick. (Los Angeles’ favorite sharpshooter is one of only a few players in the league to have a wingspan shorter than his height.) Creating a simple ratio of wingspan: height should do the trick here nicely. 

Out of curiosity I found that the average American male has a wingspan:height ratio of 1.024, compared to the sampled NBA player mean of 1.059. Although the difference appears small on first glance, it must be remembered that this is the exact purpose of the number: to equalize the ratio between people of different sizes. The distribution of the sample appears fairly normal according to the histogram. If the average American male (yeah, you) was included in the data, he would find himself in the third column.

The measure that I chose to use to represent defensive effectiveness is Opponent Field Goal Percentage Difference. This statistic represents the difference in shooting percentage when a particular player is defending the shooter; a negative value indicates that a player is effective on defense and a positive value indicates the opposite. Just like any other statistic in the sport, it is useless on the small scale when used without any context. For our purposes, it will do the job nicely.

WARNING: MATH

I hate to break out mathematics as much as anyone, but in order to make sure that the results mean something, I will have to conduct a hypothesis test. The best test in this case would not be the traditional one sample z-test but instead is the Pearson Correlation Coefficient.


Stick with me for a second, and it’ll pay off, I swear.


Essentially, this test will find the r value, which will lie between -1 and 1, depending on the strength of the relationship. A value close to 1 indicates a positive relationship, while a value close to -1 indicates a negative relationship. An r value near 0 indicates that there is little to no relationship between the two variables. (If we wind up with that, then I just wasted a whole lot of time on SportVU.) A good indication of the results of the test can be seen by simply plotting the data.

So far, so good. The scatter plot suggests that there is at least a moderate negative correlation as indicated by the inverse relationship between WS:H and OFG%. Whether this is accurate will be reflected in the actual testing. At the very least, we got a nice chart to point to when this whole thing wraps up.

Before beginning a hypothesis test, it is necessary to check that all required conditions have been met. In order to find a Pearson Correlation Coefficient the data must be “either an interval or ratio scale” This is satisfied, as both variables are in the form of a ratio (percentage is simply another form of a ratio x:100). Also, the data must be appear to be linear in its relation. Taking a quick look at the chart above, and there doesn’t seem to be any weird bends or dips. Fortunately, statistics allows for a bit of liberalness when dealing with this sort of thing.

With the necessary assumptions confirmed, the data can actual be tested. For the purposes of this test the null hypothesis (H0) will be that there is no relationship between wingspan and OFG%. (Hint: We really don’t want to accept that) The alternate hypothesis ( H1) will be that there is evidence to reject the null hypothesis and state that there is at least some sort of relationship between having long arms and being a plus defender.

We’re almost done with the math, I promise. It will get worse before it gets better, though.

The formula for conducting the Pearson Correlation is:

I’ll spare you the details but this is what the final function will look like:

Yada, yada, just plugging in some number while we wait for the NBA season to finally start...

Essentially the r-squared value indicates that 26.1% of the changes in OFG% can be attributed to the change in relative wingspan.

And for the other 73.9%? That would be everything else. Maybe the shooter got a nice bounce. Maybe the defender bit on a silly head fake. The results are hardly perfect, but they do make an interesting piece of evidence in the discussion.

TL;DR

As painful as it may be to admit, this test doesn’t tell us too much. Wingspan is just another tool in a good defender’s repertoire. Even the most physically gifted of defenders can be a detriment if they lack the IQ to capitalize on their advantages. There will always be players that have all of the tools to be transcendent, but lack the mindset or dedication to put it all together. This is pretty much what any student of the game knows already; you wouldn’t be Gary Payton if your arms were a little longer, so hold off on that “corrective” surgery.