In November 2017, Wouter Hoogkamer, a research associate at the University of Colorado, published, with his colleagues, an online version of a study that forms the basis of Nike’s claim that one of its most innovative shoes, the Nike Zoom Vaporfly 4% (VF4%), reduces the energetic cost of running compared with other established marathon shoes by some 3.4–4%.1 Although both the VF4% and its claims to energy cost reduction are by now quite well known to many runners, it seems to me that the study is not very well known at all. In any case, the 4% claim is often put differently by Nike in its marketing materials and, all things considered, the corporation does a respectable job of not overstating the science. In the original release note, Nike noted as follows:
[The] Zoom Vaporfly 4% pairs a Nike ZoomX midsole (for responsive cushioning) with a full-length carbon plate (intended to minimize energy loss during toe bend without increasing demand for the calf). Together, these features can make runners, on average, four percent more efficient than Nike’s previous fastest marathon shoe.2
The use of the word “can” and the description of the scientific finding—that it is the combination of the so-called ZoomX midsole with a full-length carbon plate that is determinative of the claimed efficiency improvement—was, in my view, a reasonable and fair description of the findings of the original paper. Even the insertion of the words “on average” is a reasonable qualifier, one that picks up on one aspect of the experiment, albeit without clarifying what that aspect is. To be precise, it refers to the fact that the experiment tested runners across three different speeds or velocities: namely, 14, 16, and 18 kilometres per hour.
Notably, the paper defined running economy or efficiency in its own original way, and it openly stated as much. It reasoned that measuring energy cost via the rate of oxygen uptake (or consumption) in millilitres of oxygen per kilogram of body mass per minute—i.e., through a kind of VO2 test (but not necessarily a “VO2 max” test)—does not reflect metabolic substrate differences among runners. In making this claim, the paper cited a finding from another paper by Fletcher et al. which found, in 2009, that differences in oxygen cost were virtually non-existent when they were measured in different trained runners who ran at different submaximal speeds. Instead, the paper found that what did change dramatically in these runners who ran at various speeds was “caloric cost,” meaning that runners did not use more or less oxygen when running at different speeds but used more or less calories.
Thus, calories were a better index of efficiency for this varying-submaximal-speeds-efficiency test. As the study put it, “expression of running economy in terms of caloric unit cost is more sensitive to changes in speed and is a more valuable expression of running economy than oxygen uptake, even when normalized per distance traveled.”3 This study reflects the view that, although calories themselves are understood to affect the way energy is produced through metabolic substrates, so does an athlete’s existing metabolic system, including the extent to which it is capable of producing energy efficiently through, say, catabolisis, to determine how much energy they may use and for how long. In a nutshell, the Hoogkamer study wanted to adopt the definition of running economy indicated by the Fletcher study. As Hoogkamer et al. wrote,
Running economy has traditionally been defined as the rate of oxygen uptake in mL O2/kg/min required to run at a specified velocity. However, since oxygen uptake alone does not reflect metabolic substrate differences, we prefer to define running economy as the energetic cost of running at a specific velocity expressed in W/kg.4
But the purpose of this note is not to suggest anything about the claim Hoogkamer or Nike makes or made about the shoe—neither in terms of the veracity of Hoogkamer’s science or its basis (which, for what it’s worth, I do not question, having worn the shoes myself and read the science as carefully as I can), nor Nike’s rough summation or “translational” representation of those scientific findings. Rather, I wanted to quickly revisit another aspect of the Hoogkamer et al. paper — specifically, its discussion of the marathon world record. Having established according to its novel (or adopted) definition of running economy that the prototype of the VF4% (as it then was) does represent an improvement in running performance of some 4%, the paper then goes on to discuss the history of the marathon world record in terms of statistical probability. Although I have removed the citations, the discussion paragraph is worth quoting in full:
How much of an improvement in running performance would be predicted from a 4% reduction in energetic cost? Hoogkamer et al. established that percent changes in the energetic cost of running due to altered shoe mass translate to similar percent changes in 3000-m running performance, when both are evaluated at the same running velocity. But, as recently summarized by Hoogkamer et al., the energetic cost of overground running increases curvilinearly with velocity, due in part to air resistance. Such curvilinearity implies that a 4% average energetic savings observed should translate to *3.4% improvement in running velocity at marathon world record pace (20.59 km/h). Consistent with that calculation, in the two years leading up to her amazing world record in the women’s marathon in 2003, directed training allowed Paula Radcliffe to reduce her energetic cost of running at 16 km/h by 2.8% and marathon performance by 2.4%. An acute 3.4% improvement in the marathon world record would be historic. For example, it took nearly 29 years for the men’s marathon record to be reduced by 3.4% to the current 2:02:57, and not since 1952 has the men’s marathon record been broken by more than 3.4% in one race.5
Now, in the wake of Eliud Kipchoge’s recent world record of 2:01:39 in September 2018, it is worth having a quick look at what this record represents statistically. Specifically, I want to know how the statistical figures that Hoogkamer throws out, above, relate to the statistical improvement in marathon time represented by the Kipchoge world record time.
Before Kipchoge’s Berlin Marathon race, the world record for the marathon was held by Dennis Kimetto with a time of 2:02:57 (2014). Although as of today’s date (4 October 2018) Kipchoge’s time is yet to be ratified by the IAAF, Kipchoge’s winning Berlin marathon time of 2:01:39 represents a 1.07% improvement on Kimetto’s 2014 time. Interestingly, Kipchoge’s unofficial time of 2:00:25 from his Nike Breaking 2 project run in Monza Italy of 2017 represents a 2.1% improvement on Kimetto’s 2014 time. And although Hoogkamer does not actually specify a time in his paper when predicting the world record potentially achievable via the use of the prototype shoes, the VF4% (indeed, one might conjecture that superstition proscribes it), the predicted improvement of 3.4%—which he and his colleagues predicts is the “real” improvement to be expected from a 4% energy cost decrease—translates, with respect to Kimetto’s world record, to a marathon time of 1:58:55. No wonder Hoogkamer and colleagues were so excited by the prospect of breaking the 2-hour marathon. On his figures, the predicted time would have been a sub 1:59:00.