I was there this morning when Senator Mary Landrieu voted at McMain High School on Claiborne Avenue in New Orleans. As usual, the senator “hit all her marks” in very brief remarks and Q&A with the press after she voted. She didn’t miss a single point in her messaging. Interestingly, she clearly was targeting Representative Bill Cassidy, repeatedly listing supposed problems with his record, as if she were already campaigning in the expected runoff.

But here’s what was really interesting: Her aides there — very bright young guys who have impressed me during the past few months — not only were peddling the line that Landrieu might win today outright, without a runoff, but actually seemed to believe it is a real possibility. It has been a recurrent theme with them for several weeks, but I thought until today they were just doing their job spinning for their boss in order to keep morale up. But when I see somebody in person, I have a fairly good antenna for what is spin versus what somebody really believes. These guys really seemed to believe that absentee-ballot numbers and reported early-morning turnout favored them so much that they could win outright.

We’ll know in a few hours, but I think their belief is ludicrous.

But . . . I write this not to say that they are silly or out of touch with reality for believing it. I write it because the arithmetic in Louisiana does at least suggest a way that they could be right — if they pull off the equivalent of one of those shots in pool where the cue ball jumps over another ball, banks off two walls, and then knocks two different balls in different corners. It’s not at all likely, but we’ve all seen trick-shot artists do such a thing.

What’s important is that observers understand this arithmetic when the runoff starts taking shape. Republicans should not be overconfident in this runoff, no matter what happens nationally or in Louisiana tonight. Those young aides do understand the arithmetic, even if they are assuming a larger Landrieu starting number than most people think exists. The arithmetic says that if African-American turnout hits 31 percent — not likely, but not utterly unreasonable — and Landrieu gets 95 percent of that vote (unlikely, but she’ll be close); and then she gets 30 percent of the remainder of the electorate (again, within reason), then she would eke out a win with 50.15 percent of the vote.

This is why Landrieu has been trying to ramp up the black vote by raising the specter of white opposition to Obama based largely on race. She knows what she is doing. I don’t think it will work. But it’s gonna be quite a runoff to watch.