Kobayashi Maru, or How to Referee the Last Ten Seconds

In the NC game Monday night, the referees made two pivotal no-calls in the last 10 seconds of the game. Both calls went (ostensibly) in Memphis' favor, but ended up benefiting Kansas in the long run.

1. With 10 seconds left, a Memphis player is frustrated and slams the ball into the floor. The ball bounces 20 feet in the air and skitters away. Ordinarily, this is a technical foul, but with 10 seconds left in a 62-60 game the referee lets it slide. Memphis ends that possession up 3.

2. Then, with Kansas driving to score the tying basket, Memphis tries to foul, hoping to force Kansas to shoot 2 free throws rather than a tying 3-pointer. Again, the fouls are clear to see, but no call. Kansas hits a 3-pointer with 2 seconds left and wins in OT.

Both no-calls were motivated by an unwritten axiom of officiating -- let the players decide the outcome. Swallow the whistle late in close games so that the outcome is decided by players making plays rather than by referees making calls.

But I would argue that this is ultimately a no-win situation for the referee. If he makes either or both calls, he is violating a philosophical principle. But if he swallows his whistle, he is violating the actual rules of the game, which demand that he call what he sees.

The opinion of referees varies widely over what they should do in that circumstance. But while the stated opinions of experienced referees might be many and varied, their behavior is remarkably uniform. Most swallow the whistle, choosing principle over legal code.

But what I'm interested in is not the basketball argument but the philosophical (and ultimately moral and ethical) one.

What do you do in a no-win situation? And what do the choices you make in those situations say about you?

Take, for instance, a contestant on The Price is Right. She's the first spinner in the Showcase Showdown, and she land on 70 cents. She has a choice of spinning again to try to improve her score, or standing pat and hoping for the best. If she goes over $1.00, she's eliminated immediately.

Mathematically, the risk of losing by going over $1.00 is slightly less (a 70% chance) than the risk that one of the other two players will post a better score (a 75% likelihood), so the numbers say spin. But whether it's ignorance of the math, or crowd pressure, or simply conventional wisdom, most people stand pat on 70 cents.

It's a no-win situation; no matter what she does, the poor spinner has at least a 70% chance of losing. But, like the referee above, in a situation where there is a coin-flip type choice, over 90% go the same way.

Another game show example: Over on the Jeopardy boards we talk about a FJ scenario called "Stratton's Dilemma." Basically it goes like this:

1st place: 15,000
Second place: 10,600
Third place: 6,800

The second place player has a choice to make. Do you bet enough to keep 3rd place from passing you, or do you stand pat knowing you need 1st place to be wrong to have a chance anyway and hoping the 3rd place player won't know something the 1st place player doesn't?

According to the J-archive, players in Stratton's Dilemma end up winning the game less than 10% of the time. Yet even though there is just as much mathematical reason to bet small as there is to bet big, most bet at least enough to lock out the 3rd place player.

Again, maybe this indicates ignorance of the math involved. Or maybe this reflects the mindset of a Jeopardy player, namely, "If I have to lose, I'd rather lose because I bet too much than because I bet too little."

I have no conclusions on this yet. But it is curious. Why do people in no-win situations behave so predictably? And what do the choices we make when faced with an undesirable outcome say about us?