What would a one-free-throw rule mean for the NBA?

Kevin Pelton's NBA mailbag is back, featuring your questions on an experiment using a single free throw attempt for all points, Russell Westbrook's shooting numbers, the best way to enforce 3-point shooting fouls and how scoring relates to win projections.

You can tweet your questions using the hashtag #peltonmailbag or email them to peltonmailbag@gmail.com.

This question stems from the discussion about the NBA experimenting with a single free throw for all points this season in the G League, as first reported last month by my colleague Zach Lowe. It's well established that this change would diminish scoring because players are historically more likely to make the second free throw of a trip to the line than the first one, but I wanted to dig deeper on how much that might matter.

With the help of ESPN Stats & Information research, I went through every free throw shot in the league during the 2018-19 regular season. As expected, players did shoot better on the second attempt (78.9%) than the first (73.6%). To explore further, I treated players' shooting on the first of two attempts as their "base" free throw percentage and then used this to get what we'd expect them to shoot on a variety of different attempts. (This adjustment is necessary because three-shot fouls and technical free throws typically go to better shooters.) That yields the following results for types of free throws attempted at least 100 times last season.

(To answer one question before you ask it: There are slightly fewer second free throws than first ones because of lane violations that wipe out the second attempt.)

Looking over all these free throws, the value of repetition is clear. I recall theorizing that players shot worse on technical free throws than overall because the circumstances were different without any other players on the line, but it turns out this isn't the case at all. They shoot worse simply because technicals are typically the first free throw taken. (I separated out cases where the same player shot multiple consecutive free throws, a tiny sample but one on which they did shoot better on the second attempt.) It's also intriguing that players actually shot worse last season on the third free throw on a 3-point foul than the second, which certainly might be noise in the data.

If players shoot the way they do on the first of two attempts, we'd expect shooting a single free throw for all points to reduce the value of a two-shot foul from 1.52 points per play to 1.47 and a three-shot foul from 2.55 points per play to 2.4 points per play. Overall, this would reduce scoring efficiency by about 0.5 points per 100 possessions once we factor in additional offensive rebounds -- probably not a noticeable difference to the naked eye, but a real one nonetheless.

"I had a realization after listening to a story about James Harden and how getting fouled on a 3-pointer is now the most valuable shot in basketball. Right now the free throw average is about 75% for the NBA so a foul on a 2-point shot is worth ~1.5 points, but ~2.25 for a 3-pointer! This difference incentivizes one of everyone's biggest complaints about the NBA -- flailing appendages on 3-point attempts. It seems to me that giving only two foul shots on a 3-pointer is fair and would reduce the incentive to draw fouls." - Michael Lutter

Taking up a similar topic, my analysis of the first question shows this back-of-the-envelope calculation undervalues a three-shot foul in practice because players fouled in the act of shooting 3s are naturally better 3-point shooters. The actual 2.55 points per play on three-shot fouls is equivalent to shooting 85% on a 3-point attempt and an impossible 127% on a 2-point attempt.

The tricky line to walk on shooting fouls is we want them to be at least valuable enough to keep defenses from exploiting them by fouling intentionally without making them so valuable that offenses desperately seek them. We've probably hit the latter extreme with three-shot fouls. Could we return to two free throws for a shooting foul beyond the arc -- the rule from the introduction of the 3-point line through 1993-94 -- without going too far in the opposite direction?

I think the answer is yes. A shooting foul on a 3 would still be worth about 1.7 points on average, equivalent to making 56% of 3-pointers. According to Second Spectrum tracking, that's still way better than what the average player shot last season on the easiest possible 3-pointers -- uncontested catch-and-shoot attempts from the corner, hit 43.1% of the time. As long as we went back to three shots on a 3-point shooting foul in the final two minutes to prevent teams from fouling intentionally when up by three, I'd endorse this rule change.

Staying on the free throw theme ... the short answer here is my SCHOENE projection system forecast 73.5% shooting from Westbrook, about what he shot two seasons ago (73.7%) and also close to the average of his previous three seasons (74.6%).

Now the long answer. Westbrook's decline isn't really unprecedented. Among players who have shot at least 100 free throw attempts two seasons apart since the ABA-NBA merger, the 18.9% difference between his 2016-17 and 2018-19 accuracy ranks just 15th largest. What is unusual is Westbrook doing so while attempting so many free throws. If we increase the sample to at least 400 attempts both seasons, only Tim Duncan from 2001-02 through 2003-04 (79.9% to 59.9%) has fallen off more since the merger.

History suggests some level of regression to the mean is likely. Returning to the larger sample of players who shot at least 100 free throws in Year 1, Year 3 and Year 4, that group saw their free throw percentages improve by an average of 9.5%. Add that to what Westbrook shot last season and you get 75.1%, again in the same ballpark as SCHOENE's projection. Odds are Westbrook will be a worse foul shooter than he was through 2016-17 (when he hit at least 80% of his free throws in all but one of his NBA campaigns) but a substantially better one than last season.

"Is one point per game still thought of as worth 2.7 wins?" - David Locke

The Utah Jazz's radio broadcaster is referring to a rule of thumb that I believe John Hollinger of the Athletic popularized that each extra point per game in differential will typically translate to 2.7 wins over a full season. This formula gets used less frequently than Pythagorean wins, which is a more accurate predictor of win percentage at the extremes because it takes into account the total points scored per game in addition to differential. The difference in predictive accuracy is marginal, however, and having a value of one point per game in terms of wins is useful conceptually.

As it turns out, 2.7 wins might overstate the value of one point per game of differential now that games are higher scoring. Looking year by year at the relationship between differential and record, one point per game has indeed been worth 2.7 wins on average over the past two and a half decades (prorating the two lockout-shortened seasons to 82 games). But the last time it reached this mark was 2014-15, and last season's 2.4 wins per additional point was the lowest mark in that span.

Rationally, the more total points scored, the less important one additional point will be, and there's a linear -- albeit imperfect -- relationship between leaguewide points per game and the value of a point. Based on that, you'd expect an additional point per game to be worth about 2.5 wins given last season's scoring average. So I'd go with that as a value for now.