You’ve been running for a few months. You’re signed up for a 10K. And the question you can’t stop thinking about is: how fast can I run it?
Pacewright answers this — but not with a single magic number. It gives you a range, built from up to three different mathematical models, each approaching the problem differently. Here’s how.
Model 1: The Riegel Formula
The most widely used race prediction model in running. Published in 1981, it’s elegantly simple:
T2 = T1 × (D2 / D1)^k
Where T1 is your known time at distance D1, and T2 is the predicted time at the target distance D2. The exponent k is the fatigue factor — how much you slow down as distance increases.
The population average for k is 1.06. But individual runners vary significantly. Elite marathoners with exceptional endurance might have a k of 1.03-1.05 — they slow down very little as distances increase. Runners with a speed-oriented physiology might have a k of 1.08-1.10 — they’re relatively faster at shorter distances.
How Pacewright personalizes it: If you have two or more race results at different distances, Pacewright calculates your personal k value. This makes the Riegel prediction specific to your physiology rather than a generic estimate. Your k is clamped between 1.03 and 1.10 — outside that range, the data is probably noisy rather than meaningful.
What it’s good for: Predictions across a wide range of distances, from 5K to marathon. Simple, robust, and well-validated across decades of data.
What it’s not good for: Short distances (under 2 miles) where anaerobic capacity matters more than endurance, and predictions based on a single data point where k can’t be personalized.
Model 2: VDOT (Jack Daniels)
Jack Daniels’ VDOT system estimates your running fitness as a single number — your “VDOT” — derived from a race performance. It works by calculating the oxygen cost of running at your race pace, then estimating what percentage of your maximum oxygen uptake (VO2max) you sustained for that duration.
The math is more complex than Riegel:
- Convert your pace to oxygen cost (VO2) using a quadratic equation
- Estimate what percentage of VO2max you used based on race duration
- Divide to get VDOT (your effective VO2max for running)
- Use the same equations in reverse to predict times at other distances
Why it’s different from Riegel: Riegel extrapolates from a simple power law. VDOT models the underlying physiology — oxygen uptake and the duration-dependent limit on what fraction of your max you can sustain. This makes VDOT predictions slightly different from Riegel predictions, especially at extreme distance ratios.
What it’s good for: Predictions where the reference distance and target distance are within a reasonable range (5K-marathon). Also useful for setting training paces — Daniels’ training zones are derived from VDOT.
Model 3: Critical Speed (PT Test Distances)
For shorter distances — 1.5, 2, and 3 miles — Pacewright uses the Critical Speed model, which is built on the hyperbolic relationship between speed and sustainable duration.
D = CS × t + D’
Where CS is your critical speed (the fastest pace you can sustain aerobically) and D’ is your anaerobic distance reserve (how much additional distance your anaerobic system can contribute). With two or more time trials at different distances, Pacewright calculates both values via linear regression.
Why a different model for short distances: At distances under 5K, anaerobic capacity becomes a significant factor. The Riegel formula doesn’t separate aerobic and anaerobic contributions — it just extrapolates. Critical Speed explicitly models both systems, producing more accurate predictions for 1.5-3 mile efforts.
The Ensemble: How Pacewright Combines Them
When multiple models are available, Pacewright doesn’t pick a winner. It runs all applicable models and takes the median prediction as the headline time. The spread between the models, combined with data quality factors, determines the width of the confidence interval.
The range is always P20-P80 — meaning there’s roughly an 80% chance your actual finish time falls within the range. This is deliberately wider than a “best guess” because race day introduces variables no model can predict: weather, terrain, crowd pacing, sleep the night before, race-day nerves or adrenaline.
What Widens the Range
| Factor | Additional Width |
|---|---|
| Reference data is more than 60 days old | +3% |
| Target distance is 4x+ longer or shorter than reference | +3% |
| Low overall data quality | +4% |
| Based on training data only (no race result) | +2% |
A prediction based on a recent race at a similar distance will have a tight range. A prediction based on a 3-month-old training run extrapolated to a distance four times longer will have a wide range. Both are honest — they just have different confidence levels.
Minimum Range
Even in the best case — multiple models, recent race data, similar distance — the confidence interval never goes below ±3%. Because even with perfect data, race day is not a lab experiment.
What Makes a Good Prediction
The quality of Pacewright’s prediction depends entirely on the quality of your input data:
- Best case: Two or more recent race results at different distances. This lets the algorithm personalize your fatigue factor and cross-validate between models.
- Good case: One recent race result. The algorithm uses population averages for what it can’t personalize.
- Okay case: Recent hard training efforts (tempo runs, time trials). Training data is less reliable than race data because most people run harder on race day.
- Poor case: Old data, single data point, or training-only with no race efforts. The prediction will have a wide range to reflect the uncertainty.
Pacewright tells you which case you’re in. Every prediction comes with an explanation of which models were used, what data they were based on, and what factors widened the range.
What the Prediction Is Not
It’s not a promise. It’s not a pace target. It’s a mathematically informed estimate of what your current fitness suggests you’re capable of, given the available data.
Run your race by effort, not by prediction. The prediction tells you what’s plausible. RPE tells you what’s sustainable in real time. If mile 1 feels harder than expected, trust the feeling, not the number.