For Mr. Rubio and Mr. Romney, these simulations came up 356 times out of 50,000 instances, or about 0.7 percent of the time. The interpretation of this is simply that, other things being equal, the choice of Mr. Rubio as his vice-presidential nominee would increase Mr. Romney’s chances of winning the Electoral College by 0.7 percent, based on Mr. Rubio’s home-state impact.

Other candidates swayed the outcome a bit more often. The top-ranking one was Mr. Portman of Ohio.

Even though Mr. Portman is not all that well-known and not all that popular with voters back at home — we assume that he’d improve Mr. Romney’s position in Ohio by about 1 percentage point — that single point could matter since Ohio is such a disproportionately important state. That extra point in Ohio changed the outcome of the Electoral College in 965 of the 50,000 simulations, or just less than 2 percent of the time.

Mr. McDonnell and Mr. Sandoval had a similar impact.