Chapter 1

Streaks

1. Introduction

Most people who watch or participate in sports think that hot and

cold streaks occur. Such streaks may be at the individual or the

team level and may occur in the course of one contest or over many

consecutive contests. As we will see in the next section, there are

different probability models that might explain such observations.

Statistics can be used to help us decide which model does the best

job of describing (and therefore predicting) the observations.

As an example of a streak, suppose that a professional basketball

player has a lifetime free throw percentage of 85%. We assume that

over the course of her career, this probability has remained roughly

the same. Now suppose that over the course of several games, she

makes 20 free throws in a row. Even though she shoots free throws

quite well, most sports fans would say that she is “hot.” Most fans

would also say that because she is hot, the probability of making

her next free throw is higher than her career free throw percentage.

Some fans might say that she is “due” for a miss. The most basic

question we look at in this chapter is whether the data show that in

such situations, a significant number of players make the next shot

(or get a hit in baseball, etc.) with a higher probability than might

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http://dx.doi.org/10.1090/stml/057/01