Before this, there was no model. What explains the ability to run 1609 meters in 4 minutes? Exeter built two equations that answer the question.
21 middle-distance athletes. Lab and track testing. Two predictive models. The first mathematical framework for the 4-minute mile.
Osborne & Jones — University of Exeter | Kirby — Nike Sport Research Lab
Middle-distance running is a collision of aerobic and anaerobic physiology. The Mile sits right at the crossover — too long to sprint, too short to rely on endurance alone.
Exeter's team brought 21 elite middle-distance runners (11 male, 10 female) through a comprehensive battery of lab and field tests to identify which physiological variables actually predict 4-minute performance.
The strongest single predictor (r = 0.84). CS represents the highest speed you can sustain in a metabolic steady state — your aerobic ceiling.
D′ is your finite anaerobic reserve above critical speed. The ratio D′/CS captures how much kick you have relative to your aerobic base. Both variables were significant (P < 0.001).
Maximum speed during a 20-second all-out sprint captures peak anaerobic power and fast-twitch fiber recruitment. It is the strongest predictor in this model — the faster the sprint, the faster the 1500m (P < 0.001).
The speed at which lactate begins to accumulate exponentially — a direct marker of aerobic capacity at high intensity. Higher LTP means you can sustain a faster pace before anaerobic reserves are tapped (P < 0.001).
Both models tell the same story: you need both engines. The aerobic system sets the floor. The anaerobic system determines how far above it you can go.
Until this work, there was no mathematical framework that explained what it takes to cover 1609 meters in 4 minutes. Coaches and athletes relied on intuition, race splits, and training tradition — but no model existed to identify the specific physiological levers that predict 4-minute performance.
The 4-minute mile demands a high aerobic ceiling (Critical Speed) and a substantial anaerobic reserve (D′). Neither alone is enough. Both models converge on the same conclusion — and together they explain 81–87% of the variance in performance.
These models don't just predict performance — they diagnose where the gap lives for any individual athlete. Measure their CS, D′, sprint speed, and LTP, and the model tells you exactly which engine needs work.
of variance in 4-minute performance explained by CS and D′/CS — the aerobic-anaerobic interaction
of variance in 1500m time explained by sprint speed and lactate turnpoint — two measurable, trainable variables
For the first time, we have the formula.
The Exeter models give us something that didn't exist before — a mathematical framework that explains what it takes to run 4 minutes. Two equations, built from 21 elite athletes, that identify the exact physiological variables that determine performance at the barrier. The formula for sub-4 is no longer a mystery. It's an equation.
This study is one chapter in a multi-institution scientific expedition exploring the limits of the women's 4-minute mile.
See the full series →