koufax kicks orie glen, ph.d. contributing editor july 21 1998 |
Kicker/goalie = pitcher/batter American soccer-bashing pundits reserve a special place for penalty kick shootouts. Sports Illustrateds Rick Reilly describes the current procedure for breaking ties as analogous to a free throw contest. He wants action. (You want action? Go here.) You know what? He's just plain wrong. To people with a brain, a shootout is like deciding a basketball game by having the teams play baseball. Yep, baseball. America's national blankin pastime. Babe Ruth. Rajah Clemons. 3000 Ks. Tony Gwynn. Greg Maddux the great cerebrist on the mound. Did you ever consider that Brazils goalie might anticipate tendencies as well as Maddux does? Here at the Jones, we could bury you with hypertext consisting of our collective musings as to how Americans can (a) find poetry in the mental and physical competition between two guys standing sixty feet, six inches apart, one wielding a bat, one armed with an apple-sized pelota, yet (b) dismiss as ridiculous soccer's isomorphic scenario, but we'll let you fill in the blanks yourself. Weve got bigger fish to fry. We want to explain why
you should get your kicks from those life-stopping kicks, and why they reveal yet another
dark side of ego in sports.
Before soccer there was Matching Pennies. Matching Pennies is really about baseball. Heck, everything is really about baseball. Economics professors teach Matching Pennies in game theory courses around the world (much like soccer is played around the world). In fact, three game theorists recently received Nobel Prizes in economics. So, even if you cannot shake that predisposition to abhor
anything soccer related, and you're counting the days til The Deuce returns to those
Superfights of the 70s, stick around. Game theory rocks. Here we go. Rajah and Clemente each have a penny they can place heads up (H) or tails up (T). Rajah wants to avoid matching. Clemente wants to match. Rajah throws fastball. Clemente thinks fastball, Clemente wins. Clemente thinks curve, Clemente loses. So, what should Rajah do? If he always plays H, then Clemente will figure it out and also play H. Therefore, Rajah should randomize 50-50 between H and T (taking the quality of the pitches out of the equation for now). If Rajah does this, it doesnt matter what Clemente does hell win half the time. If Clemente plays H, half of the time Rajah is playing H, so Clemente wins, and half of the time Rajah is playing T, so Clemente loses. If Clemente plays T, he also wins half the time and loses half the time.
Now, lets apply this logic to soccer. Two players, a goalie we'll call Gehrig and a kicker Koufax. In watching the World Cup (or at least the highlights), you may have noticed that Koufax seems to have two options. Left or right. Gehrig has the same two options. Computing the probability of a goal gets a little more difficult here. It depends upon Koufaxs skill level. Koufax may be able to score with incredibly high probability, even if Gehrig guesses correctly. How? By lofting the ball into the upper corner. However, a lesser player aiming for the corner may either miss high or hit low. Were going to summarize all of this information by
letting Q be the probability that Koufax scores even if Gehrig guesses correctly. Q stands
for quality. (Formerly, it stood for Quentin Dailey, but hes long gone.) A dead guy
has a Q of 0, and Pelé a Q of 1. The rest of us are in between. You might be tempted to say that it doesnt take game
theory to say that (a) better players score more often and (b) the players should
randomize. |
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