We'll have robot quality umps by 2059

In school, a report card with grades of 87 percent probably would have gotten you ice cream or the keys to your parents' minivan for the weekend, depending on your age. Do it all through high school and you'll probably get a decent scholarship to the college of your choice and onto a professional degree and lucrative career choices if you kept it up. But if you're a Major League Baseball umpires and you worked a game behind home plate the night before, it means you're just league average, and you're probably getting an earful about where you can improve.

But improve is what umpires have done every year since we've had access to robust PITCHf/x data. When you plot out every pitch umpires had to call a ball or a strike from Baseball Savant and judge accuracy using its strike zone definition, the consistency of this improvement stands out immediately. Over the past seven seasons, umpires have improved their accuracy by 0.37 percentage points each year, a value that seems negligible until you work out that over the course of the season the decision to call a ball or strike comes down to the umpire on roughly half of pitches thrown. This represents more than 350,000 strike zone judgement calls home plate umpires, as a group, must make each year.

This is not new information. Over the past few years, these same data have been mined to draw a similar conclusion. While the strike zone may have succumbed to gravity over the past several seasons, overall umpires are calling the true strike zone more accurately with every year.

There are two types of errors the home plate umpire can make when judging a ball or strike. Balls outside the strike zone can be called for strikes. These are noted in the figures below as "BCS" and are typically reported as the percentage of total calls made (%BCS), not total number of pitches thrown. Alternatively, a pitch in the zone can be called for a ball. We'll call those strikes called as balls (%SCB).

There are two main takeaways from the figure below, which also mirrors results presented elsewhere. Umpires are more likely to call a ball as a strike than they are to mistake a strike for a ball. This is how umpires have ruined the game, by racking up undeserved strikes against a league of oppressed batters. It's also clear that the gains in strike zone accuracy have come primarily by reducing %SCB, which has been nearly halved. %BCS, on the other hand, has shown a negligible decrease since 2008. Keep that in your back pocket, it will be important later on.

While other studies looking at the changes in umpire accuracy as a function of experience and relating this to exposure to first the QuestTec Umpire Information System and, more recently, the league's Zone Evaluation policy, there is a compelling reason to look at umpires by age.

Considerable academic attention has been devoted to the study of how our cognitive ability diminishes with age. Among the many areas where we see declines is our ability to process and to learn and recall new information. For most of us, this deterioration will be so gradual that clear signs won't present themselves until our golden years. The most sadistic of us will work our whole lives for the right to decide whether a 95 MPH cutter or a looping 12-6 curve caught in a portion of an invisible box several feet in front of us at least somewhat obscured by a large man in protective padding is a ball or a strike. For these people, a decline in cognitive ability may impair their ability to improve their accuracy.

Since 2008 there have 118 umpires have called balls and strikes in a game. Their birth years range four decades, spanning Quinn Wolcott and Pat Hoberg, born in 1986, to Derryl Cousins, who was born in 1946 and retired in 2012 at the age of 66. If we break these umpires out into four fairly equal groups by birth year, it's clear that, overall, the youngest umpires have been about 1 percent more accurate than their older counterparts.

So the younger umpires have been slightly better, but how have umpires of different ages adapted as they've been coached on their accuracy? Plotting out the improvement in umpire accuracy by the birth year bins used above shows that younger umpires have improved the most over time. Most of the young umps didn't enter the league until 2010, so the data for the prior two years was suppressed. Nonetheless, this seems to support the hypothesis that younger umpires have greater facility in applying the evaluation and feedback they receive on their strike zone judgement.

While steeper improvement seem the most likely root of this trend, potential confounds do exist for the youngest group of umpires. Most umpires make it to MLB around 30 years of age. In 2008 and 2009, there were only five umpires born after 1976 in the majors. This past season, there were 29. It could be possible that baseball has changed the selection criteria for umpires promoted to the majors, but even if you remove that group, the trend of decreasing improvement in accuracy with age remains for the other three. Similarly, the dismissal of poor performing umpires could also cause an improvement year over year for umpires as a collective. This may not, however, be age specific, which make these dismissals akin to waning tides lowering all ships.

That younger umpires have been able to improve their strike zone accuracy to a greater degree than their aged brethren seems intuitively valid and to be supported by scientific evidence. But, what's surprising is how they're doing it.

Recall that most of the drive behind improved accuracy has been achieved by reducing the number of pitches outside the strike zone that were called balls. Well, if we build charts like the one above for %BCS and %SCB and look at the trends, you'll see another striking difference between the age groups.

Each cohort of umpires has seen roughly the same degree of improvement in %SCB. But look at the trend of %BCS and you'll see most of the change concentrated in the youngest group of umpires. As umpires get older, their ability to improve in %BCS decreases, and the oldest umpires have shown almost no change

Umpires' mastery over the strike zone has been on a steady, linear progression toward robotic perfection since we've been able to track it in the public domain. The adjustment that younger pitchers have been better able to make is calling fewer balls as strikes each year. If the yearly changes continue on, we'll have robot quality umpires in the summer of 2059. Maybe even sooner, as the older, less adaptable umpires are replaced.

. . .

Matt Jackson is a featured writer for Beyond the Box Score and a staff writer for Royals Review. You can follow him on Twitter at @jacksontaigu.