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koufax kicks
(continued)
orie glen, ph.d.


A third option

The question that just nags nags nags is why the heck doesn’t Koufax kick the ball into the center of the net? If Gehrig is jumping left or right, that means that the center is open.

Good question.

Let’s expand the game and find out what’s up. We’ll assume that if Gehrig plays C (for center) and Koufax goes with either L or R, Koufax scores. But, if Koufax and Gehrig both play C, Koufax loses every time. After all, Gehrig is just standing there, like Bill Buckner, only he stops the ball.

Now, if Gehrig always chooses L or R, then Koufax can just play C, score for sure, and make Gehrig look foolish. In that case, Gehrig would want to play C sometimes as well. And Koufax should randomize so that Gehrig doesn't know whether to play L, C, or R.

And, since Koufax would have three options instead of two, the chances that Gehrig could match would be reduced. So, why don’t we see kicks in the center of the net?

Two answers: ego and ego.


Pride goeth before a dive

First, ego. Let’s say Koufax has a quality of Q=1/2 and both players play like game theory says they should. Then, one out of five times, Koufax kicks it into the center of the net. And, one out of five times, Gehrig just stands in the center.

Since their actions are independent (Gehrig doesn’t know what Koufax will do and vice versa), the probability of Koufax kicking into the center and Gehrig standing there waiting for it equals 1 in 25 (that’s 1/5 x 1/5). This means that four percent of the time, Koufax kicks the ball to a stationary Gehrig.

Imagine this scenario. Koufax is one of the greatest athletes in the world, he’s dating a Spice Girl, and he kicks the ball into the center of the net, where Gehrig has luckily decided to stay. Koufax returns to England and goes on the BBC to explain: "I know that I kicked the ball to the center of the net to a waiting goalie and we lost the Cup, but it was an equilibrium strategy according to game theory."

Fact is, this won't happen. As badly as these guys want to win, they don’t want to win that badly. Neither do the goalies. That’s why they never just stand in the center. A German goalie who stood mid-goal would be practically begging some guys from Stuttgart to rearrange his face, if he dared show it.

Second, ego. By not kicking into the center, players signal their quality. Who benefits the most by using the additional strategy of kicking in the center of the net? A player with a Q of zero increases his chances of scoring from 50 percent to 66 percent, a 16 percent increase. But, a player with a Q of 0.8 increases his chances of scoring from 90 to 91 percent. Hardly worth it. Therefore, by kicking into the center, not only would a player risk humiliation, he would be announcing, "Hey, I suck!" Would Nike pay for that?

We could go on and on with this. If the first two players score by going left, should the third go left? Wouldn't center be an obvious choice if the game were totally on the line?

Hey, this is actually sort of exciting. Wait, imagine this. A limping Kirk Gibson softly left-foots a roller toward the gaping middle of the net, having stolen Joe Gibbs sign. Lawrence Taylor reverses midflight, just nicking the ball, which nonetheless skips, bounces, creeps over the line.

You spell it like this: Gibson Outguesses Anticipatory Lawrence. G-O-A-L.

Don't care? Go watch Heidi again, ‘cause you'll never understand sports.
 


JONES

Orie Glen is the pen name of Scott Page, associate professor of Economics at the University of Iowa. In addition to maintaining an oral history of University of Michigan football (AC was way better than Desmond!), Scott runs a summer workshop in computational economics at the Santa Fe Institute and is part of a MacArthur Foundation working group on income inequality. He has done analyses of the economic impact of the Rose Bowl and the World Cup.

 

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