Only four independent parameters model running performance. The MIT-developed model accurately predicts performance and establishes training paces. These parameters correspond to a speed close to Velocity at VO2max (vVo2max), a time close to vVO2max support time, short distance endurance and long distance endurance.
I present the model to which I contributed in a research project at MIT (Boston), in a CNRS and MIT laboratory. It is the subject of a scientific publication “A minimal power model for human running performance” which I co-authored with Thorsten Emig and Matthew Mulligan.
This article explains the model’s main features and how training speeds are calculated in RunMotion Coach.
Contents
2 important definitions: Velocity at VO2max and Endurance
The Velocity at VO2max (vVO2max or MAS) is the speed at which a runner consumes the maximum amount of oxygen their body can use (VO2max). In practical terms, above vVO2max, a runner exhausts themselves very quickly.
Studies indicate that a runner can maintain vVO2max for 4 to 7 minutes, which is the vVO2max support time.
Endurance is a runner’s ability to sustain a given intensity over a long period of time.
There are 2 types of endurance: short and long distances
I present below my own performance curve with all my personal records.
We can see in the graph that it is possible to group these points into 2 groups.
We’ve identified two endurance types: short distance endurance (in black) for roughly 2 to 6 minutes, and long distance endurance (in blue) for approximately 6 minutes to several hours (typically 4 to 5 hours).
The 6-minute duration isn’t fixed but corresponds to the intersection of the two straight lines. This point (with the coordinates Vm and tc in our model) is close to the vVO2max and the support time of the vVO2max: 22.9km/h for me.
The flatter the slope, the longer a runner can hold a given intensity — in other words, the more enduring they are.
Although it may seem surprising, endurance doesn’t depend on a runner’s overall level. Two runners finishing a marathon in 2h30 and 4h can have the exact same endurance, even though the 2h30 runner’s vVO2max is higher.
Personally, my short distance endurance is very good, and my long distance endurance is average.
To establish the 4 parameters, you need a minimum of 2 races under 6 minutes and 2 races over 6 minutes, each at varying distances. Typically: 800 meters, 1500 meters, 3000 meters and 10 kilometers.
What are the limits of our model?
If a runner doesn’t have results across this full range of distances, we can fix certain parameters and focus only on short (under 6 minutes) or long (over 6 minutes) distances.
In RunMotion Coach, we focus on races between 6 minutes and 5 hours, which covers the vast majority of our users’ road and trail races. We also assume the athlete raced these events flat-out and was in comparable form for each of them.
My graph illustrates my best races – the 1500 meters, 3000 meters, and the “Duc’s Race” (a 19.5km road race), all of which exceed the two reference lines.
By contrast, my 1000m, 5000m, and half marathon results sit well below the line. These are the three distances I’ve optimized the least in competition, or that I ran in seasons when I wasn’t in peak shape. On the half marathon, for instance, the model predicts 1:06:26 — about 2 minutes faster than my actual personal best.
In the marathon, I adjusted for the New York Marathon’s roughly 250m of elevation change using a correction coefficient. A German coach, after comparing a large number of races run with and without elevation gain, worked out coefficients for positive and negative elevation to convert results to an equivalent flat speed.
RunMotion Coach app factors in elevation and adjusts these coefficients automatically, especially on trail routes given how technical they can be.
When a runner’s results aren’t all at a comparable level, we also apply a filter to exclude their “worst” races — the ones well below the line. This is typically the case when conditions were poor: too hot, or otherwise unfavorable.
The model no longer holds at the very short end (pure sprinting), and beyond 4 to 5 hours of effort, muscular and central nervous system fatigue start to dominate performance.
How to calculate your training paces?
You may have already come across tables of % vVO2max for intervals — for example, running 1000m at 90% of vVO2max. The problem with these tables is that they only work if your endurance profile is “typical.”
With our model, training paces are calculated directly from the focus of the session. For example, a 6×1000m session at 10K pace will be based directly on your own theoretical 10K time. We also apply progressive adjustments to your paces as you aim to beat your records.
My practical recommendations to get the right training paces
If your training paces feel too easy or too hard, get in touch via the contact form at the bottom of the page so we can review your calculated vVO2max and endurance. Adjustments are sometimes needed — particularly on trails, where elevation coefficients don’t always fully capture technicality or weather conditions.
I recommend that you enter at least 2 of your best performances over distances that are twice as long as each other. For example 5km & 10km, 10km & half marathon, or half marathon & marathon.
If you already know your vVO2max, you can add a 1.6km race at 6 minutes to your past results — for example, if your vVO2max is 16km/h, just divide it by 10 to get the distance, and enter it with a time of 6 minutes.
The long distance endurance index
In conclusion, it’s worth noting that Peronnet and Thibault recognized the linear relationship between speed and the Naperian logarithm of time for long distances back in the 1980s. The endurance index is calculated in this way :
Endurance index = (% of vVO2max held during the race – 100) / Ln (race time / 6)
There are sometimes variations, with the 6 replaced by a 7, depending on whether you take the vVO2max support time in 6 or 7 minutes.
Go further with our model
If you want to know more about our model and find all the mathematical formulas 😉, I invite you to read our scientific publication “A minimal power model for human running performance”. The model has been validated in thousands of runners.
You can calculate your own endurance profile using our performance prediction calculator — it derives your vVO2max and endurance from just two race results.
From this model, it might even be possible to detect abnormal performances (a doping signal) or identify runners with high untapped potential. It also shows, for a given runner, whether it’s more effective to prioritize developing vVO2max or endurance in order to optimize performance.
Beyond individual runners, the model also applies to world records, as I explored in this article. World records in the half marathon and marathon appear to be benefiting from recent advances in shoe technology.