# The Cost of Throwing Away Free Throws

An article published in the New York Times last week began as follows:

**For Free Throws, 50 Years of Practice Is No Help**

**by John Branch**

**CEDAR CITY, Utah –**

Yes, an article from the New York Times was filed from Cedar City, Utah.

Now Cedar City is home to a number of wonderful things. There is

- Southern Utah University, a school that I think deserves far more attention than it receives (it’s really a very good school, and no, I am not just saying this).
- the Utah Shakespearean Festival, which won a Tony Award in 2000 (yes, it’s quite good).
- within a very short drive, a number of national parks including Bryce Canyon, Cedar Breaks, and Zion National Park.

Although all of this deserves more national attention, the New York Times ignored it all. No, what John Branch wanted to focus upon was free throws.

**Coming to Utah to Discuss Free Throws?**

And why would Branch come to Cedar City to discuss free throws? It turns out that the Southern Utah Thunderbirds lead the NCAA in free throw percentage.

And that leads us to ask…. why would the New York Times send someone to Cedar City to cover the Thunderbirds ability to hit shots from the charity stripe? Although the story involved a trip to Cedar City, the focus was on the following:

- Free throw percentage is remarkably consistent across time. An average college player hits 69% of his free throws. Players in the NBA and WNBA hit about 75%. With respect to the NBA and NCAA, these averages have persisted since at least the 1960s.
- It’s argued in the article that coaches can impact free throw percentage. At least, that is a reason offered for the superior free throw shooting observed at Southern Utah.
- Most coaches, though, do not focus on free throw shooting (hence performance does not change). And coaches ignore free throw shooting (again, according to the article) because other aspects of the game are considered more important. After all, as the article note:

*“There is little correlation between free-throw percentages and winning percentages. Only one of the 25 best shooting teams, No. 2 North Carolina, is also in the latest Associated Press top 25 rankings. Southern Utah has a losing record. That is why, despite accounting for more than 20 percent of scoring in men’s college basketball and just below 20 percent in the N.B.A., free throws receive a fraction of the attention from coaches, players and fans.”*

**The Importance of Free Throw Shooting**

If we look at the NBA we can see evidence for why coaches should ignore free throw shooting. From 1977-78 to 2007-08 the correlation between a team’s free throw percentage and team winning percentage is only 0.18. In other words, free throw percentage explains only 3% of team wins [correlation is r, explanatory power is r^{2}]. Given these numbers it’s clear that teams should just ignore free throw percentage.

Of course, there’s a problem with these numbers. Our simple model of winning percentage supposes that wins are only explained by free throw percentage. In other words, we didn’t include any other explanatory variable. And since other factors definitely matter, our model is mis-specified. In simpler terms, because we didn’t consider any other factor that impacts wins, our simple model really really won’t tell us the actual link between winning percentage and free throw percentage.

When we do specify the model for winning percentage properly we do see that free throw percentage does matter quite a bit. And to see how much it matters, consider the productivity of players who struggle at the free throw line.

**Shaq and Superman**

Perhaps the most famous poor performer at the line is Shaquille O’Neal. Shaq entered the league in 1992-93. Across the next 16 seasons (ending with the 2007-08 campaign), O’Neal posted a 0.307 WP48. Certainly this is an excellent mark (average is 0.100). But relative to the following sample of all-time greats, Shaq comes up a bit short:

- Magic Johnson: 0.429 Career WP48
- Larry Bird: 0.365 Career WP48
- Michael Jordan before his first retirement: 0.390 Career WP48
- Michal Jordan before his second retirement: 0.362 Career WP48
- Michael Jordan before his third retirement: 0.332 Career WP48
- David Robinson: 0.350 Career WP48

What do these numbers tell us? Well, MJ – if he wanted to maximize his career WP48 (not that this was his motivation) – should have limited his retirements. But more important to our story, Shaq comes up short relative to these all-time greats.

Of course, Shaq comes up short because he has trouble hitting free throws. For his career he only hit 52.4% of his free throws. What if Shaq hit at a 75% rate? Across his career he attempted 10,376 free throw attempts and made 5,441. If he was average from the charity stripe, though, he would have hit 2,361 more free throws. With each additional point worth 0.033 wins (which we know from our complete model of wins), if Shaq scored 2,361 more points across his career – with no change in free throw attempts or field goal attempts – O’Neal would have produced 76.9 additional wins. And this means Shaq’s career WP48 would be 0.405 prior to the 2008-09 season. In sum, if Shaq just hit his free throws, his productivity would have compared more favorably to a few more of the all-time greats.

A similar story could be told about Dwight Howard in 2008-09. Currently Howard is posting the following numbers (prior to Sunday’s game):

- 60.4% free throw percentage
- 18.5 Wins Produced
- 0.417 WP48

If Howard could hit 75% of his free throws, though, he would have scored 95 more points, produced 3.1 additional wins, and he would be currently posting a 0.486 WP48.

The examples of Shaq and Howard illustrate the importance of hitting free throws. Missing these shots reduces the number of points a team scores and that reduces the ability of a team to win.

Of course, hitting free throws – by themselves – are not enough to win games. You also have to efficiently shoot from the field, rebound, create turnovers, and avoid turnovers. So coaches do have to focus on more than free throws. But if it’s true that coaches can change free throw percentage (and I am not sure this is the case), then they are throwing away points by not spending more time on this issue.

As for Southern Utah, obviously we need to do more than just hit free throws. In fact, if we did all the things I noted above, we would be a dominant team in the Summit League. As it is, the Thunderbirds – after winning their first game in the Summit League tournament today — will need to win two more games to reach the NCAA tournament. And if that happens, SUU might start to become known for something besides an underrated academic program (really, it’s quite good), a wonderful Shakespearean festival, and the scenic beauty of Southern Utah.

– DJ

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Our research on the NBA was summarized HERE.

The Technical Notes at wagesofwins.com provides substantially more information on the published research behind Wins Produced and Win Score

Wins Produced, Win Score, and PAWSmin are also discussed in the following posts:

Simple Models of Player Performance

What Wins Produced Says and What It Does Not Say

Introducing PAWSmin — and a Defense of Box Score Statistics

Finally, A Guide to Evaluating Models contains useful hints on how to interpret and evaluate statistical models.