Aim high but don’t shoot for the moon, mathematicians say 

A new mathematical study suggests that while ambition is important for achieving success in uncertain situations, aiming for extreme outcomes may not always be the best strategy—challenging popular motivational wisdom that encourages people to “shoot for the moon.”

Researchers have found that the most effective approach in decision-making scenarios is to aim above average results, but not to chase the absolute maximum possible outcome.

The study, led by mathematician Matt Burgess and colleagues, used statistical modelling to examine how people evaluate risk and reward when choosing between uncertain outcomes such as career opportunities, relationships, or political decisions.

Their findings suggest that optimal ambition is “strictly above average and strictly finite,” meaning individuals perform best when they aim higher than typical outcomes—but avoid setting unrealistically extreme goals.

The results were published after extensive mathematical simulations conducted in collaboration with researchers including Thomas Hills, who noted that while human ambition has long been studied, the precise balance between caution and overreach had not been rigorously quantified.

Mathematical model of ambition and decision-making

The researchers developed a statistical framework to represent how individuals weigh potential outcomes based on a personal “satisfaction threshold”—a point at which a result is considered acceptable or worthwhile.

Using this model, they simulated thousands of scenarios with varying conditions, including the number of choices available, differences between good and bad outcomes, and the time and effort required to make decisions.

They then compared the model’s predictions with real-world datasets, including university applications and U.S. election polling data. Across these examples, the results consistently showed that the best outcomes occurred when individuals aimed slightly above average expectations, rather than targeting extreme highs.

When conventional wisdom breaks down

The study also found that commonly accepted ideas about risk do not always hold true.

In scenarios where most outcomes are moderate but a rare, extremely negative outcome exists—such as an economic downturn occurring periodically—the model suggests individuals should actually be more ambitious than average, rather than more cautious as typically assumed.

The reasoning, researchers say, is that overly cautious strategies may be distorted by rare negative events that drag down average expectations.

Conversely, in situations where outcomes are highly skewed toward a single extreme success—such as startup investments that either fail or produce massive returns—the optimal strategy shifts slightly downward, suggesting less extreme ambition is more effective than expected.

“Compared to the average, you want to be a little bit more ambitious in some cases and a little less in others,” Burgess said, noting that some results initially appeared counterintuitive even to the researchers themselves.

Experts caution against one-size-fits-all advice

However, experts emphasize that mathematical optimization does not necessarily translate into universal life advice.

Thomas Hills noted that individuals differ in their tolerance for risk and reward trade-offs. Some may prefer stable outcomes over potentially higher but uncertain gains.

He also pointed out that certain environments—such as highly competitive “winner-take-all” systems—may reward greater risk-taking and more aggressive ambition than the model’s average predictions suggest.

The study ultimately highlights a nuanced conclusion: ambition is beneficial, but only when calibrated carefully to the structure of uncertainty in each situation—challenging the idea that the highest possible goal is always the best one to pursue.