Even though Mr. Perry is truly ahead of Mr. Santorum (in our hypothetical world), Mr. Santorum occasionally surpasses him because of sampling error. The rank order of the other candidates, which could affect podium location or question order, also changes. To be clear, we don’t know whether the current average is correct; Mr. Santorum could actually be ahead of Mr. Perry, if we knew the true preferences of Republican voters. Our point is that at least one spot on the stage may come down to luck.

Consider one recent national poll, a survey of 336 registered Republican voters, conducted by Monmouth University from July 9 to 12. In this poll, Carly Fiorina was preferred by 1 percent of respondents — or about three people, if everyone counted the same. But in polling, responses are weighted based on demographics, so the makeup of respondents resembles that of the entire population. Take, for example, a 2012 Republican primary poll conducted for The New York Times and CBS News. In this poll, some respondents, including a young high-earning man in the West and a Hispanic woman, counted as much as four average people.

So it’s entirely possible that Ms. Fiorina’s 1 percent came from a single person, if this person came from a demographic group that is hard for pollsters to reach. For candidates with very low levels of support, the responses of a very small number of people may well determine the final spots on the stage.