to foul or not to foul this stroke

Foul? An excessively long answer to an excessively long email.

Brain & Staff -

I'm a templar with high INT.

Here is my question - Would it have been a better move for Michigan to commit two quick fouls and put Kentucky on the line shooting 1 and 1 at the end of the game? After Michigan tied the game there were about 27 seconds left. After two fouls Michigan would likely have 20 seconds remaining to take the ball and make a game winning shot of their own.

Oh man, you are about to enter the final frontier of basketball strategy. For starters, this is never happening. John Beilein is a genius but he's not the kind of mad genius who would, say, leave his guys out there with two fouls in the first half even though they don't foul very much. This is a bridge too far.

But, yeah, I thought about it too. Let's look at it.

Here is why I think this is a superior strategy - please feel free to poke holes in it.

1) Kentucky was making 53.40% of their shots. Assuming this is a reasonable expectation for Kentucky's chance of success on its last possession and that they hold for the last shot, Michigan has a 53% chance of losing and a 47% of going to overtime. Michigan has no chance of winning (in regulation) under this scenario baring a huge mistake by Kentucky.

This is optimistic for your strategy. Last shots are bad shots, as Kentucky amply demonstrated. Ken Pomeroy frequently tweets out the fact that teams tied and in possession with the shot clock turned off win 67% of the time, which means they're hitting 34%. Last shots also usually don't provide much of an opportunity for a putback, and anyway that stat about winning the game folds all results in.

2) Putting Kentucky on the line for a one on one yields the following probabilities (assuming a 75% free throw shooter - which is higher than Kentucky's 54.5% average for the game):

56.25% chance Kentucky hits both shots = 2 points

18.75% chance Kentucky hits one shot = 1 point

25.00% chance Kentucky misses the first shot = 0 points

I'm assuming Michigan is able to grab any rebounds (perhaps a big assumption). The key here is that Michigan heads back down the floor with a 25% chance to win with a made shot and tie with a miss, an 18.75% chance that any shot will win the game. and 56.25% chance that any made shot will win or tie.

This is a bit pessimistic for your strategy. Hack-a-blank has been an infrequently deployed strategy throughout basketball history, and never has it drawn an intentional foul call. Michigan had two attractive targets: Alex Poythress, a 64% shooter, and Dakari Johnson, a 45% shooter. Johnson was on the floor. Hack-a-Dakari gives you the ball tied over half the time.

Well, about half the time. The rebound assumption is kind of a big one. In the NBA, about 14% of FT misses are grabbed by the offense. Michigan was giving up an epic OREB rate in this game, though that's somewhat mitigated by the fact that in our hypothetical scenario one of Kentucky's bigs is stuck on the free throw line and can't move until the ball hits the rim. But since your FT% assumption is high it's probably a wash.

3) Assuming we use Michigan's 47.8% field goal percentage in the game as a proxy for their changes of making a shot. I'm also assuming that the chance of taking a 2 or 3 mirror the game percentages as well.

Again, late shots are bad shots.

although sometimes they go in

The impact on Michigan would presumably be less since they're just running their offense looking for the best shot they can in about 25 seconds, so maybe the assumption about Michigan is on more solid ground. But then you've got a potential response from Kentucky and things get complicated fast.

I'm eliding the math based on this assumption in the email provided to cut to the chase, which is that fouling for a one-and-one against a 75% FT shooter looks like this:

Win
27.63%

Overtime 
32.89%

Loss
39.47%

This breakdown looks better to me than Kentucky holding for the last shot:

Overtime 
46.60%

Loss
53.40%

So, where am I going wrong OR why don't we see this strategy more often - especially with teams who have better free throw shooters (ie trading fouls at the end of the game would typically be a losing strategy for the other team).

Thanks,

Jamie (6th Generation - still have never posted)

The main thing that's off about this analysis is the assumption that Kentucky hits a shot at the same rate they did during the game; this is clearly not true otherwise teams would be winning closer to 75% of their games when they've got the ball with the shot clock off in a tie game.

The other thing that's off is that 75% assumption. Here's what the universe looks like if you foul someone you should foul:

Down one is worse than being tied but it's hardly worse than a coinflip. When Arizona got the ball back with 31 seconds to go against Wisconsin down 64-63 Kenpom gave them a 45% shot at the game. It's basically compressing overtime into one shot. Meanwhile, being down two means you're now in a lose-or-OT situation similar to the one Kentucky just had with win-or-OT, except you have the option of hitting a 3. Michigan's quite good at this.

Things get complicated fast, but there is a threshold at which the foul is the right move. I think that threshold was breached once Calipari put Johnson on the floor. Part of this is the fact that Michigan is a brilliant offensive team. If the game's coming down to a last shot I want it to be Michigan's. And part of it is the stark line in the table above. Even including a standard OREB chance of 15%*, about 70% of the time you send Johnson to the line you get the ball and any bucket wins. The rest of the time you have a shot to go to OT or win with a three. I'm taking that chance.

…in the long-delayed aftermath, anyway. This isn't (much of) a criticism of Beilein. It's more of a thought experiment. Most people who have brought this up have done so in the context of "I wonder what if…" and then scribbled out assumption-laden percentages. During the event I was just trying not to die. I'm not sure Michigan should have spent any time figuring out how to shift the odds a bit in their favor if this one particular situation came up.

But, yeah, I think if there's a 45% FT shooter on the floor and you have the opportunity to put him on the line for a 1-and-1 in a tie game you do it.

*[Given the way the game was going you may question this but remember that Johnson's at the line and Kentucky is unlikely to have anyone other than Randle as a post since a Michigan rebound would then put Kentucky in a very awkward place defensively. Also Michigan can put two bigs in and call timeout after. Seems fair enough.]