Yet new research shows that umpires choose not to devote equal attention to every call, and it shows further that they’re doing the right thing. The rest of us should follow their example.

The new findings, from researchers at Columbia University, the University of Maryland, and the University of Ottawa, hold implications that go far beyond baseball. They extend into all decision making and into much of economics. In economic theory, humans are calculating machines constantly figuring odds and outcomes in order to make decisions. In reality, we all know that isn’t true. We just can’t give full attention to all the decisions we make—some 35,000 a day, says one study. We don’t have enough time, nor do we have enough mental firepower; focusing intensely is hard.

The new research considers attention more realistically as “a depletable stock that may be rationally managed,” and umpires are near-perfect subjects for studying it. A home plate umpire makes about 120 ball-or-strike decisions in a typical game. Staggering amounts of data are available for every one of them, including, crucially, whether the call was right or wrong. TV coverage of games routinely includes a strike-zone box superimposed on the camera shot of every pitch, and it turns out this technology, called PITCHf/x, has been in operation at every MLB ballpark since 2008. Thus the researchers could obtain “the objectively correct call” and compare it with the umpire’s call. From the MLB website they collected this data and much more on 3.2 million calls by 127 home-plate umpires in 26,523 games between 2008 and 2018.

The researchers combined this ocean of data with what they call the “mild” assumption that, all else equal, a correct call reflects more umpire attention than an incorrect call. Then they went to work. Here’s what they found:

Umpire decisions get worse later in the game. That finding is no surprise; several other studies support the existence of “decision fatigue” in many settings.

But it isn’t just the number of decisions that use up an umpire’s stock of attention; it’s also the importance of the decisions. Using MLB data to simulate five million games, the researchers identified scenarios for ball-or-strike calls with the highest “leverage,” a term used by baseball afficionados for the importance of any event to the game’s outcome. The more high-leverage calls that umpires have to make, the more likely it is that their later calls will be wrong.

But a benefit comes with that cost. Because umpires devote more attention to high-leverage calls, those calls – the most likely to determine the game’s outcome – are more likely to be correct.

Most important, umpires will deliberately allocate less attention to calls—and make more errors—if they have good reason to expect high-leverage calls ahead. As the researchers write, umpires will “optimally conserve attention by strategically ‘allowing’ more errors in the present” so they’ll have more attention available for anticipated high-stakes calls in the future. With more attention to use on the most important calls later, umpires are more likely to make those calls correctly.

Which is where Mark Zuckerberg, Barack Obama, and Steve Jobs come in. They all made the choice to wear the same thing every day so that first thing in the morning they could “conserve cognitive capital,” as the researchers observe, to expend on more important decisions later. “I wear only gray or blue suits,” Obama told Vanity Fair in 2012. “I don’t want to make decisions about what I’m eating or wearing. Because I have too many other decisions to make.” Zuckerberg, who was inspired by Steve Jobs’s blue jeans and black mock turtleneck to adopt his own daily uniform (gray t-shirt), told a public Q&A session in 2014, “I feel like I’m not doing my job if I spend any of my energy on things that are silly or frivolous about my life.”

The researchers call this “rational inattention,” and it’s a model for us all. We have only a limited supply of attention, and, once depleted, it can be restored only by time and rest. Logical conclusion: Automatize recurring low-value decisions, and don’t spend attention on new low-value calls; save it for the high-leverage ones. You’re more likely to get the small ones wrong, but the benefits are worth it.