UPDATE (July 22, 9:30 p.m.): Hillary Clinton made it official Friday night, telling her supporters in a text message that she had chosen Tim Kaine to join her ticket.

If Hillary Clinton chooses Sen. Tim Kaine of Virginia as her running mate, as betting markets and journalists suspect, then in some ways, it’s a dull story. Kaine has traditional credentials, having served as Virginia’s governor before joining the U.S. Senate. He’s young enough, at 58, that he could run for president himself in 2020 or 2024. He’s not especially liberal, but he’s no Blue Dog Democrat, either. He’s a white guy, although he speaks good Spanish. If Mike Pence is a “generic Republican,” then Kaine is a “generic Democrat.”

The difference is that Kaine comes from a swing state, whereas Donald Trump would likely lose Pence’s home state, Indiana, only in a national landslide. If you’re going to pick someone from a swing state, is Virginia among the better options? And how much difference does the vice presidential nominee really make in his or her home state?

Our previous research suggests that a vice presidential pick adds about 2 percentage points to his party’s margin in his home state. So, for instance, if Clinton would otherwise win Virginia by 3 percentage points, her margin would theoretically increase to 5 points with Kaine on the ticket. Not all VP bonuses are created equal, of course; there’s some evidence that VP nominees chosen from less populous states (for instance, Joe Biden of Delaware or Sarah Palin of Alaska) make more difference than those picked from larger ones. But Kaine seems like a fairly typical case: Virginia is a medium-size state, and Kaine’s approval ratings there are solid but not spectacular.

It actually takes quite a confluence of circumstances, though, for those 2 percentage points in one swing state to change the winner of the Electoral College. For Kaine to swing the election for Clinton, she’d have to be losing Virginia without him (otherwise he’d be superfluous) but not losing it by more than 2 percentage points (otherwise, he wouldn’t help enough). Likewise, she’d have to be losing the Electoral College without Virginia’s 13 electoral votes, but she’d need to have at least 257 from other states or Virginia wouldn’t make a big enough impact.

What are the odds of all of that happening? About 1 chance in 140, according to our polls-only model, based on a set of simulations I ran early Friday afternoon. That translates into only about a 0.7 percent chance that a VP pick from Virginia would swing the election to Clinton.

Not very impressive, right? Actually, it’s pretty good as far as these things go. A home-state VP pick would make more of an impact in Florida (where it would increase Clinton’s chances of winning the Electoral College by 1.8 percentage points), Ohio (1.3 points), Pennsylvania (1.1 points) or North Carolina (0.8 points). But Virginia is fifth on the list.

HOME STATE OF VP NOMINEE PERCENTAGE POINT CHANGE IN CHANCE OF WINNING ELECTORAL COLLEGE Florida +1.8 Ohio +1.3 Pennsylvania +1.1 North Carolina +0.8 Virginia +0.7 Michigan +0.4 Iowa +0.4 Colorado +0.4 Minnesota +0.4 Nevada +0.3 Arizona +0.3 Wisconsin +0.3 Georgia +0.3 Where would a running mate make the biggest impact for Clinton? Calculations are derived from FiveThirtyEight’s polls-only model and assume that the running mate would add a net of 2 percentage points to Clinton’s margin in his or her home state.

I’ve seen some griping that Kaine is a poor pick because Clinton ought to be able to win Virginia without him. In theory, that makes sense. Virginia’s demographics don’t seem very Trumpian. And mathematically, you stand to gain more from a VP pick in a state that’s slightly below-average for you than one that’s slightly above-average. But based on the polls, Clinton is vulnerable in Virginia. She leads there by only 2.6 percentage points in the polls-only model as of this afternoon, almost exactly matching her 2.5-point lead nationally.

Of course, a 0.7 percent increase in your chances of winning the Electoral College wouldn’t be worth it if your VP pick caused you problems in other respects. Presidential candidates seem to realize this, which is why there have been running mates from non-competitive states such as Delaware and Wyoming in recent years. But elections are won on the margins, and Clinton would be marginally better off with Kaine’s help in Virginia than without it.