Yes, we encounter regression to the mean almost every day and, yes, almost nobody understands it.
I was riding a stationary bike this morning and watching some ESPN talking heads speculating about Peyton Manning’s fantasy football value. They talked about his age (38), his teammates, and the teams he would be facing. They didn’t talk about regression to the mean.
I looked up ESPN’s fantasy football projections and found this:
2014 Outlook: The reigning fantasy points champion lost Eric Decker, arguably the Broncos' most productive wideout, to free agency. But don't shed a tear for Manning, who still has two dominant receivers in Demaryius Thomas and Wes Welker (provided he recovers from his latest concussion), an impact tight end in Julius Thomas and another superb dink-and-dunk receiver in free-agent acquisition Emmanuel Sanders. Don't expect him to repeat last year's record-breaking season, especially since he is 38 and has four matchups against the tough NFC West. But even if Manning takes a step back, he has a very good shot at defending his fantasy points title.
ESPN predicts only a slight drop off in Manning’s numbers: 48 touchdowns instead of 55, 12 interceptions of 10, 368 fantasy points instead of 406. They project Manning to be the top quarterback, above Aaron Rodgers (347 points), Drew Brees (329), Matthew Stafford (284), and Andrew Luck (282). They didn’t talk about regression to the mean.
To understand regression, suppose that one hundred people are asked twenty questions about the NFL. Each person’s “ability” is what his or her average score would be on a large number of these tests. Some people have an ability of ninety, some eighty, and some near zero.
Someone (let’s call him Cory) with an ability of, say, 80 is not going to get 80 percent correct on every test. Cory will know the answers to more than 80 percent of the questions on some tests and fewer than 80 percent on other tests. Cory’s score on any single test is an imperfect measure of his ability.
What, if anything, can we infer from a person’s test score? A key insight is that someone whose test score is high relative to the other people who took the test probably also had a high score relative to his or her own ability. Someone who scores in the 90th percentile on a test could be someone of more modest ability—perhaps the 85th, 80th, or 75th percentile in ability—who did unusually well, or could be someone of higher ability—perhaps the 95th percentile in ability—who did poorly. The former is more likely because there are more people with ability below the 90th percentile than above it.
If this person’s ability is in fact below the 90th percentile, then when this person takes another test his or her score will probably also be below the 90th percentile. Similarly, a person who scores well below average is likely to have had an off day and should anticipate scoring somewhat higher on later tests. This tendency of people who score far from the mean to score closer to the mean on a second test is an example of regression toward the mean.
We encounter regression in many contexts, pretty much whenever we see an imperfect measure of what we are trying to measure—which includes athletic ability.
Many sports fans are convinced that champions choke—that athletes who achieve something exceptional usually have disappointing letdowns afterward. Evidently, people work extraordinarily hard to achieve extraordinary things, but once they are on top, their fear of failing causes the failure they fear. The same seems to be true in many professions.
After Roger Maris surpassed Babe Ruth by hitting 61 home runs in 1961, he hit only 33 homers in 1962 and 23 in 1963. After Martin Scorsese made Taxi Driver in 1976, he made the god-awful New York, New York in 1977.
The most famous example is the Sports Illustrated cover jinx. After Oklahoma won 47 straight college football games, Sports Illustrated’s cover story was, “Why Oklahoma is Unbeatable.” Oklahoma lost its next game, 28–21, to Notre Dame. After this debacle, people started noticing that athletes who appear on the cover of Sports Illustrated are evidently jinxed in that they do not perform as well afterward. In 2002, Sports Illustrated ran a cover story on the jinx with a picture of a black cat and the cute caption “The Cover No One Would Pose For.” More recently, we have the Madden Curse, which says that the football player whose picture appears on the cover of Madden NFL, a football video game, will not perform as well afterward.
Athletic performances are an imperfect measure of skills and consequently regress toward the mean. Among all major league baseball players with batting averages above 0.300 in any season, 80 percent did worse the previous season and 80 percent do worse the following season. Among pitchers with earned run averages below 3.00 in any season, 80 percent did worse the previous season and 80 percent do worse the following season. Of those baseball teams that win more than 100 out of 162 baseball games in a season, 90 percent did not do this well the previous season and 90 percent do not do as well the next season. It is not their abilities that are fluctuating. Their performances are fluctuating around their abilities.
The Sports Illustrated Curse and the John Madden Curse are extreme examples of regression toward the mean. When a player or team does something exceptional enough to earn a place on the cover of Sports Illustrated or Madden NFL, there is essentially nowhere to go but down. To the extent luck plays a role in athletic success, and it surely does, the player or team who stands above all the rest almost certainly benefited from good luck—good health, fortunate bounces, and questionable officiating. Good luck cannot be counted on to continue indefinitely, and neither can exceptional success.
Peyton Manning’s phenomenal 2013 season surely benefited from more good luck than bad. Defensive players slipping, offensive players not slipping. Defensive players making bad guesses, offensive players making good guesses. Fumbles lost and recovered. Passes caught and dropped. Holding penalties called and not called. The list is very long. Luck—good and bad—is why the best team doesn’t win every game, why player stats go up and down from one game to the next.
Manning is a Hall-of-Fame quarterback, but 2013 was not a below-average season for him. Manning is surely not as good as he seemed last year, and almost certainly will not do as well this year. You can take that to the bank.