Academic journal article ETC.: A Review of General Semantics

A Sporting Proposition

Academic journal article ETC.: A Review of General Semantics

A Sporting Proposition

Article excerpt

If you could on average - dream along with me here - win four out of ten points playing tennis against Andre Agassi, then, based on pure chance, how many of your matches would you likely win from him?

Before getting to the answer, let's just take a quick look at what's involved. To simplify, let's ignore tie-breakers and the advantage the server has. Let's look only at putting points together into games and then games into sets in a three-out-of-five-set match. To win a game, you have to win at least four points by a margin of at least two points before Agassi does. This means you have to figure out all the sequences in which you could win points, say, you-1, Agassi-1, Agassi-2, Agassi-3, you-2, Agassi-4, and therefore that game to Agassi, that sort of thing. Then to win a set, you have to win at least six games by a margin of at least two games before Agassi does. Finally, to win the match, you have to win three sets before Agassi does.

The mathematical work, therefore, requires summing all the probabilities of all the sequences in which points could be won. I'm not going to get into that. I'm just going to report, based on good mathematical authority (1) that even if you win an average of four points in ten, your chances of winning a whole match against Agassi, are only one in two thousand.

Mathematicians and statisticians apparently love to examine sports in terms of the workings of pure probabilities. They ask such questions as "Can we build a model to account for the frequency [which averages about 3.0 per year] of major-league-baseball no-hitters?" Answer: Yes. (2) "Are the success-rate differences of National Football League (NFL) field-goal kickers in any given year more a result of skill or chance?" Answer: Chance, given the remarkable skill each kicker needs to get into the NFL in the first place. (3) "Which 1941 mark is likely to fall first: Joe DiMaggio's record 56-game hitting streak or Ted Williams's status as the most recent .400 (or better) hitter?" Answer: Ted Williams's status. (4)

The questions seem intended to hold attention while the actual work demonstrates the power of probability theory. Such analyses are not without a beating on mathsemantics. The last three analyses, for example, make the mathsemantic point that one can take many things (like winning streaks in sports or mutual funds) that seem to be under human control and explain them as just the normal variations of random events. That's an important mathsemantic point, one that children and many, perhaps most, adults fail to grasp. (5) But to extract the point convincingly from such examples requires considerable mathematical skill.

Mathsemantics differs from math in that it's less interested in the great power of math than in the confusing place where math and English meet and overlap, a place that happens, curiously, to be one that neither math nor English claims as its own territory. Thus the Mathsemantic Monitor finds no ready home either in math or English for most of his concerns. His examples are usually too simple to entice mathematicians and too number-laden to entice English specialists. He notes that the many mathsemantic errors that bedevil our lives receive little academic attention, including, of course, those errors that infect reports of sporting events.

You may remember that the first article in this series dealt with the case of the "80,000 books read," the investigation of which led to a library of only 9,500 books and an event more properly described as "80,000 presumed book-exposures." Or you may remember from the same article that the Federal Aviation Administration reported for fiscal 1992 that it had safely handled "about 143 million aircraft," an observation that completely obscured the fact that the entire U.S. scheduled air-carrier fleet at the time amounted to only about 5,000 planes. (6)

Well, here's a sports example of the same ilk, but on about the simplest possible level, taken from TV. …

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