Regression Toward the Mean
The phenomenon of regression toward the mean was first noted by Sir Francis Galton in
the nineteenth century. He observed that in any series of random events clustering around
an average, an extraordinary event is, by mere chance, most likely to be followed by an
ordinary event. Thus, very tall fathers are likely to have slightly shorter sons and very
short fathers, somewhat taller sons. Regression toward the mean helps explain why great
movies are often followed by poor sequels, why poor presidents often have better
successors, and why extremely intelligent women tend to have slightly duller husbands.
Paul Schaffner provides an excellent example of regression toward the mean that you can
present in class. Participants in his study assumed the role of a teacher attempting to
encourage a hypothetical student to arrive promptly for an 8:30 A.M. class. The student’s
arrival time, which varied from 8:20 to 8:40 for 15 consecutive days, was recorded on a
computer. Each day the teachers could choose to praise, reprimand, or say nothing to the
student. As expected, they praised him when he was early and reprimanded him when he
was late. Unknown to the teachers, the student’s arrival time was pre-programmed and
thus unrelated to the teacher’s response of the previous day. Due to regression alone, the
student’s arrival time tended to improve, that is, regress to 8:30, after being punished for
being late and to deteriorate (again by regressing to 8:30) after being praised for arriving
early. Schaffner found that 70 percent of his teachers concluded that reprimand was more
effective than praise in producing prompt attendance by the student.
Regression toward the mean operates with regularity in sports, particularly when luck is
mixed with skill. While sports commentators recognize its effect, they often offer
different explanations. Amos Tversky notes, “Listen to the commentators at the Winter
Olympics. If a ski jumper has done well on his last jump, they say, ‘He’s under immense
pressure, so he’s unlikely to do as well this time.’ If he did poorly, they say, ‘He’s very
loose and can only improve.’”
Perhaps the so-called “Sports Illustrated Jinx” can also be understood in terms of
regression toward the mean. According to sports folklore, the “Sports Illustrated Jinx”
dooms teams or athletes appearing on the cover to lose after they are featured. For
example, Earvin “Magic” Johnson of the Los Angeles Lakers graced the cover when his
team was leading the NBA championship series. The Lakers then lost the title to the
Boston Celtics in seven games. Similarly, the New York Islanders were on the cover
going for their fifth straight Stanley Cup. They lost four straight to Edmonton. Tennis
players and golfers seem to suffer the most after appearing on the cover. Researchers Tim
Leone and Robbie Gluckson found that the performance of these athletes fell off more
than 83 percent of the time. The performance of swimmers, skiers, foot-ball rushers, and
crew members also dropped off significantly after cover appearances. At the same time,
the researchers found that baseball pitchers and teams, as well as basketball players and
teams (“Magic” Johnson being one exception), did well more than 70 percent of the time
after they were on the cover. Several observers have noted that athletes appear on the
cover only after performing unusually well. Regression toward the mean would explain
their poorer subsequent performance.