Free Throw % Splits Based on Shot Type

I've always been a solid free throw shooter: I shot 75% over 4,250 attempts during the insane three-year stretch where I tracked every single shot I took on the basketball court (and 85% over 630 attempts in 2016)). But when I played organized basketball when I was younger I would always brick free throws when I shot technical foul shots and was alone at the line (although never as badly as my intramural teammate who had an 0 for 34 stretch shooting free throws). Was this just an abnormal anecdotal observation, or does NBA play-by-play data back it up?

It's been previously established that free throw shooters improve from their first shot to their second/third. Nylon Calculus has a great database on this phenomenon from 1999-2016, and TrueHoop suggested in 2011 that the first attempt is like getting to practice free throws in the middle of the game. But what about other splits like when you're alone at the line, or when you can take only one shot (such as an and-1)?

I pulled down NBA play-by-play data for the full 2016-17 season from BigDataBall (a great source at a relatively cheap price for all play-by-play data back to 2006) and looked at every shot attempt and found the same thing previous studies had:

Free throw shooters get better on their second/third attempts, to a very high degree of statistical significance. Comparing the shooting percentage between the first vs second/third shot gives a z-score of 13.56, which has an associated p-value of 1. Even comparing first vs second attempts gives a z-score of 12.54, which has an associated p-value of 1 as well.

But what about my earlier considerations regarding being alone at the line (with no rebounders around you)? I looked at "normal" free throws (on an and-1, two-point shot, or three-point shot) compared with technical/flagrant/clear path foul shots where the shooter is "alone":

3% of all free throw attempts last season occurred where the shooter was "alone", and players shot significantly better in this case, going against my hypothesis. But these "alone" attempts include technical foul shots, which are taken by the best free throw shooter on the floor (the shooting team gets to choose who shoots them). If I remove technical foul shots I get a different picture:

A picture that illustrates no significant difference in make percentage (z-score of 0.35 with an associated p-value of 0.64, which is inconclusive).

My final look focused on only the first free throw taken in a set: does the shooter perform better or worse if they know they're getting additional attempts? I.E. Is an and-1 different from the first shot from a set of 2 or 3 attempts?

As before, I filtered out technical shots, and as before, there's no significant difference (z-score of 0.29, p-value of 0.61).

All in all it seems my experience was abnormal: NBA free throw shooters do improve after their first attempt, but make their shots regardless of whether there are other players around them. This makes sense, since they are professional athletes and I am not.

Whether Punt Returners Should Return Punts Inside Their Own 10 Yard Line (NCAAF)

A couple of years ago I wrote this post assessing whether a kick returner should return the kickoff out of the end zone, stemming from my frustration when a college kick returner chooses to forgo the free 25 yards and tries to be a hero and run the kick all the way back. I concluded that the risk/reward balance was actually fairly even when accounting for turnovers. So I now have a new source of frustration to investigate from a game theory perspective: whether punt returners should return punts from inside their own 10 yard line.

I've always thought that a standard unwritten rule for punt returners is to plant yourself at the 10 yard line and let anything kicked over your head go into the end zone. Instead, I've observed many a punt returner attempt to return it from inside their own 10 (UNC's own Ryan Switzer would notoriously make me irate doing this). Are they making a negative risk/reward decision or am I wrong in my steadfast belief that it's a bad decision?

I gathered three full seasons of play-by-play data, using 2011-2013 (since that's what was readily available from this great Reddit thread for NCAAF data). There were almost 15,000 punt returns over this stretch, of which 1,387 were inside the 10 (9.3%). Whittling it further, 669 were actually fair caught (48%), leaving me with 718 punt returns that were caught inside the 10 yard line and returned.

The average punt meeting this criteria was caught at the 7.36 yard line and was returned for 8.98 yards, thus bringing the ball out to the 16.34 yard line. 76% of the time the returner gained yardage, while 12% of the time the returner lost yardage (the other 12% resulted in no gain).

Of the 718 returns, 10 times the punt was ran back for a touchdown (1.4%). On the flip side, 30 returners fumbled and lost the fumble (4.2%), and an additional 2 returns resulted in a safety (0.3%). On its face, it appears my intuition is correct: it's way more risky to try to run it back. But which option is optimal? Return it, fair catch it, or let it bounce towards the end zone?