Nylon Calculus: Quantifying the impact of length
Earlier in the year, I looked at the usefulness of the defended field goal percentage statistic and while I found that it’s not particularly useful, I think it’s important to remember what the statistic is trying to measure: individual shot defense.
While the particular metric available isn’t useful as presented. I wanted to see if there is a way to measure individual shot defense. Specifically, can a defender’s length impact the shot?
We can measure a defender’s length by looking at their wingspan. And while the NBA does not unfortunately have wingspan data for every player, there is data for enough players to attempt to model it (there is wingspan data for 366 players from 2013-14 to 2014-15). Additionally, the NBA used to publish SportVU shot logs for those seasons which can help us model the data.
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Previously, I had used this data to develop a shot difficulty model called KOBE. We can develop a similar shot difficulty model and add in a length variable (wingspan) and determine if length of the defender has an effect on the shooter making or missing the shot (whether length is statistically significant as a variable).
Since we only care about shots where the defender is close enough to impact, we’ll filter our shot logs by whether the shot was contested (as defined here, we’re filtering by very tight or tight). To determine the impact of length (wingspan) on shot difficulty, I created four separate models: 1) for contested shots near the basket (<5 feet), 2) for contested 3-pointers, 3) for contested jump shots (10+ ft) and, 4) for contested 5-10 feet shots.
Each of these four models were run with and without the length variable (wingspan) to total eight separate models. You can see each of the models here.
At each shot distance type, the length variable was statistically significant and improved the overall fit of the model (slightly), indicating that the length of the defender (wingspan) does have an impact on the player’s ability to make a shot.
This isn’t particularly surprising and a team like the Thunder has used it’s superior length in the past to fashion good defenses. So what might be more useful to know is the magnitude of the effect. We can test this by entering in dummy inputs into each of the four models and holding all other variables constant (other variables include shot distance, closest defender distance, catch and shoot vs. off dribble, height differential of the shooter and defender, touch time and shot clock) to determine how much the shot difficulty goes down for every one inch increase in wingspan.
As we can see, the length of the defender has the biggest impact around the basket where a one-inch increase in wingspan leads to a 0.75 percentage point decrease in field goal percentage. For 3-point shots, a one-inch increase in wingspan leads to a 0.55 percentage point decrease in shot difficulty.
A few caveats though: first, it’s important to note this is an estimate based on assuming there is a linear relationship between wingspan and shot difficulty. It’s worth testing whether a different type of relationship exists (a squared term, exponential, etc.). Perhaps, there is a greater increase in shot difficulty for one inch as you get towards the players with the longest wingspans relative to an increase of an inch for a player with a league average wingspan.
Second, we are making the massive assumption that most of these shots in our dataset are actually contested with the defender getting a hand/arm up (the only way wingspan would be relevant). Intuitively, it seems like a perfectly reasonable assumption — if you are in close proximity to the shooter (and as I mentioned earlier, we’re looking at shots where the closest defender is within four feet), you probably are getting your hand up to contest the shot (we’re assuming basic level effort here). Still, the caveat exists that we don’t actually know how many of these shots or what percentage will have a defender putting their hand/arm up. However, the fact that the wingspan variable was significant probably indicates that it’s a fairly high percentage.
Let’s apply these estimates and gauge the value of a few player’s length on their ability to decrease the opposing shooter’s field goal percentage:
Now I know what you’re thinking- Nylon Calculus has written a ton about how opponent 3-point percentage is mostly noise. So it must seem like this entire article contradicts our previous research including my own piece from just a few months ago.
First, let’s circle back to the defended field goal percentage metric that I and others have found has no year-to-year correlation. Let’s think back to what it’s measuring or at least what we THINK it’s measuring. We think it’s measuring a player’s ability to defend shots. And you can only defend a shot if you are in close proximity to the shooter (for example, a player who puts their hand/arm up to contest a shot when they’re 15 feet away is probably not affecting the shooter). But after compiling league wide totals, I actually found that it’s not really measuring that at all:
So as we see here, the league average on all of the defended field goal attempts is much higher than what SportVU has for shots marked as very tight or tightly defended. In fact, the league average on the defended field goal attempts is roughly equal to the overall league average on 3-point percentage. This seems to indicate that the defended field goal percentage stat is including ALL 3-point shots rather than the ones that are actually physically defended.
To use an extreme example, it seems like if the closest defender was 20 feet away, that defender would be “credited” with defending that shot in the defended field goal percentage stat even though they are not even in position to be able to contest the shot. Now I don’t know for sure if this is the case nor do I know to what degree but the difference in field goal percentage on very tight/tight shots versus the defended field goal percentage metric seems to indicate that the defended field goal percentage metric is including shots that are actually open shots. This seemed to be the case for all of the different shot locations. So basically, the defended field goal percentage metric isn’t even measuring what we want it to measure.
The larger issue is whether the findings in this article contradict our previous findings.
Previously, our research has indicated that the best way to defend the 3-pointer is to avoid it due to the variation in the 3-point shot. And yet, in this article, I’ve indicated that having longer defenders can affect the shooters’ 3-point percentage on an individual shot. However, let’s recall the methodology I outlined earlier in the article: I filtered by contested shots. This is an important distinction for defending the 3-point shot on the aggregate versus defending one individual 3-point shot.
As we already know, 3-point percentage goes down as the defender is closer to the shot. So naturally, if you are the defensive player, you want to get as close to the shooter as possible so that you can properly contest the shot. When the defender is actually in close proximity to the shooter, the length of the defender can make a difference. However, according to the NBA.com definitions of
and
coverage, this does not happen very often. A majority of 3-point shots are open. We can see that breakdown here:
With such a low percentage of 3-point shots being contested, it makes sense that the best way to defend the 3-pointer on the aggregate is to avoid it. And intuitively, this makes a lot of sense. If a defender does a great job of closing out and is in the offensive player’s air space, the offensive player may be deterred from shooting altogether. That is the best type of defense you can play because it forces the offense to take more time of the shot clock, where offense becomes less efficient.
And what if the offensive player isn’t deterred from shooting the 3-pointer? Well, this is where having longer defenders to impact the shot can be helpful (and in fact, longer players are probably more likely to deter shots as well). And again, intuitively it makes sense. If Isaiah Thomas is attempting to contest a 3-point shot, it makes sense that he’s less likely to impact the shot going in versus say Giannis, whose longer arms are more likely to bother a shooter.
Interestingly, better shooters are more likely to take those contested threes. We can see this effect by comparing the career 3-point percentage and free throw averages of all the players who took contested shots versus all the players who took open shots (I used career percentages because it’s more likely to give an indication of how good a shooter the player is versus a one- or two-year sample where 3-point percentages can be volatile).
Of course, one of the issues with the above table is better 3-point shooters tend to shoot earlier in the shot clock (also updated here where I used career 3-point percentage and free throw percentage instead) and so it’s possible that a bunch of poor 3-point shooters who are taking shots late in the clock (and probably more likely to be contested) are biasing our results. We can fix this by removing all late shot clock situations (as well as situations where the shot clock is turned off).
As we see here, when removing the late shot clock situations, the difference in shooting ability of players taking contested 3-point shots versus open ones becomes even more apparent. Again, this makes a lot of sense. Steph Curry is more likely to take a highly contested 3-point shot than Draymond Green who will need more time and space to feel comfortable shooting.
And the same still applies for catch-and-shoot specialists like Kyle Korver, who also needs less space and time to get his shot off than a poor or average 3-point shooter would.
So what does this mean in conjunction with what we found earlier regarding length impacting contested 3-point shots? It means that longer defenders can have an effect on even the best shooters’ ability to make a 3-pointer provided they are within proximity to actually contest the shot.
So in summary, the best way to defend the 3-pointer is still to avoid it. And 3-point percentage is still highly variable and a bad measure for team defense because of the number of open 3s teams get. It is still better to judge a defense based on 3-point attempt rate. However, there does appear to be some ability of individual defenders, specifically those with longer wingspans, to affect contested 3-pointers which generally come from better shooters. Unfortunately, the defended field goal metric on NBA.com does not show this and includes open 3s as well (and here’s a plea for the NBA site to fix this). This seems to be true for the other shot locations as well (but doesn’t make as big a difference because shots near the basket are mostly contested).
Finally and not surprisingly, the length of the defender seems to have the largest effect on shot difficulty near the basket.
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Ultimately, while measuring individual shot defense is still very difficult, it is worth noting that a defender’s length can have a big impact on the player’s ability to defend shots.