What the Puma Fast-R Nitro Elite 3 is worth to a 3:30 marathoner
The headline is a percentage of running economy. The number that matters is minutes, and after that, the probability of finishing ahead of somebody who did not wear them.
Three steps, each with a source
A treadmill study gives an economy figure. Kipp's cost curve converts that to speed, and it converts to less than one-for-one, because the cost of running rises with speed faster than linearly. Race-to-race variation, about 1.8% over a marathon, converts a time gap to a probability of winning.
Who paid for the studies
Two of the studies behind this shoe were funded by the maker and two were not, and the funded ones sit at the top of the range. Both are carried and both are flagged. Excluding funded work quietly is how a catalogue becomes a marketing document.
DerSimonian–Laird random-effects pooling within a product, empirical-Bayes shrinkage across the class, then Kipp, Kram and Hoogkamer's cost curve and a normal model of race-to-race variation.
A percentage from a treadmill is not a promise on a road. The interval is wide, the shrinkage is deliberate, and individual response to a shoe varies more than the average effect.