Sen. Thad Cochran (R-Miss.) greets a supporter at Mama Hamil's restaurant on Tuesday in Madison, Miss. (Photo by Justin Sullivan/Getty Images)

Sen. Thad Cochran (R-Miss.) won his primary runoff Tuesday against state Sen. Chris McDaniel (R), overcoming a slight deficit on primary day three weeks ago to pull what many regard as a significant upset.

And there's a reason it's an upset.

That's because it's rare for an incumbent to improve his or her performance in a runoff, as Cochran did. And more often than not, the challenger surges in a big way.

Of the last seven incumbents facing primary runoffs in big-ticket races, all but two have fared significantly worse in the runoff, ceding around 75 percent (or more) of the "up for grabs" votes to the challenger.

Here's the shift in the last eight primary runoffs, with the challenger in green:

And one of those successful incumbents just happened to be running in a highly unusual post-Hurricane Katrina race in New Orleans.

Cochran trailed McDaniel narrowly in the June 3 primary, and while both were close to the all-important 50 percent threshold, conventional wisdom (which is conventional for a reason) suggested the race was McDaniel's to lose.

Cochran benefited from an all-hands-on-deck approach to the runoff, which included appealing to non-GOP constituencies like African Americans.

Exactly what led to the upset is a question for the hours and days to come. But for now, it's clear that Cochran beat history.