In no other sport is there such a controlled experiment as the free throw. While statistical analysis of basketball can be more challenging than other sports in numerous ways, at least we have this. And it’s about time we took advantage of it.

Specifically, there is a weak connection between 3-point shooting and free throw shooting. Even though the connection is weak, it does appear that we can use it to our advantage when projecting how a player’s 3-point accuracy will change from one season to the next.

In this exercise, I took the top 100 returning players ranked by their 3-point attempts in 2005. Everyone from Syracuse’s Gerry McNamara (315 attempts in ‘05) to Lipscomb’s James Poindexter (165). I labeled the top 33 by accuracy as “good” 3-point shooters, and the bottom 33 as “bad.” I then sorted them by free throw accuracy in the same manner.

One thing to note is that this group shot about the same on 3’s in ‘05 (37.7%) and ‘06 (37.5%). In addition, 3P% is not well-correlated on an individual level from year-to-year, with a correlation coefficient of .371. To illustrate what that means, the following plot shows how well each member of this group shot 3’s in ‘05 and ‘06. You can see some relationship, but there’s quite a bit of scatter.

The lack of year-to-year correlation and nearly steady mean of the population provides another tool to use in a prediction – the concept of regressing to the mean. For instance, of the 33 good shooters in ‘05, only 8 improved their accuracy in ‘06. Of the bad shooters, 19 showed improvement the following season. So knowing nothing else, we can predict that the best shooters will see a decline and the worst shooters will improve.

But adding free throw shooting into our primitive model appears to increase the certainty of a prediction for a select few players. Of the 3-point shooters I labeled “bad” based on their ‘05 performance, eight of them happened to be good free throw shooters. The list:

                       2005  2005  2006    3P%
Player                  FT%   3P%   3P%   Diff
Bettencourt, Bucknell  88.8  35.3  40.3  + 5.0
McNamara, Syracuse     87.4  34.0  33.4  - 0.6
Washington, Delaware   87.2  34.5  39.6  + 5.1
Golob, N. Arizona      85.2  34.7  42.8  + 8.1
Gardner, Missouri      83.1  27.0  39.7  +12.7
Brown, CS Fullerton    82.7  34.8  37.7  + 2.9
Kruger, Arizona St.    82.1  35.4  40.3  + 4.9
Williams, Long Island  81.3  35.7  41.8  + 6.1
Average                85.0  33.9  39.4  + 5.6

Seven of the eight shooters improved in ‘06, and the improvement was substantial in many of the cases. By comparison there were 11 players that were bad outside shooters and bad free throw shooters, and only 3 of them improved their 3-point shooting.

Now let’s look at the opposite group – the good shooters in ‘06 that were unusually poor from the line. I should point out that the 100 players as a whole were much better free throw shooters than the general college hoops population (77.8% vs. 68.7%). Therefore, one must shoot better than 74.4% from the line to avoid being in the “bad” free throw shooting group for the sake of this discussion.

There were nine players that fell into the bad free throw shooting/good 3-point shooting group in ‘05.

                       2005  2005  2006    3P%
Player                  FT%   3P%   3P%   Diff
Stewart, USC           58.8  40.0  39.7  - 0.3
Jointer, S. Alabama    65.4  39.7  33.7  - 6.0
Agudio, Hofstra        65.8  42.3  42.1  - 0.2
Trotter, Alabama A&M   68.1  40.0  35.8  - 4.2
Dixon, Troy            69.0  39.9  38.0  - 1.9
Smith, Houston         70.3  40.2  34.9  - 5.3
Butler, George Mason   73.6  43.1  37.8  - 5.2
Carroll, Utah St.      73.8  47.6  45.1  - 2.4
Winters, Davidson      74.0  43.4  33.9  - 9.5
Average                68.8  41.8  37.9  - 3.9

Every one of the nine saw a drop in their 3-point shooting in ‘06, although the effect was not as dramatic as for the first group, perhaps because free shooters labeled as bad by me aren’t really that bad in the grand scheme of things. For instance, nobody at Hofstra was concerned about Antoine Agudio’s 0.2% drop in accuracy. He was still excellent from beyond the arc. By the way, for the 15 good 3-point shooters that were also good free-throw shooters, only eight were worse 3-point shooters in ‘06.

The funny thing about the two not-so-random groups listed above is that while the good shooters outshot the bad ones by an average of 7.9% in ‘05, the same group of bricklayers actually outshot the good shooters in ‘06 by 1.5%.

I have a couple of cautionary notes, though. First, there are plenty of exceptions to be found. They include Troy’s Jacob Hazouri had shooting numbers of 36.8/60.0, and saw his 3-point shooting rise to 41.1% in ‘06. On the one hand his 60% free throw percentage was only on 20 attempts, but on the other, he shot 56.4% in 39 attempts from the line in ‘06. At the other end, St. Peter’s Keydren Clark posted 36.7/83.5 in ‘05, but saw his 3-point shooting dip to 32.6% in ‘06. There are a bunch of others out there.

Second, I have to add the obligatory note that context also plays a role here. One notable player that just missed making the last list was Dee Brown. In 2005, he shot 43.4% from 3, and a pedestrian (for this group) 77.2% from the line. Knowing this, we would have expected Brown to come back to the pack slightly on his 3-point accuracy in 2006, even had his supporting cast remained the same, if only due to the pull of the mean for 3-point shooting. Of course, he lost two of his teammates to the NBA, and that had much to do with his tremendous drop in 3-point accuracy to 32.1% in 2006.

In my next post, I’ll use the dual power of regressing to the mean and free throw shooting to examine some interesting cases for 2007. And there are plenty of them.