# Nylon Calculus: Expanded free throw splits since 1997

In the current era of NBA basketball, free throws are unique in that they aren’t subject to any of the common concerns with play-by-play and player tracking data. The shots are always uncontested. The types of free throws, unlike shot types for field goals, can be trusted, though things were weird in the early seasons of play-by-play data. We can also point to where a player attempts his free throw because it’s a set shot. A player doesn’t fade away or have his momentum carry him to one side or the other.

Free throws are simple scoring opportunities to analyze. There are basic splits for how a player shoots when given one, two, and three shots, but we can also look at the results of the latter two sequences. A notable finding from the basic splits was confirmation that players typically shoot worse on their first of two free throws than the second, but it doesn’t tell us how often a player missed both, split them, or made both.

One example was Gordon Hayward this season. In 164 pairs of free throws, Hayward shot 84 percent on the first shot and 87 on the second. Of those 164 pairs, he finished 116 with two points and came up empty in none. Since 1997, Hayward had the fourth-most trips to the line in a season without ever yielding zero points. Below is a table looking at the top ten players, showing free throw percentages in each of the two attempts but also the players’ four possible outcomes when given a pair of shots. I shared a few tables throughout this post. That’s partly so whoever views the splits in a Tableau dashboard at the bottom of this post has a better idea of how to read them.

The lists for the other two scenarios, meaning the most pairs of free throws without making both or without splitting them, feature significantly smaller samples. Eric Montross started his career with a bang, winning arguably the most important jump ball of 1995, but left quietly in 2002 after none of his 15 pairs of free throws ended with two points, and after he injured his left foot. Chris Mills in 2001 had the most trips without ever splitting, with 16. Now you know.

Going back to the table with Hayward, those players were all excellent free shooters and expected to rarely miss two in a row. The accuracy from Hayward on his first and second free throws suggest he would miss both free throws only three times out of 164. Reggie Miller’s percentages in 2000, specifically on his second attempts, meant he’d need 312 pairs before coming up empty in exactly one.

But not every player with similar basic splits as another got there in similar ways. An extreme example from this season was between Dion Waiters and Maurice Harkless. Both players shot just below 60 percent on their first of two attempts with slight improvements on their second, but that’s where the similarities ended. Waiters split his free throws far more often than Harkless, who had more trips to the line where he made both shots, but also more where he came up empty.

The table below has the same first nine columns as the one featuring Hayward, but to further show the differences between Waiters and Harkless, I looked a little closer at their accuracy on the second of two free throws and how frequently each player scored zero, one, or two points on their trips to the line. I also included league averages from this season as a guideline. Note that the league’s number of free throws will be smaller than the totals in basic splits. That’s because of turnovers like lane violations and offensive goaltends. I only tracked free throw possessions here with two or three attempts.

Waiters was a complete outlier. When considering his free throw percentage on the first and second free throws, he was expected to split his pairs about 48 percent of the time. His actual frequency was 19 percent higher. When looking at all players since 1997 with at least 50 couples of free throws in a season, no player split their attempts more often than expected than Waiters. Because of this, he also had one of the largest differences in percentage on his second shot depending on what happened in the first, at 39 percent.

Below is a look at the ten players who split their free throws most higher than expected. The other nine players aren’t as interesting as Waiters, but it shows how the odds of each player scoring zero, one, or two points differed from their actual results. Once again, I included league averages as a guideline.

If we drop the filter to 20 pairs from the stripe, James McAdoo’s season was the most all-or-nothing type when adjusting for accuracy. In exactly 20 pairs this season, McAdoo shot 50 and 55 percent on his first and second free throws, but made both attempts nine times and missed both on eight. That trend has continued in the playoffs. With two trips to the line so far, he finished one with two points and the other with none.  Of course, some players are robots. Wesley Matthews was right on with his odds this season, making none, one, or both of his free throws as often as his accuracy on both attempts said he should.

Next: Nylon Calculus -- Lessons from the Spurs-Rockets regular season matchups

Trips to the line featuring three free throws were touched on when Stephen Curry went one-for-three for the first time in his career a few weeks ago. The sample sizes for fouled 3-point attempts were much smaller than two-free-throw sequences, so I didn’t go as in-depth with those. There were no Waiters-like splits, but a few like Hayward because of the extra free throw.

Hopefully these examples help read the Tableau dashboard below, though I have another without width restrictions. Overall, this all probably isn’t a huge deal for strategy, but in the future we can use trips to the free throw line to tweak more commonly used statistics.

Right now, at the very least, it shows how weird you can get with play-by-play data.