In Game 3 of the 2011 World Series, Albert Pujols tied a record with three home runs in a World Series game as the St. Louis Cardinals defeated the Texas Rangers. This extraordinary feat has been accomplished only by Pujols and two guys named Babe and Reggie. You know you are in elite company when the other record holders are nearly universally recognized by sports fans by only their first name.
In fact, Pujols hit home runs in three consecutive at bats, leading sports analysts everywhere to talk about how "hot" Pujols was at the plate. As good a hitter as baseball has seen in the past decade, Pujols career .328 batting average and 445 home runs are nothing short of remarkable. For his career, he has averaged a home run for every 14.2 at bats. Thus, the odds he would hit home runs in three consecutive at bats is 1 / 2,852! Add to that the fact that Pujols walks nearly once every seven plate appearances and the odds go up further. His performance in Game 3 seems like a hot streak to the casual observer and novice statistician.
On the other hand, in Games 1, 2, 4, and 5, Pujols is a combined 0-12. The odds that a lifetime .328 hitter goes 0-12? Less than 1 in 100 streaks of 12 will be hitless. Thus, Pujols appears to have had an extraordinary cold streak with an even more amazing hot streak sandwiched in the middle of his slump.
Of course, Tom Gilovich and other psychologists have demonstrated that streaks in sports (and other areas of life) are less predictable than we might think. For one, we tend to notice streaks of hits or strike outs, but fail to notice (or disregard) the more frequent occurrences where what appear to be streaks are nothing more than random variation in outcomes. This is particularly likely to happen when we base our conclusions on a small sample of data such as the eighteen World Series at-bats Albert Pujols has had in 2011.
The take home message? Pujols is a good bet to get a hit or two in Game 6 (and 7, if necessary), possibly with a home run, but the odds of this happening are probably more similar to his 2011 and career averages, and less affected than we might think by his "streaks" in the 2011 World Series.
