Mathematician’s Advice: Aim High, But Don’t Shoot for the Moon

There’s a popular saying: “If you shoot for the moon, even if you miss, you’ll land among the stars.” However, mathematicians suggest that aiming directly at the stars may yield even better results.

In life, individuals often exhibit a balance of ambition while pursuing their goals, be it a better job, finding a compatible partner, or reaching political aspirations.

Although the dynamics of this balance have not been extensively examined, many studies show that people often display a tendency to stop pursuing their goals prematurely. Researcher Thomas Hills from the University of Warwick elaborates on this phenomenon.

By utilizing a mathematical model, Matt Burgess and his colleagues at the University of Wyoming discovered that optimal outcomes in uncertain situations typically involve setting high yet realistic goals. “We can demonstrate that optimal ambition is both above average and finite: aiming high, but not to the extent of unrealistic hopes,” states Burgess.

Initially, Burgess and his team developed a statistical model to examine how individuals evaluate various outcomes based on their willingness to compromise on ambition. This led to a formula that predicts overall compensation based on individual satisfaction criteria.

The model was tested with random potential outcomes, altering factors such as the number of choices available, the ratio of bad to good outcomes, and the time and effort required to select a specific outcome. Through thousands of simulations, the researchers compared their results against real-world data sets, including college admissions and U.S. election polls.

Findings revealed that optimal results are achieved when people aim for compensation that exceeds average compensation yet falls short of maximum compensation.

While this aligned with traditional wisdom, Burgess expressed surprise at how the results shifted when scenarios were skewed towards extreme outcomes, either good or bad.

Generally, most outcomes are mediocre; however, during a significant downturn, such as a rare recession, it’s prudent to exercise caution. Surprisingly, Burgess’s team found that during such times, it’s better to be slightly more ambitious. “In scenarios like these, being a bit more ambitious than average is advisable,” he notes, as you want to avoid being discouraged by a rare bad outcome skewing your average negatively.

In similar reasoning, if a startup has one particularly lucrative outcome, such as earning $1 billion compared to zero, the approach should also be slightly more ambitious than average. Burgess shared, “Initially, the findings were so unexpected that when my colleagues first presented them, I assumed there had been a mistake.”

Hills, who was not part of the research, remarked that individuals may possess varying perspectives regarding risk versus reward. “For instance, some may prefer a stable income over a potentially ‘optimal’ but risky one,” he explains. “Additionally, certain sectors operate in a winner-take-all framework where social comparisons significantly influence the appropriateness of risk-seeking ambition.”