Over the past few years, the NFL has been haunted by the early deaths of some former players whose brains showed signs of chronic traumatic encephalopathy. CTE is a neurodegenerative disease characterized by memory loss, mood disorders, dementia and other brain-related problems. But how prevalent is CTE, and how likely are players to develop it? Those remain unanswered questions, despite ongoing attempts to answer them.

A paper published last year in the Journal of the American Medical Association found that among 111 brains from NFL players donated to a brain bank created to study the long-term effects of repetitive head trauma, 110 had CTE. Sounds bad. But as alarming as those numbers seem, they really can’t tell us much about the actual risk of CTE among football players, nor can they reveal how common the condition is among people who’ve played the game. If you wanted to know the true prevalence of CTE among NFL players, you’d have to check the entire population of NFL players for CTE. That’s impossible because right now, CTE can be definitively diagnosed only by looking at the brain post-mortem. And the the brains that were examined for the JAMA study didn’t end up in the brain bank by chance — they were donated, for the most part, because the deceased’s next of kin suspected he might have had CTE.

So the statistical quandary remained: how to get a sense of the prevalence of CTE in the NFL? An analysis published last month in the journal Neurology tried to get around the problem of sample bias with what amounts to a thought experiment. Epidemiologists Zachary Binney and Kathleen Bachynski took what we know — that 99 percent of the NFL brains in the brain bank had CTE — and then tried to figure out what that could mean about the prevalence of CTE among the entire group of 1,142 former NFL players who died during the eight-year time frame during which the brain bank collected its samples (February 2008 to May 2016).

The estimates vary depending on how completist you think the brain bank’s collection was. If you assumed that half of the brains from NFL players with CTE who died during the study period ended up in the brain bank, that would mean the prevalence of CTE in the broader group of deceased players was 19.3 percent, according to Binney and Bachynski’s calculations. On the other hand, if 90 percent of the brains with CTE were sent to the bank, the prevalence of CTE would be 10.7 percent. “I’m reasonably confident that it’s somewhere north of 10 percent, and I would not at all be surprised — and indeed it’s my best guess right now — that the prevalence is probably more in the 20 to 30 percent range,” Binney said.

But even if that’s correct and as many as 1 in 3 NFL players who were in the league at the same time as the players whose brains ended up in the JAMA study had CTE, that doesn’t mean that those numbers also apply to the current pool of players, said Bhramar Mukherjee, a biostatistician and epidemiologist at the University of Michigan’s School of Public Health. “The probability of developing CTE could be changing over time, because the protective gear and the style of play is changing over time.”

And Binney and Bachynski’s numbers are still just “back of the napkin” estimates that should be taken with a grain of salt, said statistician Donna Stroup, a consultant on study design and statistical methods in Atlanta. The Neurology paper is a “contribution that’s helpful,” but it doesn’t tell us a lot about the true prevalence of CTE, she said. It’s just a guess.

And it’s a guess based on ways of diagnosing CTE that are still evolving as researchers work to understand the condition. The study of CTE is relatively new, and researchers are continuing to work out some of the condition’s most basic details. So far, there’s no telltale symptom of CTE in a living person, and the diagnosis of CTE in brain samples is still subject to some debate. In a written response to the JAMA study, Vanderbilt University School of Medicine researcher Scott Zuckerman and some colleagues criticized the criteria used to diagnose CTE as potentially too lax. The study of the correlation between abnormal-looking features seen in brain samples and specific neurological symptoms is “in its infancy,” the researchers wrote. And if the original JAMA study overestimated the number of CTE cases, the prevalence ranges that the Neurology analysis calculated are overestimates too.

“The uncertainty is still very large,” said Jesse Mez, a professor of neurology at Boston University and lead author of the JAMA study. His group recently secured funding for a study that will look for CTE in brains collected from the general population. But Mez said that to really understand the prevalence of CTE among NFL players, what’s needed are longitudinal studies that follow players throughout their careers.

In the meantime, Mez and a working group of other researchers are holding a consensus meeting this spring to continue discussing criteria for the condition’s diagnosis. The long-term goal is to find biomarkers and other diagnostic tools that can be used to recognize CTE in living people. “We definitely have a sense that it’s the repetitiveness — the hits over and over and over again — that matters,” Mez said. But researchers are still a long way from being able to pinpoint exactly how CTE develops and how many players might be affected.