For unto
everyone that hath shall be given, and he shall have abundance; but
from him that hath not shall be taken even that which he hath.
In other words, the rich get richer and
the poor get poorer. Merton suggested that the positive behaviors of
high status people are more likely to be recognized and rewarded than
those of low status individuals, while high status people's mistakes
are more likely to be overlooked. This creates a positive feedback
loop in which increased confidence causes their performance to
improve and their reputation to increase over time. The opposite
happens to low status individuals. Their mistakes are more apparent,
leading to negative feedback, stress and disruption of performance.
Merton also coined the term
self-fulfilling prophecy, in which predictions result in
behaviors that cause the predicted outcome to occur. The Matthew
effect is a type of self-fulfilling prophecy in which the observer's
positive (or negative) expectations cause more (or less) successful
behavior in the target over time. This has broad implications for
people's self-esteem and the inequality of their social and economic
outcomes.
Two business school professors, Jerry Kim and Brayden King, looked for evidence of the Matthew effect in
major league baseball. They predicted that a pitcher's status would
influence calls by the home plate umpire. Pitcher status was defined
as the number of times he had previously been chosen to the All-Star
team. It was predicted that, as the number of All-Star appearances
by a pitcher increased, more of their balls would be called strikes
(over-recognition) and fewer of their strikes would be called
balls (under-recognition). The study was made possible by the
Pitch f/x system, in place in all major league ballparks, in which
cameras objectively measure whether each pitch is in the strike zone.
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The data base was all the pitches taken
(not swung at) by the batter during every game of the 2008 and 2009
seasons. These pitches must then be called either a ball or a strike
by the umpire, and each call was evaluated for correctness. These
data were related to over two dozen pitcher, batter, catcher, umpire
and situational characteristics. Some of these variables are of real
importance to baseball fans, but they could all be statistically
controlled in order to evaluate the status hypothesis.
Baseball fans may be interested in the
big picture—the distribution of correct and incorrect calls among
the almost 800,000 calls the researchers measured.
Called Ball
|
Called Strike
|
|
Actual Ball
|
87.10%
|
12.90%
|
Actual Strike
|
18.80%
|
81.20%
|
The umpires were correct about 85% of
the time. (There were more actual balls than actual strikes.)
Umpire bias favored the batter, since more strikes were called balls
than balls were called strikes. The count (the number of balls and
strikes to that point) had a big effect. For example, the likelihood
that the umpire mistakenly called a strike was 62% lower when the
count was 0-2 and 49% higher when the count was 3-0. Apparently,
umpires don't like their call to end an at-bat. Umpire calls also
tended to favor the home team. Errors of both over- and
under-recognition increased with the situational importance of the
at-bat.
The hypothesis was strongly confirmed.
Look first at over-recognition: Holding all other variables
constant, the more trips a pitcher had made to the All-Star game, the
more likely a ball was to be called a strike. The probability of a
mistaken strike call increased from 12.8% among pitchers who had no
All-Star appearances to 14.9% among pitchers with five or more
appearances. Each additional trip to the All-Star game increased the
likelihood of over-recognition by 4.9%.
The situation was reversed for under-recognition, also confirming the hypothesis. A strike thrown
by a pitcher with no All-Star appearances was mistakenly called a
ball 18.9% of the time, but only 17.2% of the time if the pitcher had
five or more appearances. Each trip to the All-Star game decreased
the likelihood of under-recognition by 2.7%.
In further analyses, the authors were
able to show that, with this large data set, pitcher status also had
statistically significant effects on the outcome of the at-bat (the
total bases reached by the batter) and the game (whether the
pitcher's team won). In an analysis that made some admittedly
questionable assumptions, they calculated that umpire errors alone
were worth approximately $575,000 in salary to a high status pitcher
over the course of his career.
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Of course, Matthew effects can occur
any time one person evaluates another—a teacher grading a student,
a boss rating a worker, a reviewer reading a manuscript, etc.
As a demonstration of how quickly performance expectations can occur,
consider a study by Ned Jones and others. Participants watched a
videotape of a college student answering 30 difficult questions, with
feedback after each item indicating he had answered 15 of them correctly. In the
ascending condition,
the student gradually improved. He got three of the first ten right,
five of the second ten, and seven of the last ten. In the descending
condition, the pattern was
reversed. (The difficulty of the questions was held constant by
asking exactly the same questions in the opposite order.) First
impressions mattered a great deal. The student was rated as more
intelligent in the descending than in the ascending condition. The
authors had hoped the ascending student would get some credit for
improvement, but it didn't happen.
In
this experiment, as in baseball, the expectations were based on the
target's actual past performance. However, expectations can be based
on gender, race, class or other social categories. In other words,
stereotypes based on
group membership can create self-fulfilling prophecies leading to
discrimination.
There
is no reason to think that umpires and ballplayers are consciously
aware of the systematic nature of these errors. A New York
Times article about the Kim and King study included the usual quotes from baseball people expressing
their surprise at or disbelief in the results. Most teachers, bosses
and reviewers probably think they're being objective, too.
In major league baseball, the
technology is already in place to have balls and strikes called
automatically using the Pitch f/x system. Why would anyone (except maybe Clayton Kershaw) not
think that's a good idea?
You may also be interested in reading:
Is Democracy Possible? Part 1 (see also Parts 2 and 3)
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