At the end of the Ohio State/Iowa State game Ohio State had the ball with 29 seconds left and a 75-75 tie. Iowa State let Ohio State run down the clock and take the winning shot. This seemed like a bad strategy to me.

With 29 seconds left, both teams in the double bonus, and a tie game, what would be the best strategy?

Do you let them take the last shot, let them run down the clock to a certain point and foul, or foul right away and trade free throws?

Playing straight defense was almost assuredly the better strategy. You’re not losing, so a turnover or a missed shot either gives you a quick chance to win, or you go to OT. Aggregate FG% in the NBA is only about 45%, and while sometimes you get FTs, at other times you turn the ball over without even taking a shot. So you’re probably more likely not to score on a possession than to score.

If you foul, especially in the double-bonus, you have a *very* good chance to give up the lead. Even a 30% FT shooter would be expected to make 1-2 or more about half the time. So you’re conceding the lead, and you now have to score to tie. Your chances of scoring are still under 50% on a typical possession, so you likely lose.

It could work out, of course - maybe you hit a shot after one or two missed FTs, or you tie after the FTs and go on to win in OT. But the odds are against you.

The person fouled would have to shoot less than 70.7% from the line just to have a 50/50 shot at tieing the game on your final possession.

Thompson, Smith, Ravenel, and Scott all shoot less than the above from the line.  If you could foul one of them the EV would be 1.207 or less as you get into the worse FT shooters. For the EV to be 1 they would need to shoot 61.8% from the line.  Scott does shoot that poorly, but he is 7th in minutes and I’m not sure if he was on the floor.  FWIW Williams is also terrible from the line and he is 8th in minutes.

Using the 45% conversion from above they would have to shoot 57.2% from the line or worse to make that the right strategy.  For reference Shaq averaged 52.7% over his career.

Yes - at 70.7% a player is 50/50 to make both FTs. Now fouling in a 1-and-1 situation is a better prospect, but still not advisable even against mediocre foul shooters. There’s a big risk you lose the lead, and even if they miss the free throw, there’s some chance of an offensive rebound, so you’re not guaranteed possession.

If you’re down a point, the whole situation changes: now time ticking off the clock is your main enemy, so you foul as quickly as you can and hope they miss a FT. And even if they make both, you still could tie by making a 3.

Or, as Pat Reilly often did with the Knicks and Lakers in such situations, rather than go for a 3 to tie, try to score very fast, and then press to force another turnover. Often the defense when ahead by 3 is heavily contesting the 3, making it much easier to drive for an easy layup.