"Marathoning made easy"? Um, not really

October 23, 2010

PLoS Computational Biology just published a study by Benjamin I. Rapoport titled “Metabolic Factors Limiting Performance in Marathon Runners.” The article is already generating some buzz, as exemplified by the Science News summary “Marathoning made easy.” I myself consider the article useful as a synthesis of previously published information on fuel usage during distance running. However, in my opinion, the extent to which this paper offers new insights or useful advice is being vastly overestimated.

As stated in the Abstract, the essence of the paper is:

The analytic approach presented here is used to estimate the distance at which runners will exhaust their glycogen stores as a function of running intensity. In so doing it also provides a basis for guidelines ensuring the safety and optimizing the performance of endurance runners, both by setting personally appropriate paces and by prescribing midrace fueling requirements for avoiding ‘the wall.’

The first sentence above covers the aspects of the paper that I consider most worthwhile. The author explains how the distance one can travel before running out of glycogen depends on exercise intensity and the amount of glycogen stored in the liver and muscles. This is well-trodden territory in the world of exercise physiology, but Rapoport provides equations for all of the key relationships. Writing out the equations is useful as a way of more carefully defining relationships that are often described qualitatively.

From these equations, Rapoport generates several complicated graphs, such as Figure 2. The conceptual basis of this figure is: (A) the faster you go, the more you rely on carbohydrates (as opposed to fat); (B) fit people (with a high VO2max) will use less carbohydrate at a given pace than unfit people (with a low VO2max); (C) having larger leg muscles allows you to store more glycogen; (D) glycogen levels can be increased by carbo-loading. Again, these are not new ideas, but trying to capture them all quantitatively in a figure is commendable.

A key point about Figure 2 and the equations underlying it is that they describe the relationships of variables on average. Rapoport certainly understands this and devotes a subsection of the Methods section to “Identifying and Quantifying Sources of Error.” What he does not fully appreciate, in my view, is that the many sources of variability between and within individuals make it virtually impossible to derive individual recommendations from his equations and graphs.

Let’s consider an example from the paper:

For runners of typical builds with glycogen stores loaded according to ordinary training regimes, this aerobic capacity [60 mL O2 per kilogram of body mass per minute] is marginally insufficient to run a marathon at the pace (13.3 kilometers per hour, or 7:15 per mile) required to finish in 3 hours 10 minutes, the current principal male qualifying time for the Boston Marathon…. This situation can be inferred from Figure 2, in which the green curve corresponding to a VO2max of approximately 60 mL O2 per kg per min intersects the lower limit of the shared ‘Glycogen Loading to Supercompensation’ region at a pace slightly slower than 3:10… The typical male runner hoping to run a qualifying time for the Boston Marathon must therefore either achieve some degree of supranormal glycogen loading (through a glycogen supercompensation protocol prior to the race) or strategically refuel during the race.

It’s fine to define a “typical” male (who in this case has a VO2max right at the 90th percentile before increasing it further through training) and estimate his carbohydrate needs, but who is really typical, and how do you know? This typical runner is not only assumed to have a very specific VO2max, but also a typical running economy (oxygen burned per distance traveled) and a fully glycogen-loaded liver (not true if he didn’t have a big breakfast after fasting overnight). The individual’s effective VO2max on race day may differ somewhat from his usual reading due to tapering or mild illness or whatever. In addition, the rate of glycogen use varies somewhat with factors such as time since the start of exercise, glycogen levels remaining, and body temperature.

If a runner hasn’t had his VO2max checked repeatedly by a reliable lab, estimates of glycogen use will be even less certain. As Rapoport explains, VO2max can be estimated from heart-rate data, but this introduces further uncertainty into the calculations.

Am I blowing the issue of inter- and intra-individual variability out of proportion? Consider EnduranceCalculator.com, a web page created by Rapoport and “designed to enable endurance runners to determine safe, personalized racing paces over distances such as the marathon.” If I plug in the requested information — weight, age, resting heart rate, and target marathon time — I am told that a “Conservative Best Marathon Performance (Normal Glycogen Loading)” would be 3:20:07 and that an “Aggressive Best Marathon Performance (Maximal Glycogen Loading)” is 2:17:16. In other words, a bunch of intricate calculations based on typical parameters can predict the marathon time of an individual such as me … to within a one-hour window. Not very specific, is it?

This online calculator is in some ways a “worst-case scenario” because it estimates VO2max from resting heart rate, which in fact is a poor predictor of VO2max. But even with additional information, there will usually be a window of uncertainty that precludes personalized recommendations such as “Runner A needs to carbo-load, whereas Runner B does not.” The huge time ranges spit out by Rapoport’s website may be a tacit acknowledgment that truly exact pace prescriptions are not possible without a much more highly individualized analysis than what is provided by this study.

But there is an even more fundamental and important point here. Predicting whether runners need extra carbohydrates before or during a marathon is useful only if there are significant costs to ingesting these carbohydrates. That may be true in selected cases — some runners do overeat at pre-race pasta feeds to the point of discomfort, and others have finicky stomachs that don’t tolerate sports drinks well — but, in general, the problems associated with carbohydrate supplementation are minor. If ingesting extra carbohydrates before and during a marathon might help you avoid “hitting the wall,” why wouldn’t you do it? Especially after investing all of that time and effort in training, traveling to the race, etc.? Are runners really going to think, “This mathematical model tells me that, based on my physiological parameters, I should be able to run my goal pace for 27.7 miles with normal glycogen stores, so I’m not going to bother with carbo-loading?” Given the uncertainties associated with these calculations, wouldn’t it make sense to carbo-load (and grab Gatorade at aid stations) anyway, in case one’s actual rate of glycogen use is a bit higher than predicted?

Again, I believe Rapoport is at least somewhat cognizant of these uncertainty-related issues. However, his attempts to demonstrate the utility of his analysis leave me underwhelmed. He “validates” his model by comparing its predictions with experimental data published by Karlsson & Saltin (1971). He reports, that, on average, the actual glycogen use by the runners during a 30-kilometer race was about what was predicted, which is OK but provides no evidence that the predictions are accurate at an individual level. Moreover, given that exercise physiologists have been studying glycogen and endurance for over 40 years, comparison to a single study of a relatively homogeneous group (ten pretty fit physical education students) is not ideal.

Rapoport states that his paper “sheds physiologically principled light on … the qualifying times for the Boston Marathon.” What he actually shows is that there is a good chance that the typical male mentioned above will benefit from carbo-loading if aiming for a 3:10 (the standard for males 18 to 34), and that a benefit is slightly less likely for a female who has a VO2max of 52 and is aiming for a 3:40 (the standard for females (18 to 34). As far as I can tell, this observation has no real significance beyond suggesting that (A) it’s challenging for some people to qualify for Boston, (B) carbo-loading may help, and (C) the standards for males and females are not horribly misaligned. Didn’t we know that already?

Rapoport also makes a big deal of the fact that runners who have reported “hitting the wall” do so at about mile 21, on average. Figure 3 of his paper attempts to show that this is consistent with his equations for a wide range of runners. However, he assumes that the runners are operating at 80 to 95% of VO2max during their marathon, which is an overestimate for all but the fittest and most motivated athletes. Moreover, his curves show a broad range of distances at which the wall may be hit, consistent with anecdotal experience. The new analysis thus offers a rough confirmation of, but no particular insight beyond, the decades-old rule of thumb that people tend to hit the wall at mile 20 or so.

As I noted at the outset, there is merit in some aspects of this work. However, I suspect that the paper was reviewed by computational biologists with limited knowledge of exercise physiology. Reviewers with greater expertise in endurance exercise could have helped the author mold the paper into a more valuable contribution.


  1. After reading his paper and your critique I was pretty skeptical. Punching my stats into his calculator, though, gave me my exact finishing time of my last marathon as the "conservative" estimate.That said, the aggressive numbers seem a bit crazy. I have a hard time performing at 95% VO2max for 10 mi, let alone a full 26.2.

  2. Thanks for so precisely articulating the shoulder shrugs I felt when I read about this and then when people started querying wanting to base articles on it.

  3. helloit has been quite some time since my mathematical & journal reading days.i think i understand the basic idea of his article & your response.for endurance athletes – what does all this mean in basic terms?is there a (semi simple) formula for people to calculate how much & when to take in fuel (both before & during the marathon)?or is that still in the works?in other words – how do people who are less scientific take the information & use it?hope all be wonderful

  4. elysa: My opinion is that there is no formula that is both simple and useful. In terms of carbohydrate ingestion, my advice to a marathoner would be to experiment with carbo-loading and sports drinks in training, confirm that they do not cause problems for that individual, and then use them before and during the race. Feeding frequency is also something best established through personal experimentation, I think.

  5. […] of Lore of Running by Timothy Noakes, Born to Run (part 1; part 2) by Christopher McDougall, “Metabolic Factors Limiting Performance in Marathon Runners” by Benjamin Rapoport, Wheat Belly by William Davis, and “Misconceptions Are So […]

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