Hello and welcome back to the Endurance Lab newsletter.

In last week's newsletter, I talked about:

In short, the two are very similar, although they are measured differently. Depending on how lactate threshold is defined, critical power is generally going to be closer to the second lactate threshold or lactate turnpoint than the first lactate threshold. You may also see some skewing depending on what race distances you use to estimate critical power, but from a physiological perspective, these measurements are trying to tell us something similar about the highest intensity at which exercise can remain relatively stable.

This past week, I had a podcast with Riley Witt, the CEO of Bicarb Shop. It was a really fun episode where we got to talk about all things performance-enhancing, legally. He's going to come on for a second episode where we're going to finish talking about some other, more niche applications of these or similar methods. I also was lucky enough to have on Bryan Poerner, the CEO of Diadora. That should be self-explanatory. Go give it a listen.

All right, this newsletter is actually inspired by a podcast I did with Andy Jones. During the podcast, Andy talked about the physiology of elite marathoners. He shared that earlier in his research, when they were measuring elite runners, they used something called the Joyner model to determine whether these runners had the physiology required to break the two-hour marathon.

As usual, if you’re interested in coaching, apply on my website and we’ll hop on a call for a chat. It’s between $120-200 a month and comes with unlimited access to all the Dr. Evans banter you could ever want.

Also, many people ask me, “why are your prices so low”, to which I respond much like the CEO of Diadora, if we’re not trying to get people to hit their goals, then what are we doing here?

Maybe a time will come where I’ll have to up my prices, but for now, I’m just here to help as many people as I can and to justify the time to my wife. I love what I do.

The original paper was published by Michael Joyner in 1991 and was titled “Modeling: Optimal Marathon Performance on the Basis of Physiological Factors.”[1] In short, the paper examined the physiological factors that limit marathon performance, and the three that were most apparent were:

At the time, the idea was that VO₂max represents the upper limit for aerobic metabolism, while lactate threshold is related to the fraction of VO₂max that can be sustained during long-distance events. This is still true today.

Running economy, when you think about it, puts the other two together by telling you how much oxygen it costs to run at a given speed.

What's interesting about the paper is that Joyner references some legit old-school studies, including Pollock's publication titled “Submaximal and Maximal Working Capacity of Elite Distance Runners. Part I: Cardiorespiratory Aspects,” published in 1977.

In that paper, the VO₂max values of the elite runners ranged from 71.3 to 84.4 mL/kg/min and averaged approximately 76. This is the dataset that included Steve Prefontaine, along with several other elite runners of that era.

This study provided the basis for the low, medium, and high VO₂max values Joyner used in the model.

From there, Joyner moved on to lactate threshold. Basically, what he stated, which is true, at least from what I've seen in the lab, is that elite runners may be able to complete a marathon while using roughly 80 to 85% of their VO₂max.

Joyner based this part of the model on several earlier studies, including Costill and colleagues' 1973 paper, “Fractional Utilization of the Aerobic Capacity During Distance Running,”[2] and Farrell and colleagues' 1979 paper, “Plasma Lactate Accumulation and Distance Running Performance.”[3]

Fun side note: this area of research also includes Dr. Ben Hurley and Dr. Jim Hagberg's work with Doug Seals and John Halsey in 1984 on the effects of training on blood lactate levels during submaximal exercise[4]. This was some of the earlier work examining blood lactate and the adaptive response to aerobic training. I'm going to have Dr. Hagberg on the podcast, and this is one of the papers I'm going to ask him about.

The final component is running economy. Joyner pulled data from a 1980 paper titled “Running Economy and Distance Running Performance of Highly Trained Athletes,”[5] where Conley and Krahenbuhl examined how VO₂ changed with running speed. This work built on earlier research by Dr. Jack Daniels.

What you see is a nearly straight-line increase in oxygen consumption as running speed increases.

This general relationship is also part of how submaximal exercise equations can be used to estimate aerobic capacity from the physiological response to a known workload. Wearables such as Garmin use a much more complicated version of this basic idea when estimating VO₂max from the relationship between heart rate and running workload. These estimates have gotten better in recent years, although they are still not perfect, partly because the watches have gotten better at estimating the workload you are actually producing.

What's interesting about the Conley study, though, is that the runners were tested only up to 17.7 km/h. That pace corresponds to roughly a 2:23 marathon, whereas world-record marathon pace at the time was close to 20 km/h. Unfortunately, there were not good running-economy data at the much higher speeds needed to model a two-hour marathon, so extrapolating the VO₂-speed relationship to those speeds was probably the biggest stretch in the model.

What I will say is that Joyner used a very conservative estimate when he converted the physiological values into predicted marathon performances. He slowed the predicted speeds by 10% to account for the added effects of wind resistance and the duration of the race.

When Joyner combined VO₂max, sustainable fraction of VO₂max, and running economy, he produced a table of predicted marathon performances. He grouped runners according to low, average, and high running economy because we know that running economy can vary substantially between athletes.

For an individual with a very high VO₂max who could sustain a VO₂ of 70 mL/kg/min and had exceptionally good running economy, the model predicted a marathon as fast as 1:57:58.

On the other end, an athlete sustaining a VO₂ of 52.5 mL/kg/min with relatively poor running economy was predicted to run approximately 2:55. What's interesting about this model is that running economy produced a huge change in predicted performance. In the 52.5 group, for example, the estimate changed from approximately 2:55 with poor economy, to 2:46 with average economy, to 2:34 with excellent economy.

The absolute time difference gets smaller as the athletes become faster because the relationship between speed and finishing time is nonlinear. A fixed percentage change in speed produces fewer minutes of improvement when the original finishing time is already faster.

You see the same pattern in individuals who could sustain a VO₂ of 70 mL/kg/min for the marathon. Their predicted times ranged from approximately 2:12 to 2:05 to 1:58, depending only on running economy. Again, this is a massive change when everything else is the same. This, in my opinion, is one reason super shoes have played such a huge role in marathon performance.

So great, we have the model, but has it actually been validated? Well, it absolutely has.

A 2026 paper titled “35 Years of Joyner's Endurance Performance Model: Assessing the Contribution of Physiological Determinants of Performance Proxies in 888 Individuals from Recreational to World Class”[6] examined this framework in 495 runners and 393 cyclists.

The authors found that VO₂max and exercise economy together accounted for approximately 95% of the explained variation in speed or power at lactate threshold and lactate turnpoint. VO₂max made the largest contribution, followed by economy, while fractional utilization contributed relatively little across this very heterogeneous group.

Importantly, the outcomes were speed and power at lactate threshold and lactate turnpoint, which the authors treated as performance proxies. They did not directly predict marathon finishing times in all 888 individuals.

Still, the major point stands: Joyner's framework was bang on the money.

The original Joyner model uses values measured while an athlete is fresh. The problem is that how you run at mile 20 is not necessarily the same as how you run at mile one.

Andrew Jones and Brett Kirby describe this missing component in their 2025 paper, “Physiological Resilience: What Is It and How Might It Be Trained?”[7] Physiological resilience refers to how well an athlete preserves VO₂max, thresholds, and economy as prolonged exercise continues.

In Figure 1, Jones and Kirby compare actual marathon performances in 11 elite runners with predictions from the original Joyner model.

The original model was already close, but it tended to predict slightly slower performances than the athletes actually achieved. Adding a generalized resilience factor brought the average prediction closer to the actual performances, although there was still substantial variability between athletes.

One of the cooler parts of the paper is Figure 2. Across two hours of heavy-intensity cycling, VO₂ gradually increased while respiratory exchange ratio fell from approximately 0.91 to 0.84. This indicates a progressive shift toward greater fat utilization. Because fat requires more oxygen than carbohydrate to produce the same amount of ATP, Jones and Kirby estimated that this substrate shift explained approximately 30% of the rise in VO₂ during the ride.

This helps explain why carbohydrate availability may matter for resilience. In one of the studies discussed in the review, consuming 60 g of carbohydrate per hour during two hours of heavy exercise reduced the subsequent decline in critical power compared with placebo.

Joyner also published a more recent paper titled “Modeling the Marathon and Human Endurance Performances: Some Thoughts and What's New?”[8]. In it, he looks back at how he developed the original model, what has changed over the past 30-plus years, and where the limits of human endurance performance may go next.

Unfortunately, I couldn't get access to the full publication, but I intend to because it seems like a pretty cool paper and I have mad respect for Dr. Joyner. He actually mentored one of my former co-mentors, Sushant Ranadive, at the University of Maryland. Sush was one of the people who guided my thinking on blood flow and vascular control. Shout out Dr. Ranadive. Thanks for being on my dissertation committee.

I don’t have a perfect takeaway here, but I do have a simple one: if you want to figure out your ideal marathon time, go get a VO2max test. It will tell you all this data and you can figure out how far from your peak you might be. If it is massive, it’s because you lack physiological resilience, so reading papers on how to develop that might be helpful… or I could just tell you. Guess we’ll see.

References

1.         Joyner, M.J., Modeling: optimal marathon performance on the basis of physiological factors. J Appl Physiol (1985), 1991. 70(2): p. 683-7.

2.         Costill, D.L., H. Thomason, and E. Roberts, Fractional utilization of the aerobic capacity during distance running. Med Sci Sports, 1973. 5(4): p. 248-52.

3.         Farrell, P.A., et al., Plasma lactate accumulation and distance running performance. Med Sci Sports, 1979. 11(4): p. 338-44.

4.         Hurley, B.F., et al., Effect of training on blood lactate levels during submaximal exercise. J Appl Physiol Respir Environ Exerc Physiol, 1984. 56(5): p. 1260-4.

5.         Conley, D.L. and G.S. Krahenbuhl, Running economy and distance running performance of highly trained athletes. Med Sci Sports Exerc, 1980. 12(5): p. 357-60.

6.         Mougin, L., et al., 35 Years of Joyner's Endurance Performance Model: Assessing the Contribution of Physiological Determinants of Performance Proxies in 888 Individuals from Recreational to World Class. Sports Med, 2026. 56(8): p. 2047-2065.

7.         Jones, A.M. and B.S. Kirby, Physiological Resilience: What Is It and How Might It Be Trained? Scand J Med Sci Sports, 2025. 35(3): p. e70032.

8.         Joyner, M.J., Modeling the marathon and human endurance performances: some thoughts and what's new? Int J Sports Med, 2025. 46(10): p. 705-709.

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