The Journal Gazette
Tuesday, December 07, 2021 1:00 am

Decisions, decisions

Study of umpires offers insight on how we expend mental energy

Christer Watson

We all have a hard time making decisions. I usually try to avoid spending much time or effort on decisions that are not important to me. I have always assumed others do likewise.

It turns out this process, deciding when to be careful about decisions and when to be casual, can be studied – in detail.

This was a study published last summer and led by an economist from Columbia University. The best part? It involves baseball.

The scientists here analyzed data that has been collected since 2008, covering 26,000 games in all. Major League Baseball, as part of every official game, uses a technology called PITCHf/x to track the position of pitches. This technology is used to evaluate umpires and to display on broadcasts whether the ball crosses the strike zone.

This data set provides a nice way to develop a description of how humans make careful decisions. A typical home-plate umpire will observe about 300 pitches in a game. Many of those pitches are hit by the batter or at least swung at, and therefore don't need to be carefully judged. About 120 pitches per game, however, have to be judged as either strikes or balls.

The scientists evaluated each of these called pitches as either correct or incorrect, using the PITCHf/x technology. About 84% of pitches, on average, were called correctly.

That percentage, however, was not the same for all game situations. Sometimes, umpires would appear to do a better job calling a pitch. By observing these variations in pitch-calling quality, the scientists developed a description of how umpires were using their mental energy.

The basic idea is that umpires, like all other people, have to exert mental effort to make a good decision. We have a limited amount of mental energy. These two ideas, that decisions require energy and that energy can run out, lead to all sorts of patterns in when bad decisions are made.

For example, immediately after making an important decision, umpires appear mentally tired and, as a result, make more mistakes.

To make this quantitative, the scientists had to calculate the importance of each called pitch. They called this idea leverage and it comes out of modern baseball analytics.

At each moment in a game, the home team has a percentage chance that it will end up winning the game. This percentage is based on the game situation: the current score, the inning and so on. Each called pitch, either ball or strike, will change this win probability, typically by a small amount.

This is the leverage number, the difference in win probability between whether the umpire calls a ball or a strike. The higher this leverage number, the more important it is that the umpire make the correct call.

The leverage for a typical pitch is very small, about 1%. This will depend on the game situation. For example, a typical leverage would be bottom of the sixth inning, home team batting and up by three runs, two outs, no balls, two strikes, a runner on third.

A high-leverage situation would have a leverage of 8%. An example: top of the ninth inning, visiting team batting down by three runs, bases loaded, no outs, no balls, two strikes.

Analyzing all these called pitches, umpires are more accurate when the pitch is important. The effect is not dramatic, but it is enough to be measured.

For a typical pitch, umpires can be ranked on how accurate they are. Out of 0 100 umpires, a typical umpire will rank in the middle, at 50.

When the situation changes from a typical pitch to a somewhat important pitch, an umpire's accuracy increases enough to change them from ranking 50th to ranking 27th best out of 100.

That is, a middling umpire becomes a very good umpire, just by the situation being more important.

The scientists discovered even more. After important, high-leverage situations, umpires perform worse. A common shift can move an umpire from ranking 50 out of 100 down to ranking 55th best.

That is, an umpire gets tired after an important decision. He has used up his mental energy and has a harder time making the correct call.

This effect, however, disappears after each half-inning. That is, the few minutes' break is enough for an umpire's mental energy to be restored.

The last cool result is that umpires will anticipate the future. If, given a situation, umpires guess that a future situation will be really important, they will tend to save their mental energy and, as a result, they make worse calls. The shift here can move an umpire from 50 out of 100 down to 61st out of 100.

So there are probably two lessons to take away. First, remember that decision-making is tiring. Second, we can be intelligent about the effort we spend and learn to save it for only important situations.


Christer Watson, of Fort Wayne, is a visiting assistant professor of physics at Purdue University Fort Wayne. Opinions expressed are his own. He wrote this for The Journal Gazette, where his columns normally appear the first and third Tuesday of each month.

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