The races for governor, U.S. Senate and agriculture commissioner are close — even for Florida.

But are they so close that a potential recount is likely to change the result?

History says almost certainly not.

As of Saturday's reporting deadline, about 12,500 votes separated Republican Gov. Rick Scott and Democratic Sen. Bill Nelson in the most contentious of the three upcoming recount fights. Former Republican Congressman Ron DeSantis led Democrat Andrew Gillum in the governor's race by about 34,000 votes. Democrat Nikki Fried held about a 5,300-vote lead over Republican Matt Caldwell in the agriculture commissioner race.

Florida law mandates that any election decided by 0.5 percent or less must go to a recount. All three races fit that bill.

Yet all three candidates who appeared to lead their races — Scott, DeSantis and Fried — have declared victory.

They may not be premature.

Math says Caldwell likely has the best chance to reverse his fortune in a recount. Plus he also might get a bump from the thousands of potentially Republican-leaning overseas votes that have yet to be counted.

In the Senate race, Nelson's lawyer, Marc Elias, said he also expects Nelson's losing margin to be erased by a recount.

"If I had to place a bet, it is more likely than not Sen. Nelson will prevail in a recount," Elias said on a conference call with reporters Friday.

But a recount that reverses an initial margin of more than a few hundred votes would be unprecedented in the recent history of American elections.

According to an analysis by the nonpartisan group FairVote, which advocates for electoral reforms that make it easier to vote, out of 4,687 statewide general elections between 2000 and 2016, just 26 went to a recount. Of those 26, just three recounts wound up changing the initial result of the race: The 2004 Washington governor's race, the 2006 Vermont state auditor's race and the 2008 Minnesota U.S. Senate race. The average swing in those three elections after the recounts? About 311 votes.

In none of those cases was a widespread vote-counting error discovered that wound up swaying the election.

"I think what the history of recounting has indicated is that on the whole, the errors that are unearthed in recounting are innocent errors, and they kind of balance out," said Charles Stewart III, a professor of political science at MIT.

For instance, in the 2008 Minnesota U.S. Senate race, the final result hinged in part on a few hundred absentee ballots that courts ruled were improperly excluded from the initial result. Votes for both the Democrat, Al Franken, and Republican, Norm Coleman, were added during a manual recount. (Fun Fact: Elias represented the Democrat in that race as well.)

Florida is a much larger state than either Minnesota, Vermont or Washington. More than a few hundred votes could shift in a Florida recount even if a series of random, small mistakes explain that shift. But even if that happens, it's still unlikely that enough votes will be found to change the outcome in any of the three races, the FairVote's analysis found.

"With a larger electorate, there is a lower probability that a shift in votes will be large enough to affect the final outcome of the election," the August 2018 report states.

Essentially, Nelson — and to a greater extent, Gillum — would need a systematic error to be discovered during their recounts if their results are to be reversed.

Nelson's lawyers say that's just what they're banking on: the senator's path to re-election lies in a number of potentially Nelson-leaning undervotes in Broward County.

In that county, some 25,000 voters cast a ballot in the governor's race without weighing in on the U.S. Senate race, a disproportionately high number when compared to other counties. Elias has said Nelson's campaign believes the discrepancy can be attributed to a tabulation error. Once that error is sorted out in the recount, Elias said, Nelson will likely gain the majority of the votes he needs to overtake Scott.

But there are a number of factors working against Elias' theory. For one thing, even if every one of those 25,000 undervotes are discovered in a recount and given to Nelson at the 69 percent rate he won votes in Broward, the senator would still be about 4,800 votes shy of Scott. For another, voting machines simply don't make mistakes of this scale very often, experts say.

"I don't know why the tabulators would miss that race and pick up all the others," Barry Burden, a professor of political science at the University of Wisconsin at Madison said.

More likely, Burden said, poor ballot design is to blame for Nelson's Broward troubles. Broward County sample ballots show that the U.S. Senate race was tucked into the bottom left corner of the ballot, just below the voting instructions. It's possible that voters simply overlooked the contest.

I’m at @BrowardVotes HQ. Here’s an image of a ballot to aide discussion about whether layout caused undervotes in the US Senate race pic.twitter.com/4gUkp1uR2C — David Smiley (@NewsbySmiley) November 8, 2018

Stewart said he found that the Broward undervoting rate was about the same for early voting, vote by mail and Election Day voting — which would seem to suggest that undervoting should be attributed to humans, not machines.

"Machines are very good at counting ballots," Stewart said.

If Nelson faces an uphill battle in his recount, Gillum's odds of wiping out his deficit are even longer. A margin of about 0.41 percent separates him from DeSantis, so it's unlikely that an initial recount will bring him within the 0.25 percent margin for a second, manual recount. Although Gillum rescinded his initial concession at a news conference on Saturday, DeSantis has begun his transition plans.

Gillum himself seemed to acknowledge his odds Saturday.

"I am replacing my words of concession with an uncompromised and unapologetic call that we count every single vote," Gillum said. "I say this recognizing my fate in this may or may not change."

Times/Herald Tallahassee Bureau staff writer Steve Contorno and Elizabeth Koh contributed to this report.