Race Predictors: What They Tell You and What They Don't (And Why Riegel Fails You When You Need It Most)

The Number Everyone Wants and Few Understand

You run a half marathon in 1:35, and before you even cross the line you've done the math: "so my marathon should land around 3:18." You plug the time into an online calculator, a number pops out, you write it into your training plan, and you start organizing your life around it.

The problem isn't that you calculated something. The problem is treating that number like a certain weather forecast when it's actually a statistical estimate built on an assumption that almost never holds completely: that your endurance capacity decays in a predictable, constant way across different durations.

Let's take the Riegel formula apart — where it comes from, why two exponents as close as 1.06 and 1.09 can produce differences of several minutes, and, most importantly for your training, under what conditions the model falls apart entirely.

The Origin: Peter Riegel and the 1977 Equation

Peter Riegel, an engineer and runner, published a simple mathematical model in 1977 based on human performance data across a range of distances and durations — not just road races. His formula:

T2 = T1 × (D2/D1)^1.06

Where T1 is your known time, D1 is the distance of that race, D2 is the distance you want to predict, and 1.06 is the fatigue exponent.

The logic behind the exponent is elegant: if the relationship were perfectly linear (exponent = 1.0), running double the distance would take exactly double the time, which never happens, because nobody holds the same relative pace when the duration of the effort doubles. An exponent greater than 1.0 mathematically captures accumulated fatigue: the longer the target distance, the proportionally slower the pace compared to the reference race.

Riegel didn't design this specifically for elite runners or for the half-marathon-to-marathon transition. He built it by observing performance decay patterns across a variety of human endurance events (including swimming and cycling), looking for a general rule. That generality is both its strength and its Achilles' heel: it works reasonably well on average, and it fails at the margins.

Why Does 1.06 Versus 1.09 Make Such a Difference?

Here's the detail most online calculators hide: Riegel's exponent isn't a universal constant. It's an empirically fitted parameter, and different studies and populations produce different values.

• 1.06 is Riegel's original value, derived from a large, heterogeneous sample of endurance events.
• 1.07–1.08 shows up in later re-analyses using populations of road racers specifically.
• 1.09–1.10 fits recreational runners with lower weekly volume better, where performance drop-off between distances is more pronounced than in runners with higher weekly mileage.

Let's do the arithmetic with a concrete example. Half marathon in 1:35:00 (5,700 seconds):

• With exponent 1.06: T2 = 5,700 × 2^1.06 = 5,700 × 2.0845 ≈ 11,882 seconds → 3:18:02
• With exponent 1.09: T2 = 5,700 × 2^1.09 = 5,700 × 2.1282 ≈ 12,131 seconds → 3:22:11

Four minutes of difference just from changing the second decimal of the exponent. For a runner dialing in marathon pace to the second per kilometer, that difference is the gap between a reasonable race plan and one that sends you into the wall at kilometer 32.

The reason the exponent rises in lower-volume runners is physiologically coherent: Riegel's model assumes your "resistance to fatigue" is relatively constant across distances, but that resistance depends directly on how much accumulated aerobic endurance training you have. A runner training 90 km/week has a flatter decay curve (an exponent closer to 1.06) than one training 40 km/week, whose glycogen reserves and running economy degrade faster as the duration of effort extends (an exponent closer to 1.09 or even higher).

When the Model Works Reasonably Well

Riegel tends to land within an acceptable margin (2-4%) when these conditions are met simultaneously:

1. Consistent and sufficient training volume — generally 60+ km/week sustained over the 8-12 weeks prior, with at least one long run approaching 28-32 km for a marathon target.
2. Comparable environmental conditions between the reference race and the target race — similar temperature, humidity, and altitude.
3. A recent, well-executed reference race — a half marathon run with good pacing 3-5 weeks earlier predicts better than one from 4 months ago, or one run with poor pace management.
4. A reference distance that isn't too short — predicting a marathon from a 5K is statistically far less reliable than predicting it from a half marathon, because the predominant energy system shifts substantially between those durations.

Under these conditions, the model serves as a reasonable starting point for setting a target pace range — not a surgically precise number.

When the Model Breaks: The Three Silent Killers

Heat and Humidity

This is, in my experience working with runners preparing for fall marathons in variable climates, the factor that most destroys Riegel's validity. The model has no term for temperature whatsoever. It implicitly assumes the thermal conditions of the reference race and the target race are equivalent.

The physiological reality is that thermoregulatory stress competes directly with the cardiovascular system for cardiac output: as core body temperature rises, more blood gets redirected to the skin to dissipate heat, leaving less available for active muscles. This drives heart rate up at a given pace and accelerates perceived fatigue independently of your actual aerobic fitness. If you ran your reference half marathon on a cool 8°C morning and your target marathon is run at 22°C with high humidity, any Riegel prediction becomes significantly optimistic — sometimes by 10-15 minutes or more over the full marathon distance.

Altitude

Same structural problem: the model doesn't correct for partial pressure of oxygen. If your reference race was at sea level and your target race sits at 1,800-2,500 meters, the reduction in oxygen availability impacts your effective VO2max and your ability to sustain the relative pace the model assumes is constant. Riegel's prediction in these cases needs a separate manual adjustment — typically adding several seconds per kilometer depending on specific altitude — because the mathematical model simply doesn't account for this variable.

Lack of Endurance-Specific Volume

This is the least-discussed failure point, but perhaps the most relevant for recreational runners. Riegel predicts the relationship between two events well when both are "trained" proportionally. If you ran a solid half marathon leaning on speed and good running economy, but your longest run of the cycle topped out at 18 km, you don't have the aerobic base or the fat-oxidation endurance that a full marathon demands.

In this scenario, hitting the wall at kilometer 30-32 isn't a pacing failure — it's a preparation failure that no formula can predict, because the formula assumes your physiology scales proportionally with distance, and it simply doesn't when the specific stimulus of prolonged endurance is missing (glycogen depletion, fat-oxidation adaptations, eccentric muscular strength to absorb repeated impact).

What the Evidence Says About Monitoring Physiological Response, Not Just the Final Number

Part of why this topic interests me so much is that obsessing over the calculator's final number distracts from something more useful: understanding how your body is actually responding to the training process that's supposed to support that number.

Recent research on exercise biomarkers [PMID:41922043] underscores that objective physiological metrics — heart rate variability, markers of metabolic stress, recovery indicators — offer a much richer window into an athlete's real readiness than a single formula based on one race result. If your HRV is deteriorating week over week during a marathon block, or your resting heart rate is climbing steadily, that tells you more about whether you'll hold the "predicted" pace than the second decimal of Riegel's exponent ever will.

Similarly, we know sustained aerobic exercise has measurable effects on brain-derived neurotrophic factor (BDNF) [PMID:25455510], which indirectly influences how well you manage perceived effort and mental resilience during long efforts — a component no mathematical formula captures, but one that determines whether you collapse mentally at kilometer 35 or hold pace with a clear head.

It's also worth noting that body composition and sleep quality interact with endurance performance in ways prediction models completely ignore. Research on body roundness index and its relationship with sleep disorders mediated by depression [PMID:40055626] reminds us that preparing for an endurance race is an integrated system — sleep, body composition, mood, training load — not an isolated equation of time and distance.

Cross-Training and the "Transferable Aerobic Fitness" Assumption

One interesting data point that indirectly supports why Riegel needs individual context: a study comparing cycling HIIT versus running for fat loss and gut microbiota composition in overweight men [PMID:38233990] showed that, although both modalities produced significant metabolic adaptations, the mechanisms and specificity of those adaptations varied by exercise mode. This reinforces a point I bring up constantly with athletes: general aerobic fitness isn't fully transferable between modalities or between distances. Your VO2max might be excellent, but if you don't have the specific running volume that builds running economy and localized muscular endurance for 42.2 km, no mathematical model is going to compensate for that gap.

How I Use Riegel in Practice With My Athletes

I don't throw the formula out — I use it as the starting point of a conversation, not a final verdict. Here's the process I follow:

1. I calculate a range, not a single number: I run both exponents (1.06 and 1.09) and treat the result as a 4-6 minute range, not an exact figure.
2. I adjust for environmental conditions, comparing expected temperature and humidity between the reference race and the target race, applying a manual correction when the difference exceeds 8-10°C.
3. I review training volume and the longest run of the block before trusting the prediction. Without at least 2-3 well-executed runs of 28+ km, I drop my confidence in the number a full notch.
4. I treat the result as a likely ceiling, not a starting pace. Going out at the exact pace the formula predicts from kilometer 1 is, in my experience, the most common way to turn a good prediction into a bad result. I'd rather the athlete start 5-8 seconds/km more conservatively and assess around kilometer 25-28 whether they can accelerate toward that number.

Conclusion: The Number Is a Hypothesis, Not a Promise

The Riegel formula is a useful statistical tool built on a real pattern of human performance decay. But an average pattern is not your individual physiology on a specific day, under specific conditions, with a specific level of preparation. The difference between exponent 1.06 and 1.09 isn't a trivial detail — it's the difference between assuming you have the aerobic base of a high-volume runner or one who's still building it.

Use the number. But check it against your training, your longest run, the weather on race day, and how your body has felt over the past few weeks, before you commit to it at kilometer 1.

References

• Riegel, P.S. (1977). Time predicting. Runner's World.
• Siebers M, Bizjak DA. Exercise biomarkers. Adv Clin Chem. 2026. [PMID:41922043]
• Szuhany KL, Bugatti M, Otto MW. A meta-analytic review of the effects of exercise on brain-derived neurotrophic factor. J Psychiatr Res. 2015. [PMID:25455510]
• Couvert A, Goumy L, et al. Effects of a Cycling versus Running HIIT Program on Fat Mass Loss and Gut Microbiota Composition in Men with Overweight/Obesity. Med Sci Sports Exerc. 2024. [PMID:38233990]
• Gong H, Zhao Y, et al. Association between body roundness index and sleep disorder: the mediating role of depression. BMC Psychiatry. 2025. [PMID:40055626]