Should KU have fouled?

As you arr know, this is normarry a poker brog, but I thought the occasionar sports post might be good for diversion's sake, especiarry since we've had a few prop bet posts in the past. I was chatting with my friend Justin during the end of the KU-Davidson game last weekend. At the end of a hard fought game, KU had a two-point lead and Davidson had the ball with about 15 seconds left. We had the following exchange:

me: davidson should run down the clock to 5 sec and shoot a 3

Justin:

I agree

30% chance at winning this game, that is probably what they have in OT

and they still gotta make a 2 to get there

That's what Davidson did...roughly...but afterwards I started wondering how Kansas should combat this strategy. Defending the 3-point line aggressively is one obvious choice, but here's another, much more outside-the-box option: foul. Let me make clear that, for job security and overall sanity reasons, Bill Self, nor any other actual college or pro basketball coach, would choose to do this. But just allow me to imagine that I were rooting for KU (I wasn't, I'm a Tar Heel and Davidson would be a much easier draw for us in the next round, prus Davidson is a NC team as werr), and that I were allowed to anonymously make the best decision in the interests of my team without fear of getting ripped in the press or losing my job if it didn't work out.

OK, that said, let's assume that I had noticed (and I think this is fair) that Davidson's players, particularly Curry and Richards, their stars, were absolutely exhausted, while KU, a deeper team, hadn't been nearly so taxed physically that game or in previous rounds. Based on that fact, and the fact that KU is just plain a better team, and Davidson had just lost one of its starters on a foul-out, I'd give Davidson a 30% chance of winning if the game went to OT, as Justin suggested. And that's IF they knock down two free-throws (64% chance even for an 80% free throw shooter). What's more, if KU were to foul, they'd do so as soon as possible, so even if Davidson hit both, KU would be able to take a final shot to end the game in regulation. I'm gonna say there's a 50% chance of them getting a point on that possession and winning the game (remember, the game would have been tied, so just getting to the foul line and hitting one would have done the job). The only really terrible thing that could happen is if Davidson made the first three throw, missed the second, and got the rebound. But given that KU has the much bigger team, especially after Davidson's forward fouled out, this is so unlikely I'm not even going to consider it.

All considered, fouling and putting Davidson on the line gives KU a .34 (probability Davidson misses a free throw) +.64*.5 (probability Davidson hits the free throw AND KU scores on the final possession) + .64*.5*.7 (probability KU wins in OT) = 88.4 %. So unless KU believed that Davidson had a less than 12% chance of hitting a three-pointer on their final shot, they should have fouled. Tinkering with the assumptions a little bit, say KU only has a 60% chance in OT, Davidson somehow gets Stephen Curry, a 90% shooter, to the line to take their foul shots, and KU only scores 40% of the time to end regulation. This is pretty much as pessimistic as you could possibly be about the value of the fouling strategy. KU's winning pct is still 71%. Given the busted-ass play that Davidson ran to try to get a three, and the fact that they took it too late in the clock to be able to hope for a putback, Davidson might have had a less than 29% chance of winning the game.

If it were UNC in this situation and I were able to make the decision, I'd be putting Davidson on the line. But I can guarantee you it wouldn't even cross Roy Williams's mind.

BRUECHIPS

P.S. - After writing this, I realized I had neglected a third option, which we'll call the "UCLA strategy", which would be foul, get away with it, take the ball, and dunk it at the other end as time expires.