One in 25 criminal defendants who has been handed a death sentence in the United States has likely been erroneously convicted. That number—4.1% to be exact—comes from a new analysis of more than 3 decades of data on death sentences and death row exonerations across the United States.

“This was a very carefully done and carefully considered approach,” says statistician Bruce Levin of Columbia University, who was not involved in the new study. “The analysis was quite sophisticated, and the authors were transparent about both their assumptions and methods.”

Putting a number on the rate of false convictions among criminal defendants in the United States is complicated by the fact that many false convictions are never identified and there’s no central, national database that tracks most types of criminal cases. A number of lawyers and judges, however, have publically claimed that the false conviction rate for all crimes is almost negligible—including a written comment by Supreme Court Justice Antonin Scalia in a 2006 concurring opinion, citing a rate of 0.027%. But such assumptions usually take the total number of all exonerations in the country and divide it by total number of felony convictions—an incorrect calculation because most false convictions, especially for more minor felonies, are never revealed.

To calculate a more accurate false conviction rate, Samuel Gross, a law professor at the University of Michigan Law School in Ann Arbor and a former criminal defense lawyer, decided to focus on one small subset of criminal cases: those that result in death sentences.

“Every case where you have a death sentence is recorded in a national database,” Gross says. “And the rate at which errors are detected in death penalty cases is orders of magnitude higher than in other cases.” Defendants on death row have better access to attorneys, he notes, and more attention and resources are generally devoted to ensuring that their convictions are accurate.

Gross and his colleagues gathered data from the U.S. Department of Justice and the Death Penalty Information Center, a nonprofit organization that tracks executions, on all 7482 death sentences in the United States from 1973 through 2004. But even among death sentence cases, dividing the number of known exonerations by the total number of defendants wouldn’t give an accurate estimate of all false convictions. In a third of death row convictions, defendants are resentenced to life in prison after appeals, usually within about 5 years. And after being resentenced, their access to resources that could help them prove a false conviction drops.

“Nobody doubts that the group that is removed from death row and resentenced includes more people who are actually more likely to be innocent and would be exonerated if they remained on death row,” Gross says. Indeed, he and colleagues calculated that resentenced defendants are eight times less likely to be exonerated than those on death row. In addition, once someone is executed, dies of natural causes, or commits suicide, the chance of being exonerated drops to nearly zero.

To calculate what the total rate of exonerations would be if all death row defendants remained on death row indefinitely and had equal access to resources, the researchers turned to statistical techniques normally used in medical studies. Although only 1.6% of defendants who had been sentenced to death were actually exonerated between 1973 and 2004, 4.1% of defendants were likely falsely convicted, the team reports online today in the Proceedings of the National Academy of Sciences. Because the number is an extrapolation, it doesn’t reveal exactly which defendants—out of those resentenced for life or executed—were falsely convicted.

“The main message is that false convictions are not rare events,” Gross says. “It’s something that’s going to keep happening on a steady basis, and it means we should work hard to try and avoid it.”

David Dow, a law professor at the University of Houston Law Center and founder of the Texas Innocence Network, a group of lawyers that represents death row inmates and works to reveal false convictions, says the number doesn’t surprise him. “This is really the number that people who have spent a lot of time doing capital work have intuited,” he says. “The larger hope is that it finally reaches people who have been resisting the acknowledgement of this reality, which is that we make a somewhat significant number of mistakes.”

The rate of false convictions in death sentence cases can’t be generalized to other criminal cases, Gross points out, but he hypothesizes that the rate is similar for all serious, violent crimes.

The new calculations don’t offer any insight into what most often leads to false convictions, or what can be done about them, but he hopes that illuminating the rate will lead to new efforts to study these areas.