Baseball’s Hall of Fame voting has been especially contentious this year, as the Baseball Writers’ Association of America (which elects Hall of Famers) lurches toward greater transparency. More and more voters have been disclosing their votes publicly, and in December the association announced that all members must reveal their ballots starting in the 2018 election. That’s all good news for two of the best baseball players of all time: Roger Clemens and Barry Bonds. Bonds’s and Clemens’s on-field accomplishments have been overshadowed by allegations of performance-enhancing drug use, but they’ve also tended to fare much better in the public voting results than the anonymous ones. With increasing voting transparency, Bonds and Clemens should be more likely to make the Hall of Fame — if not this year, then soon.

For years, the writers group has been divided into two camps. Some writers have chosen to reveal their ballots — either in columns, on Twitter or via Ryan Thibodaux’s Hall of Fame tracker — while others have kept their votes to themselves. And these two groups differed in more than just the visibility of their ballots: The anonymous voters displayed significantly different voting preferences.

Although we can’t directly observe the anonymous ballots, we know about the voting tendencies of the association as a whole. On top of that, an increasing fraction of the electorate releases their ballots, up from 53 percent in 2014 to 71 percent in 2016. So, using a statistical technique called latent class analysis on voting data from 2014 to 2016, we looked for patterns in the ballots that differentiated anonymous voters from public ones. Although we can’t say how any individual writer with an anonymous ballot voted, we can determine how the anonymous voters’ ballots leaned as a whole.

By far the largest factor separating the anonymous and public ballots was support for three players: Bonds, Clemens and Mark McGwire. All three players are widely believed to have used PEDs, and although McGwire lacks the ironclad Hall of Fame case that Bonds and Clemens can boast, all three would have been leading contenders for the Hall if not for their alleged steroid use. In 2016, for instance, an anonymous voter’s odds of voting for the Bonds/Clemens/McGwire trio were about 17 percentage points lower than those of a voter who disclosed his or her selection(s). The anonymous ballots made up a major source of their poor percentages in previous years — Bonds and Clemens lost 2 to 4 percentage points of support in private ballots, which adds up as both players try to make up the 11-point difference between their early public results and the 75 percent induction threshold.

It’s impossible to know exactly how the coming loss of anonymity will affect voters’ attitudes toward Bonds and Clemens. But if the formerly anonymous ballots begin to look more like the public ones, Bonds and Clemens will be due for a bump in support. Social desirability bias may push voters toward a different conclusion than they’d make privately, for instance, even if some writers may react in the opposite way. It’s undeniable that voting support for Bonds and Clemens has already changed dramatically this year.

Since both first hit the ballot in 2013, Bonds and Clemens had seen their Hall of Fame fortunes largely stagnate — until this year. So far in 2017, both names have climbed above 60 percent support in the public voting, tantalizingly close to the mark necessary for induction. Part of that is likely due to another rule change that prevents association members from voting if they aren’t actively covering baseball. That alteration went into effect in 2016, and it also greatly diminished the pool of anonymous voters — by extension, reducing the number of voters who excluded Bonds and Clemens from their ballots, since anonymous voters were much less likely to vote for players implicated in baseball’s PED scandals and older writers were more likely to keep their votes anonymous.

There are other factors working in Bonds and Clemens’s favor. Many public-ballot voters are adding the two to their ballots; so far this year, more than 20 voters have switched from “no” votes for the pair last year to “yes.” Some writers even point to the recent election of Bud Selig, the commissioner under whose watch the steroids era of the late 1980s-2000s unfolded, as a precedent to vote in the two most visible superstars of that period.

Given the storm of rule changes and public debate, we can’t offer a rigorously calculated probability that either player will ultimately make the Hall. It’s worth noting, however, that most eligible players who finish as high as this pair have in the voting eventually get enshrined. In 2016, Clemens and Bonds finished seventh and eighth, respectively, in the balloting. More than 60 percent of all players who finish in those spots eventually get elected; those who didn’t tended to be near the end of their eligibility window; Bonds and Clemens have five years to go. This year, extrapolating from the public ballots shows us that Bonds and Clemens ought to end up around fifth and sixth in the voting — rankings associated with a 70 percent to 80 percent chance of eventually making the Hall, based on the fortunes of previous players in those slots.

It may not happen this year. Although both Bonds and Clemens have marshaled more than 60 percent of the vote in the public ballots so far, that number has decreased over the past few weeks, and it’s likely to drop even more as the anonymous ballots are counted (voting closed Dec. 31, and results will be announced Wednesday). But over the long run, the odds are in the duo’s favor.

From a purely statistical perspective, Bonds and Clemens were always locks to make the Hall of Fame. Each ranks among the best players of all time by wins above replacement, so there is no performance-based reason to exclude them. Now, the baseball writers’ recent changes will only accelerate Bonds’s and Clemens’s ascents. Whether you view that as a triumph or a tragedy, Bonds, Clemens, and others who’ve been accused of using PEDs during the steroid era will probably join the Hall of Fame sooner or later.