5. Data from Various Sports 39

0.35 0.4 0.45 0.5 0.55 0.6 0.65

Winning percentage

4

6

8

10

Avg.

length

Figure 20. Actual and theoretical longest winning streak lengths

We now turn to team statistics; we seek to answer the question of

whether teams exhibit streaky behavior. One way to check this is to

recall that if a process has a positive autocorrelation (meaning that

the probability of a success in a given trial increases if the previous

trial is a success), then the lengths of the longest streaks will, on

average, be longer than in the Bernoulli trials model. This will be

true of both winning and losing streaks.

There are 390 team seasons in our data set. For each of these

seasons, we computed the lengths of the longest winning and losing

streaks. Then we grouped the team seasons by rounding the win-

ning percentages to the nearest multiple of .01. (So, for example, a

winning percentage of .564 is rounded to .56.) For each group, we cal-

culated the average lengths of the longest winning and losing streaks.

Figures 20 and 21 show these average lengths, as well as the theo-

retical average lengths in the Bernoulli trials model. (The theoretical

lengths are shown as a solid curve.) We note that the fit between the

actual and the theoretical longest streak lengths is very good, except

perhaps at the ends of the graphs. But even at the ends, there is