Setting your sights high can lead to bigger rewards – up to a point
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The adage suggests aiming for the moon, with the reassurance that even a miss will leave you among the stars. However, mathematicians propose a more direct approach: aim straight for the stars for potentially better results.
People generally strive for ambition without overreaching, whether in securing a better job, finding a suitable partner, or achieving political aspirations.
However, the precise measurement of this balance has not been extensively explored. Much of the existing research focuses on when individuals cease their pursuit prematurely, lacking sufficient ambition, according to Thomas Hills from the University of Warwick, UK.
By employing mathematical models, Matt Burgess at the University of Wyoming and his team have determined that the most favorable outcomes in uncertain situations arise from aiming high but not unrealistically so. “You can prove that the optimal ambition is strictly above average and strictly finite, meaning above average but you don’t shoot for the moon,” says Burgess.
The team initially developed a statistical model to evaluate different outcomes based on a person’s readiness to settle for outcomes of varying ambition. This led to a formula predicting the overall reward relative to an individual’s satisfaction threshold.
They tested this model against random potential outcomes, examining variables such as the number of choices available within a set timeframe, the ratio of negative to positive outcomes, and the time and effort required to select a specific outcome.
After conducting thousands of simulations and comparing these with real-world datasets, including university applications and US election polls, Burgess and his colleagues found that the optimal results were achieved when individuals aimed slightly above the average reward but not at its peak.
Although this aligns with conventional wisdom, Burgess notes that they were surprised to discover that the scenario changes when one outcome is significantly worse or better than others.
Generally, if most outcomes are average but one is extremely negative, like a recession occurring once every decade, caution is advised. However, Burgess’s research suggests that in such cases, it is better to be more ambitious than if the outcomes were more balanced. “We find, compared to the average, you want to be a little bit more ambitious [in these scenarios], because you don’t want to be thrown off by these bad years dragging the average down.”
Conversely, when one outcome is exceptionally positive, such as a start-up earning $1 billion versus nothing, it is wiser to be somewhat less ambitious than average. “It’s actually initially so counterintuitive that when my colleagues showed me the result, I thought that they had made a mistake,” says Burgess.
Hills, who did not participate in the study, emphasizes that individuals may have different perspectives on balancing risk and reward. “Some people may prefer to have a stable income rather than an ‘optimal’ but potentially riskier income, for example,” he explains. “Moreover, some environments are winner-takes-all environments, where social comparisons are more important, and in those cases risk-seeking ambition may be more appropriate.”
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