Nylon Calculus: Identifying NBA talent and why tall men can’t dribble

Pretty much ever since James Naismith affixed a peach basket to the wall in a Springfield YMCA gym, it’s been apparent that height and length were advantageous in basketball performance.

In the modern NBA players tend to be, statistically speaking, extremely extremely tall. This is easily seen compared to the general population — according to a VICE Sports article by Seth Partnow, using a Centers For Disease control calculator, adult males at 6-foot-10 are at the 99.9997th percentile, while a 6-foot-5 male is at the 99.5339th percentile. As Partnow points out, that might seem like a small difference, but it’s the difference between a pool of hundreds of US born NBA age men and hundreds of thousands.

So, why are there so many 7-footers in the NBA? To paraphrase the great basketball philosopher Antoine Walker, “Because there are no 8-footers”

Now, not every 6-foot-11 American kid makes it to the NBA. Luckily for the NBA viewership there are other skills and attributes to the game than just a standing reach contest. But, man, does height help.

Read More: The real reason for the Toronto Raptors’ playoff disasters

The mental model I use for NBA prospects is of three broad, more or less independent attributes that qualify them to get into the league — height, athleticism and skill. Height is self-explanatory. The other two attributes, while widely recognized as valuable by basketball talent evaluators, are a bit harder to define and measure. Broadly speaking athleticism includes abilities like speed, leaping, lateral quickness, strength and all of those “gross motor” functions, with skill being even less directly observable, but expressed on the court by shooting ability, court vision, handle, catching, and passing.

We can look at that extra tall population to flesh that model out a bit. While, it’s a bit hard to nail down exactly how rare the heights of 6-foot-10 or taller are, the numbers are in the hundreds for the US. The census bureau estimates that are about 32 million males 19 to 35 in the US. Using a calculator based on CDC numbers indicates that only 1 in about 128,000 US males are at least 6-foot-10. Or applied to the relevant aged population there are about 250 men in the US that tall in total, which is fewer than the total 450 NBA roster spots.

Of those, I count 47 players listed at 6-foot-11 or taller (with shoes, which is why I add an extra 1), so a US male in that age range who is 6-foot-10 or taller has about a 19 percent probability of being on an NBA roster.

That’s a tremendous advantage, but not a guarantee, which brings me back to my other attributes; athleticism and skill. In my mental model, to make it to the NBA our hypothetical prospect needs to be in the top 19 percent of combined of skills and athleticism among his height cohorts. Converting height, athleticism, and skill to standardized Z-scores, at a true 6-foot-10 our hypothetical hooper needs to be a net-plus .842 standard deviations on athleticism and skill to get to the NBA.

There are a couple of ways that net plus athleticism/skill can be met, or not met, as shown below with an estimate on international outlier Boban Marajonovic on the end.

The model forces even the very tall to bring something else to the game, and allows them to trade off skill and athleticism in order to make the cut.

Tall men can’t dribble

The interesting thing is to apply the model to less tall players, like a prospect around 6-foot-5. According to the on-line estimates using the CDC data, a 6-foot-5 prospect is in the 99.559 percentile and is 2.6 standard deviations above the average. Estimating from census bureau demographics again, there are about 140,000 US males that height or taller, which is, of course, a lot more competition.

So, in order to meet the super basketball outlier status of a an NBA player a 6-foot-5 prospect has to be much more of an outlier in skill and/or athleticism. This is even more true of a shorter player like Isaiah Thomas.

To be clear, I view the height/skill/athleticism model as a just an approximation. There are lots of reasons the model might breakdown. We don’t have direct measurement of basketball athleticism and basketball skill in the population the way we do height. The range might be less between those attributes. Prospects and gatekeepers could over-select based on height, which is more readily observable, early-on, before athleticism and skill become fully realized.

There are likely to be non-linear effects of attributes, such as base levels of athleticism needed, regardless of height. International players skew the population sample as well. In part, because basketball is less popular outside of the US. selection by height is even more pronounced. If you are a 7-foot-6 South Sudanese or 7-foot-4 Balkan goat-herder, the NBA will find you.

That said, there are a couple of useful things that come out of using this model. For one it explains why there can appear to be a negative relationship between say height and skills, even if there isn’t one. In a simulation of data supposing a random relationship between skills, athleticism, and height, selecting the top overall scores out of 10,000 cases consistently appears to show a negative correlation between the say height and skill, even though none exists in the overall data.

Positions can complicate the picture, but selecting specifically for skills for point guards and height for centers increases the appearance of a negative relationship between skill and height among those selected, even if the underlying population has absolutely no relationship between the two factors.

Next: Playoffs teams are living comfortably by the 3-pointer

To get into the NBA you have to be an outlier, if not in height, then somewhere else. Though preferably both.