I’ve occasionally tweeted about election margins and recounts. Given a number of (relatively) close elections, refusals to concede, and retracted concessions, I thought I’d offer a little perspective (and a very little math).

All (or, at this point, nearly all) of the change in the margin between candidates in Florida’s Senate, Governor, and Commission of Agriculture races, and Georgia’s Governor race, have arisen because of mere counting of the ballots. There are lots of (here I’ll focus on legitimate, by far the more common) reasons for late-added votes. Provisional ballots could be deemed valid or cured. Vote-by-mail ballots might permissibly arrive after Election Day in some jurisdictions. But these are typically smaller figures. Slow or inefficient counting, or simply more general administrative failures, by election officials might result in added later totals.

To put it obviously, only after the votes have been counted can there be a recount. It’s there that many hold great interest, but it’s there that little changes.

I draw on a few rough figures form past recounts. Minnesota’s Al Franken netted 527 votes in a recount in 2008 in an election with about 2,885,555 votes cast. That turned his 215-vote deficit into a 312-vote victory (post recount and post litigation). The 527-vote change was just 0.018% of all votes cast. (Note that this reflects a percentage of this change compared to all ballots cast. It is not that there were 527 votes that were added for Mr. Franken; votes were added for Mr. Franken and for Norm Coleman, but Mr. Franken gained 527 votes relative to Mr. Coleman.)

Washington’s Christine Gregoire recount netted 390 votes in a 2004 gubernatorial recount in an election with 2,810,058 votes cast. Her opponent Dino Rossi originally held a 261-vote lead, but after two rounds of recounts Ms. Gregoire was declared the winner by 129 votes. The 390-vote change was just 0.014% of all votes cast. (Again, both Mr. Rossi and Ms. Gregoire increased their vote totals in the recount, but Ms. Gregoire increased them at a faster rate than Mr. Rossi, and that 390-vote difference was this percentage.)

Finally, Donald Trump won Wisconsin’s electoral votes over Hillary Clinton by a reported margin of 22,617 votes in 2016. Green Party candidate Jill Stein demanded a recount, which netted Mr. Trump 131 votes and increased his margin of victory to 22,748 among 2,976,150 votes cast. That 131-vote margin reflected 0.0044% of all votes cast. (This was a much more mundane recount in some respects because neither candidate formally challenged the results.)

The long and short of this is, recounts rarely change much in absolute terms. Even in elections with millions of votes cast, the relative change in the margin of victory is extremely low. It was enough to give Mr. Franken and Ms. Gregoire victories, but it was still very little that changed.

One basic reason that’s the case? Recounts recount every ballot—an obvious proposition, of course. But that means a challenging candidate picks up votes as well as his opponent. To successfully change the outcome of an election during a recount, then, you need either extraordinary luck, or you need to establish that there are systematically more votes for your candidate that were “missed” during the first count—mismarked ballots, hanging chads, provisional ballots that were deemed invalid, and so forth.

That can be a high bar. Typically, we’d expect errors like this to be randomly distributed. But as Florida’s 2000 election showed, one county’s procedures (e.g., the use of punch card ballots and a butterfly ballot design) might differ from another’s, which may disproportionately impact one candidate over another to the extent that one candidate’s support resides more heavily in that county. And as some observers of the 2004 Washington race and the 2008 Minnesota race might argue, out-lawyering your opponent can help net a few more votes, too.

Nonetheless, absent evidence like that, or in the event that there is offsetting evidence that may have disadvantaged candidates relatively equally, we would expect little to change in a recount.

Consider Minnesota again. Mr. Franken netted 1 vote for every 5,475 votes ultimate counted, that 0.018% margin. To win, he had to not simply gain votes; he had to gain votes faster than his opponent. And he did so.

And to Washington, Ms. Gregoire fared even worse. She managed to net just 1 vote for every 7,205 ultimately counted.

For both of them, despite these overwhelming odds, the extraordinarily narrow margins of victory—low three-digit margins—helped.

So where do things stand today?

The last update in Florida’s Senate election shows Rick Scott leading Bill Nelson by 12,562 votes among 8,184,631 votes cast. That’s 0.15%, or about 10 times the gains that Mr. Franken and Ms. Gregoire ultimately made—and that would just pull Mr. Nelson into a tie. (Again, however, recall how I opened this post—much depends on whether this is even the final count, as opposed to gains being made in the recount.)

In Florida’s gubernatorial race, among 8,218,682 votes cast, Ron DeSantis leads Andrew Gillum by a margin of 33,684. That’s 0.41%, or would require Mr. Gillum to net 1 vote for roughly every 244 votes cast. (And, of course, this is a rough figure—more ballots would likely be added to the overall total votes cast as “undervotes,” those that failed to register for any candidate, were added to the totals in a recount.)

Florida’s Commissioner of Agriculture, assuredly less watched, may still be instructive once the recount dust settles. Nikki Fried leads Matt Caldwell by 5,326 votes among 8,055,348 votes cast, or a margin of 0.066%.

In Georgia, Brian Kemp needed to secure more than 50% of the vote to avoid a run-off and win outright, and 3,929,937 votes cast, or about 10,875 votes to spare, a margin of 0.28%. (The math looks a little different when looking at a 50% cut-off rather than his position relative to challenger Stacey Abrams, but this works well enough for now.)

In short—the final count matters a great deal for each of these races. Under almost no recount scenario would anyone other than the projected winners win the recount, if recent history is any guide. Only significant election administration errors—failure to count large quantities of votes in select counties, for instance—would be these margins by overcome by challengers, because they’re the kinds of things that were omitted from the count in the first place. That said, there’s a first time for everything, which is probably the news that keeps hope alive for challengers in these races.