# Is free throw defense real?

In the last installment of Offense vs. Defense, we saw that offense controls the variance in predictions of free throw percentage. But the defense still had a two-percent influence on the predictions. It’s possible this could be explained away by random error. After all, if the offense truly controls 100% of free throw percentage, any errors in the method would work in the defensive direction. In other words, the method couldn’t possibly tell you that the offense has greater than 100% control over free throw percentage.

But it appears a modicum of free throw defense may exist on the team level. While the model does a nice job quantifying results in a way that can be used to compare various stats, it’s a bit abstract. We should be able to look at the raw data and see some effects of whether offense or defense is in more control of a stat.

For example, one can compare what happens when the best free throw offenses face the best free throw defenses and compare that to what happens when the best free throw offenses face the worst free throw defenses. Here’s what the data looks like for each of the past ten seasons:

```       Good FT O vs. Good FT D    Good FT O vs. Bad FT D
Year   FT%(O) FT%(D) FT%(Game)    FT%(O) FT%(D) FT%(Game)
2015   75.5%  65.5%   74.1%       75.4%  73.4%   74.5%
2014   75.6%  65.9%   71.7%       75.9%  74.1%   74.1%
2013   75.4%  65.9%   73.1%       75.6%  73.9%   74.1%
2012   75.9%  65.2%   71.3%       76.2%  73.6%   75.3%
2011   76.1%  65.0%   73.7%       76.7%  73.2%   73.9%
2010   74.8%  64.7%   72.2%       75.2%  73.4%   73.8%
2009   75.5%  65.5%   73.3%       75.9%  73.1%   75.7%
2008   75.5%  65.2%   75.3%       75.8%  73.6%   74.6%
2007   75.4%  65.0%   74.2%       75.4%  73.0%   73.5%
2006   76.1%  65.0%   73.5%       75.4%  73.6%   75.4%
Total  75.6%  65.3%   73.2%       75.8%  73.5%   74.5%

```

Theoretically, there would be no difference in the difference in free throw shooting in the games found in these two groups. However, the good defenses held the good offenses to 73.2% while the bad defenses allowed the good offenses to shoot 74.5%. That’s a difference over the ten seasons of 1.3% between the two groups. (It’s 1.1% if you account for the slightly better free throw shooting offenses in the games against good defenses.) That is not huge, but we’re talking about 1,068 games and about 21,000 free throw attempts in each sample, so the difference can’t be explained by randomness.

Another clue that free throw defense is possibly real is found by simulating the season while assuming that the defense has no control over its opponent’s free throw shooting. In doing this, I found that there isn’t as much variance in team-level defensive free throw percentage in the simulation as is observed. So there must be something else going on.

To be clear, we’re talking about the defense’s impact on team free throw percentage. It probably has no impact on opposing player free throw accuracy, but it can affect the distribution of who is actually taking the free throws. UCF led the country in free throw defense last season partly because they play in a conference with bad free throw shooters and partly because their bigs foul much more often than their smalls. Since big men tend to be worse free throw shooters than guards, the Golden Knights are sending the opponents’ worst free throw shooters to the line more often than the average team. While the effect exists, it seems to be very small.

While we’re here, it’s worth noting that a team’s free throw percentage is a representation of the past. If a team is near the top of the national leaderboard, it’s free throw percentage is likely an overestimation of its true ability. A team that is leading any statistical category is usually very skilled in that area, but they’ve almost surely benefited from some good fortune as well.

One way to demonstrate this is to simulate the season assuming a team’s ability is it’s free throw percentage. Invariably, the simulation will produce a leaderboard with higher free throw percentages than real life. That’s because some of the top teams are going to benefit from random variance, and their free throw percentage will exceed their underlying ability. That random variance could be in the form of better shooters getting to the free throw more often than one would expect, or the shooters themselves making a few more free throws than their ability would suggest.

This is why mid-season proclamations that a team is on pace to set a record in something are somewhat misleading. In a small amount of games, luck can have a larger impact on a team’s numbers than over the entire season. But even over a full season random variance plays a role. Based on modeling, it’s best to assume that a team’s true free throw ability includes an additional 100 free throw attempts with national average accuracy. It probably won’t be enough for a team to be great at free throw shooting to beat 1984 Harvard’s single-season record of 82.2%. They’ll need to be lucky as well.