About a decade ago, he began to wonder whether his rate of performance decline was typical and, being a predictive statistical modeler, decided to find out.

He turned first to information about world records for runners by age group. These times represent what is possible by the best runners in the world as they age.

And cumulatively, he found, the records proved that champion runners slow like the rest of us.

But there was a pattern to the slowing, Dr. Fair realized. As he reported in a 2007 study, the masters world record times rose in a linear fashion, with some hiccups, until about age 70, when they begin to soar at a much higher rate.

Using statistical modeling based on this pattern, Dr. Fair developed a formula that could predict how fast other, less-exceptional runners might expect to run as they grew older. He incorporated this formula into an influential calculator that he made available free on his website. (The calculator also predicts age-related performance declines in swimming and chess, using the same statistical techniques.)

The calculator soon became popular with runners, for whom it provided age-adjusted viable goal times, allowing them to swap despondency about their current plodding for gratification if they had managed to remain at or near their “regression line,” as Dr. Fair termed the age-adjusted predicted finishes.

But recently, Dr. Fair began to question whether his statistical model provided the best estimates of people’s likely race times and, for the new analysis, which was published in print this month in The Review of Economics and Statistics, he approached a Yale colleague, Edward Kaplan.

Dr. Kaplan is an expert in a complex type of statistical analysis known as extreme value theory, which focuses on exceptional deviations from the norm.