The Language of Argument

2 4 3

The Language of Probability

heuristics when the situation is nonstandard—that is, when the situation is

complex or out of the ordinary.

To avoid such mistakes when making important judgments about prob-

abilities, we need to ask, “Is the situation sufficiently standard to allow the

use of heuristics?” Because this is a mouthful, we might simply ask, “Is this

the sort of thing that people can figure out in their heads?” When the answer

to that question is “No,” as it often is, then we need to turn to more formal

procedures for determining probabilities.

In a remarkable study,^3 Thomas Gilovich, Robert Vallone, and Amos Tversky

found a striking instance of people’s tendency to treat things as statistically

significant when they are not. In professional basketball, certain players have

the reputation of being streak shooters. Streak shooters seem to score points in

batches, then go cold and are not able to buy a basket. Stated more precisely,

in streak shooting, “the performance of a player during a particular period is

significantly better than expected on the basis of the player ’s overall record.”

To test whether streak shooting really exists, the authors made detailed study

of a year’s shooting record for the players on the Philadelphia 76ers. This team

included Andrew Toney, noted around the league as being streak shooter. The

authors found no evidence for streak shooting, not even for Andrew Toney.

How would you go about deciding whether streak shooting exists or not? If,

as Gilovich, Vallone, and Tversky have argued, belief in streak shooting is a

“cognitive illusion,” why do so many people, including most professional

athletes, believe that it does exist?

Discussion Question

THe lanGUaGe oF ProbabiliTy

The first step in figuring out probabilities is to adopt a more precise way of

talking. Our common language includes various ways of expressing prob-

abilities. Some of the guarding terms discussed in Chapter 3 provide exam-

ples of informal ways of expressing probability commitments. Thus, someone

might say that it is unlikely that the New England Patriots will win the Super

Bowl this year without saying how unlikely it is. We can also specify various

degrees of probability. Looking out the window, we might say that there is

a fifty-fifty chance of rain. More vividly, someone might have remarked that

Ron Paul does not have a snowball’s chance in hell of ever winning a presiden-

tial election. In each case, the speaker is indicating the relative strength of the

evidence for the occurrence or nonoccurrence of some event. To say that there

is a fifty-fifty chance that it will rain indicates that we hold that the evidence is

equally strong that it will rain rather than not rain. The metaphor in the third

statement indicates that the person who uttered it believed that the probabil-

ity of Ron Paul winning a presidential election is essentially nonexistent.

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