If a running shoe made you 25 percent faster, would it be fair to wear it in a race? What about 10 percent? Or 2 percent?

The Nike Zoom Vaporfly 4% — a bouncy, expensive shoe released to the public one year ago — raises these questions like no shoe in recent distance running history.

Nike says the shoes are about 4 percent better than some of its best racing shoes.

The measurement is based on how much energy runners spend when running in them. That is an astonishing claim, an efficiency improvement worth almost six minutes to a three-hour marathoner, or about eight minutes to a four-hour marathoner.

And it may be an accurate one, according to a new analysis by The New York Times of race data from about 500,000 marathon and half-marathon running times since 2014.

Using public race reports and shoe records from Strava, a fitness app that calls itself the social network for athletes, The Times found that runners in Vaporflys ran 3 percent to 4 percent faster than similar runners wearing other shoes, and more than 1 percent faster than the next-fastest racing shoe.

We found that the difference was not explained by faster runners choosing to wear the shoes, by runners choosing to wear them in easier races or by runners switching to Vaporflys after running more training miles. Instead, the analysis suggests that, in a race between two marathoners of the same ability, a runner wearing Vaporflys would have a real advantage over a competitor not wearing them.

The advantages for runners wearing Vaporflys were consistent for slower racers and fast ones; for men and women; for runners on their second marathon or their fifth.

The Vaporflys — which retail at $250 a pair — were widely released to the public by Nike last summer. Unlike most running shoes, they have a carbon-fiber plate in the midsole, which stores and releases energy with each stride and is meant to act as a kind of slingshot, or catapult, to propel runners forward. Compared with typical training shoes, the Vaporflys are believed to wear out quickly: Some runners have said they lose their effectiveness after 100 miles or so.

The apparent effectiveness of the shoes highlights an issue that has vexed sports officials for decades: how to determine which technological advances constitute an unfair competitive advantage. Golf officials barred the use of certain balls that fly straighter, the NFL barred the use of a sticky substance that helped players catch the ball, and swimming officials barred high-tech suits that were said to have enhanced buoyancy and speed.

The swimsuits were believed to lower times by as much as 2 percent — comparable to the apparent advantage derived from Nike Vaporflys relative to the next-best-performing popular shoes in our data.

The International Association of Athletics Federations, track’s governing body, has rules about shoes, but they are vague: “Shoes must not be constructed so as to give athletes any unfair assistance or advantage.” It does not specify what such an advantage might be.

The rules also state that shoes “must be reasonably available to all in the spirit of the universality of athletics.” The Vaporflys sell out quickly; on the secondary market, a pair can cost $400 or more. Nike’s newest version of the shoe, the Elite Flyprint, was sold to a limited number of runners in London for the 2018 London Marathon at a cost of 499 pounds (about $650).

When asked whether the shoes conform to track and field’s rules, a spokesman for Nike wrote in an email that the shoe “meets all IAAF product requirements and does not require any special inspection or approval.”

Yannis Nikolaou, a spokesman for the IAAF, said that while it is accurate to say that the Vaporflys are legal, it is actually more accurate to say there is no evidence they should not be.

“We need evidence to say that something is wrong with a shoe,” he said. “We’ve never had anyone to bring some evidence to convince us.”