Chapter 1
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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