At least four percent of death sentences in the US send an innocent person to death row, according to new research published Monday in the scientific journal Proceedings of the National Academy of Sciences. Some of those people are exonerated and freed – but not all of them, the researchers report.

The study follows a broader report earlier this year that found that a record number of people were exonerated for crimes in 2013, suggesting that innocent people go to prison far more often than had been thought.

The study authors found that over a 31-year period, 1.6 percent of inmates sentenced to death were exonerated and freed. Of the remaining innocent inmates, some see their sentences reduced to life in prison, while others are executed, the authors say.

But for those wrongly convicted inmates who are removed from death row and not exonerated, their new life sentence among the general prison population is a mixed blessing: the odds of being executed are now nil, but their chances of being freed also plummet, since, once off death row, outside efforts to prove their innocence tend to slow, or even cease, according to the researchers.

“The net result is that the great majority of innocent defendants who are convicted of capital murder in the United States are neither executed nor exonerated,” the researchers write. “They are sentenced, or resentenced to prison for life, and then forgotten.”

The new research is based on US death row records kept between 1973 and 2004, during which period 7,482 defendants were sentenced to death. As of Dec. 31, 2004, 1.6 percent of them, or 117 people, had been exonerated, some 12 percent had been executed, and about 46 percent were still on death row.

To estimate the percentage of death-sentenced defendants who were wrongly convicted, the researchers applied what is called survival analysis, a statistical technique often used in studies of medical treatments. The figure produced by the analysis assumed that all those sentenced to death remained indefinitely on death row, where their cases naturally, and consistently, receive the most scrutiny.

In reality, however, that is not the case.

“Most death-sentenced defendants are removed from death row and resentenced to life imprisonment, after which the likelihood of exoneration drops sharply,” the authors found. The 4.1 percent figure, therefore, “is a conservative estimate of the proportion of false conviction among death sentences in the United States,” they concluded.

Though death sentences represent a minuscule fraction of sentences in the US, exonerations from death row account for a disproportionately large volume of all exonerations in the US, according to the paper. That’s not necessarily because the criminal justice system gets it wrong more often in capital punishment cases, the authors argue. More likely, it’s because no one wants to execute an innocent person, and personnel throughout the criminal justice system put considerable resources into eventually getting it right in those cases, the authors say.

But, once a person is taken off death row, defense attorneys, prosecutors, and innocence projects feel far less urgency to find and correct wrongful convictions, the authors write.

Though the researchers report that the number of innocent people put to death in the US is likely small, given the energy the system expends to avoid executing the wrongfully convicted, it is not zero, they say. Those people likely include Todd Cameron Willingham, the Corsicana, Texas, man executed in 2004 for murdering his three small children but who is now widely believed to have been innocent.

“If you don’t want to execute innocent people, you don’t execute people,” says Samuel Gross, the lead author on the paper and a professor at The University of Michigan Law School.

“I don’t think we’re going to get any better than we are at not executing innocent people,” he says. “You can’t get lucky every time, and a lot of exonerations depend on luck.”

The reasons that innocent people go to prison are as varied as the crimes of which they’re convicted, and advocates have proposed numerous reforms for limiting the likelihood of convicting the wrong person. Those reforms include overhauling eyewitness identification protocols, mandating that police videotape interrogations, upping the stakes for prosecutors who behave unethically, and improving the public defender system.

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Still, “the next best thing” to preventing wrongful convictions from happening in the first place is to improve how innocence claims are handled post-conviction, especially when dealing with life sentences, says Mr. Gross.

“Innocence claims need to be taken seriously,” he says. “There are a lot of people out there whose innocence is never discovered.”