These aren’t just empty sayings. In some circumstances, they might make the difference between life and death. Scientists who model how organisms gather food, for instance, have found that survival could depend on one’s foraging strategy, like whether to aim high or settle for the status quo. Most of us today confront a similar but lower-stakes quandary. For instance, University of Wyoming bioeconomist Matthew Burgess has studied how fishermen maximize their catch. After they arrive at a patch in the ocean and catch a few fish, is it better to move on to another in hopes of more? Or keep working on one that’s already delivered? 

In a new paper, Burgess and his colleagues developed a mathematical model to explore whether aiming high is a good idea and when it’s better to settle. The numbers suggest that both of those popular rules of thumb have some truth: The best outcomes come from aiming higher than average, but not so high that expectations are unreasonable.

How can you tell when you’ve aimed high enough?

What he and his colleagues found in this new paper is that “your optimal ambition is strictly above average,” he says, “but also strictly finite.” In other words, you should always aim higher than average—but aiming too high is a recipe for disaster. In the team’s computer model, individuals, called “agents,” searched for rewards over time, and periodically had to decide whether they were satisfied with what they had. If they were not, they continued searching. Then, at the end of the process, the team assessed which agents had amassed the most rewards.

They found that aiming too high resulted in worse outcomes than being more cautious, but a little caution went a long way. Accepting results that were less than average meant missing out.

“There's so many cultural messages that say that you can always just do better, you can always just try harder,” says Ekaterina Landgren, a post-doctoral fellow at Stanford and an author of the new paper. But this model suggests that’s not always the case. “When the rewards are more abundant, you should aim higher,” she says. “When the rewards are less abundant, that's when you're maybe more at the risk of overshooting.”

Is comparing yourself to other people a good or bad thing?

Of course, few of us look out at the world with a clear understanding of how abundant rewards are.  

“They explore scenarios where the agents know the true distribution of rewards, and scenarios where they estimate it from watching their peers and the rewards they get,” says James O’Dwyer, a theoretical ecologist at the University of Illinois in Urbana-Champagne who was not involved in the study. In studies modeling optimal foraging behavior, ecologists usually assume that organisms do have a sense of what’s out there, he says.  

But humans have Instagram, and it is likely that we try to estimate our own possibilities from what our peers post on social media. 

“Our perceptions of what we see in others change our decisions,” says Landgren. “When you're looking only at people who are doing better than you…you're blind to what you can and can't get, and it really distorts your perception of what's possible. That creates this danger that you keep searching and nothing's ever good enough, and you run out of time.”

Indeed, in the model, when individuals had to base their expectations of rewards on what the others found, they had a tendency to overshoot, leaving them with fewer rewards in the end.  

That made sense, Landgren says, and was, in a way, reassuring. “When you just get a list of someone's successes, it makes sense how that can make you feel really bad about yourself in different ways, because you're basically only seeing half of the distribution, or less,” she says. “You don't actually know how everyone is doing.”

She recalls a meme that circulated in academic circles a number of years ago: a “CV of Failures” put together by an economist in response to an article about the idea.  'Here are the jobs I didn't get, here are the grants I didn't get,” Landgren recalls. “I thought it was lovely, because it was a way of looking at the entire thing… It's actually liberating to say, when I look at these things from people who are really successful, I'm not seeing the whole picture.”