The Most Valuable Shot is Worth One Point
May 2, 2014; Portland, OR, USA; Houston Rockets guard James Harden (13) loses the ball after being folded by Portland Trail Blazers forward Nicolas Batum (88) in the first half in game six of the first round of the 2014 NBA Playoffs at the Moda Center.Mandatory Credit: Jaime Valdez-USA TODAY Sports
The math has spoken, one is greater than two, and it is greater than three as well, at least in basketball.
In analytics the three-pointer gets all the glory, especially those sexy corner threes, and there are very good reasons for this. Three-pointers are undeniably more efficient than long two-pointers. There is evidence that the extra spacing of having three point shooters on the court opens space and helps get shots at the rim. Three-point shots may also lead to more offensive rebounds, at least than long and mid-range twos. But the simple math is that the average possession at the charity stripe is more efficient than the average three-point attempt. Given that most shooting fouls result in two shots at the free throw line, I am using the two-shot foul as the base of my comparison, arguably that is the least beneficial free throw play as And-1 attempts only come on top of made baskets, while technicals do not even consume a possession.
In the NBA last year, players made just under 36% of the 1766 three pointers taken, for an average of 1.078 points per three point attempt. Players made 75.6% of their free throw attempts for 1.51 points per shooting foul drawn on a two shot[1. Both per Basketball Reference.]. And for those doing the math at home, yes 1.51 is greater than 1.078.
On the individual player level, not a single player in the NBA with more than 10 total three-point attempts on the season had a higher average points per shot on their three-pointers than their league-average points per shooting foul drawn on a two point foul[2. Also per Basketball Reference]. The best three point shooter, Kyle Korver, for example, averaged an incredible 1.416 points per three point attempts and 1.852 point per two-shot trip to the line. (Good three point shooting tends to correlate highly with good foul shooting, the biggest exception being J.R. Smith who barely averaged more points per trip to the line than on his three point shots 1.182 on three-pointers and 1.304 on trips to the line[3. Ibid.]).
This isn’t news to either the analytics crowd or old school basketball types. Dean Oliver included getting to the line as one of the four factors in his in his seminal basketball analytics book, “Basketball On Paper.” Well before that, legendary college coach Dean Smith is reported to have said, “The key statistic is getting to the foul line.”
Three point shooting does have significant synergies with spacing on offense as found by numerous analysts, including my own studies. But getting to the line may also have defensive advantages as it allows your own defense to get set and a high percentage of made shots has been shown to lower opponents’ eFG% on the next possession[4. Defense Is Easier When You Don’t Have to Run Back using NBA Wowy Data.].
Knowing Vs Acting
Given this knowledge it is fortunate for the NBA’s TV ratings and upcoming contract that players can not just get to the foul line whenever they want. Last year three-point attempts accounted for 23% of all scoring attempts, while free throws accounted for just 12.5% (using the standard conversion of 0.44 possessions per FTA). The range between teams’ free throw attempt percentage is significantly less than the range between three-point attempt percentage, just over half the spread, in fact. The difference is also smaller when scaled for the lower average free throw scoring attempt percentage with a lower coefficient of variation.
It is this difficulty of acting on the that prevents free throw shooting from dominating analytics discussions or ruining basketball outside of the occasional flop and the last two minutes of sort of close games in January.
On the other hand, getting to the foul line isn’t random, both playing style and ability to ‘draw contact’ play into getting to the line. Slashers get to the line more often than spot up specialists. For example, in a previous study on shooting fouls I found that shots at the rim and unassisted twos were positively correlated to getting to the line and explained about 41.6% of the variation between players’ free throw rates. Three-point shooting is negatively correlated with getting to the rim for most players, so there wasn’t any independent relationship between foul shots and three-pointers once shots at the rim were taken into account.
On the team level, a look at the three-point rate and free throw rate shows a only a minimal relationship with a slight positive slope, only because the Houston Rockets managed to have both the highest free throw scoring attempts and the highest three-point rate. The Rockets FTA rate was pushed up by both the Hack-A-Howard strategy of opposing coaches and the, uh, stylings of James Harden, both of whom were outliers in my previous study getting to the line far more often than the model predicted[5. Where Shooting Fouls Happen and to Whom]. But there’s doesn’t appear to be any reason to choose between the favorite shot of basketball analysts, the three-pointer, and the actual most efficient one.