Brace yourself for a bit of a reality check on your influence at your own company: It turns out, leaders get too much credit for company success--and too much blame for company struggles.

That's according to a new study by Markus Fitza, a professor of management at Texas A&M.

Fitza's research builds on (and subverts) a large body of academic work connecting CEO performance to company performance--using return on assets (ROA) as the metric of the latter. These studies generally fall under a category called "CEO effect." The idea is that you can gauge how effective a CEO is--relative to other CEOs--by comparing the industry-adjusted ROAs of their tenures. For example, a few years ago, a compelling study in the MIT Sloan Management Review used ROA data (among other metrics) to compare the performances of external and internal candidates in CEO successions.

The major takeaway of Fitza's findings is that the overall value of CEO effect is statistically small, compared to the role of chance. 

Most studies, says Fitza, show a CEO effect between 13 and 30 percent, indicating that CEOs do have some influence over changes in ROA. All well and good. Until you ask yourself a few common-sense questions: Why does a CEO deserve all the credit for changes in ROA? What about the role of chance events, beyond the control of the CEO? What would happen to ROA if--instead of this particular CEO--you installed a CEO at random to helm the company?

This line of thinking led Fitza down a path where he attempted to measure CEO influence on company performance in a different way--a way comparing the CEO effect of actual CEOs to the CEO effect of chance performance. He did this by building statistical simulations for chance. His final sample crunched data from 1,425 companies and 2,634 CEO tenures in 220 different industries.

Ultimately, his study showed that chance would produce an average CEO effect of 13.3 percent, generally ranging between 12.8 percent and 13.8 percent. His calculation for traditional CEO effect was 18.8 percent--about five percent higher. "Therefore," he writes, "the only part of the measured CEO effect that can be statistically significantly attributed to leadership is five percent."

In plain English, here's what that means: The effect CEOs have on company performance--the effect that can clearly be distinguished from the effect of chance--is small. 

The Real CEO Effect.

It's a finding with significant implications for compensation. "The whole idea of paying for performance is fraught, when it can be so influenced by chance events," says Fitza.

He's right--if you're strictly speaking about the measurables from his data. But there's more to the CEO's job than that. In fact, you could argue that the whole value of the job is that it pinpoints where the buck stops when things go wrong--whether they go wrong based on chance or CEO performance.

"It is part of the CEO's job to be that scapegoat when the time comes," concedes Fitza. But the aim of his research isn't to minimize the role of the CEO. His aim is to counter the large volumes of management research which posit CEOs as potential saviors, based on statistics such as CEO effect. 

In many ways, Fitza's idea is a lot like what baseball sabermetricians conceived of when they started calculating a player's VORP--his value over a replacement player. The idea behind VORP is very simple. It's that you can't measure a player's value in absolute terms. It's far more helpful to measure a player's worth in relative terms, by comparing him to a fictitious, average "replacement player" at his position. That way, you get a stronger sense of just how valuable your player really is. You learn how much you'd suffer if you replaced him with an average Joe. 

Likewise, Fitza wants to clarify the concept of CEO effect by adding some useful relativism to it. You can't tell how great a CEO is by looking at her CEO effect in absolute terms. It's far more helpful to gauge her performance over and above what a random CEO performance would be over the same interval.

Why does the myth of the savior CEO persist? "There are psychological reasons we like to believe in these strong leaders," says Fitza. "It fits with how we like to see the world." He cites a renowned essay from 1987 called "The Romance of Leadership and the Evaluation of Organizational Performance" by James R. Meindl and Sanford B. Erlich as the best explanation he's seen for why there's an innate human need to make heroes out of CEOs.

In that essay, the authors write: "The romanticized conception of leadership denotes a strong belief--a faith--in the importance of leadership factors.... It implies that leadership is the premier force in the scheme of organizational events and occurrences.... It reduces and translates...complexities into simple human terms that [many people] can understand, live with, and communicate easily with others." 

Fitza's data explains those complexities in a way that de-romanticizes the role of leadership. But beliefs in iconic leaders are bound to persist--for reasons that transcend the findings of this or any other study.