Cadence · ground contact · vertical oscillation · vertical ratio
Two runners go past at the same pace. One is ticking over at 160 steps a minute, the other at 180. The long-legged one is the slow-cadence one, obviously, and everybody nods and says it is just physics. This is an attempt to find out how much of that 20 steps really is skeleton, using numbers rather than nodding.
Of a 20 spm cadence gap between two runners at the same speed, about 4 spm is anatomy. The other 16 is not.
That is the honest population answer and it comes out of one number: leg length explains roughly 20% of the cadence differences between runners who are going the same speed. Not some of the gap, not most of it. A fifth.
The folk version is not stupid, though, and this is the part that surprised us. Per centimetre of leg the effect is real, large, and almost exactly what the physics predicts. The reason 20 spm is not an anatomy story is not that legs do not matter. It is that two adults standing next to each other do not differ by enough centimetres. Ribbit.
Everything here rests on Malisoux and colleagues (2023), 860 recreational runners on an instrumented force treadmill, because it is the only study reporting speed-controlled coefficients with confidence intervals for all four metrics in one cohort with one method. Leg-length distributions come from ANSUR II, 6,068 adults, which this report downloaded and analysed rather than quoting from a summary table. Every claim carries a grade. A is large, controlled, with a confidence interval. B is peer-reviewed but small, uncontrolled, or derived here. C is a manufacturer or a blog. Nothing ungraded gets asserted.
Put your own dimensions in. The bands are deliberately wide, because the scatter between runners is the biggest single thing in this report and narrowing them would be lying to you.
Predictions are for a runner of your height at your pace with everything else average. The band is a 95% prediction interval for one individual, not a confidence interval for an average, which is why it is as broad as it is.
The frog is decorative. The rate it is hopping at is not.
All four metrics, one cohort, one method, speed held constant, put in the same unit so they can be compared honestly: how many standard deviations does each metric move when height moves by one standard deviation?
Cadence against pace, for three leg lengths
Short, median and long legs taken from the 5th, 50th and 95th percentiles of the real adult distribution. The shaded band is the 95% prediction interval for one individual with median legs.
The standardised effect of height on each metric
Malisoux 2023, n = 860, running speed and the other covariates held constant. Bars are 95% confidence intervals.
| Metric | per cm of leg | 95% CI | scales as | geometric predicts | pendulum predicts | verdict |
|---|
"Scales as" is the power-law exponent, written so it reads straight against the two theoretical predictions. The per-centimetre figures are the study's height coefficients converted to functional leg length using the ANSUR II ratio.
In this cohort men and women have exactly the same mean cadence: 164 spm. The men are 12 cm taller, which should drag their cadence down by about 5 spm, and they ran 1.5 km/h faster, which pushes it back up by about the same. The two cancel almost perfectly.
That is why raw watch data makes anatomy look irrelevant. In the wild, taller runners tend to be faster runners, and the speed effect hides the leg effect. The phrase "at the same speed" in the original question is doing an enormous amount of quiet work.
This is the question that decides everything, and it is an anthropometry question rather than a running one. We pulled the ANSUR II public release, 4,082 men and 1,986 women, 93 measured dimensions, and computed the distribution rather than trusting anybody's summary.
Functional leg length in adults
Trochanterion height, greater trochanter to the floor, which is the hip height the physics actually cares about. ANSUR II, n = 6,068.
Two things fall out of that distribution and both matter more than any biomechanics paper. The first is that most of your leg length is simply your height. Seventy-seven percent of the variance in leg length is variance in stature, and at a fixed height, build moves your legs by only about 2.6 cm either way. The leg-to-height ratio has a standard deviation of 0.015. Human body proportions are boring, and that is itself the finding.
The second settles the brief. To get 20 cm of leg-length difference between two people you need roughly 39 cm of height difference. That is a 157 cm runner beside a 191 cm runner. It happens, but it is about one random pair in a hundred, and it is not the pair anybody is picturing when they explain away their cadence. To buy the full 20 spm you need a little more again, about 23 cm of leg, which is rarer still.
| Leg-length gap | Equivalent height gap | How often two random adults differ by at least this much | Cadence gap it buys |
|---|
ANSUR II is US Army personnel, fitter and slightly more height-selected than the general public. If anything that understates the spread at the extremes, which makes this the conservative reading rather than the convenient one.
There are two ways the physics could work, they predict different things, and for once the data is clean enough to tell them apart.
Strict geometric similarity says a taller runner is a scaled-up copy taking a proportionally longer stride, so cadence should fall in direct proportion to leg length. The pendulum model says the swinging leg has a natural frequency proportional to the square root of its length, so cadence should fall with the square root instead. The first is the strong claim hiding inside "it's just physics". The second is gentler.
The measured exponent contains the pendulum prediction of −0.5 and excludes the geometric prediction of −1 by a mile. Step length lands at +0.487 and ground contact time at +0.464. Three metrics, three confidence intervals, all sitting on the square root. That is not three results, it is one law seen three times.
What each model predicts, and what a leg-length gap actually buys
Cadence gap between two runners at the same speed, against how different their legs are. Dashed lines are theory. The solid line is measurement.
The swamp was right about the mechanism and wrong about the magnitude. A pendulum model applied to a genuine 21 cm leg-length difference predicts an 18 spm cadence gap, which is essentially the 160-versus-180 pair in the original question. The physics delivers. It just needs two runners 41 cm apart in height to do it.
One correction, because this report nearly leaned on it. Dynamic similarity is not a law humans obey. Swinnen and colleagues tested it directly in 103 runners and concluded that "even after controlling for Froude number, human anthropometric variability produces shifts in preferred spatiotemporal characteristics, rather than the invariance that dynamic similarity theory would suggest" A. The scaling models are a yardstick here, not an authority. The measured exponents are the evidence.
Here the literature appears to fight itself. The fight is worth walking through, because the resolution is the most satisfying thing in the report.
Four studies find no effect of leg length on ground contact. Runners split by duty factor are anatomically indistinguishable, leg length 0.82 against 0.83 m, p = 0.551 B. Relative leg length does nothing to stance time, P = 0.710 A. Height does nothing to duty factor, p = 0.24 B. Bolt 60 mm of foam onto someone's feet and contact time does not budge, P = 0.159 B.
And yet the primary source finds a large, highly significant effect of height on contact time: +77.1 ms per metre of stature, CI 51.1 to 103.2, p < 0.001, at n = 860 A. Both cannot be wrong. Tiny frog alarm bells.
They are both right, because they are measuring different things. The nulls are all about duty factor, the fraction of the stride spent on the ground. The positive result is about contact time in milliseconds. And the arithmetic reconciles them exactly:
A taller runner's foot is down longer in milliseconds because their whole stride cycle is longer. The proportion of it spent on the ground is unchanged. Those two exponents were fitted separately, on different outcome variables, in the same cohort, and they cancel to three decimal places. Three other studies then confirm the cancellation from the other direction by finding nothing at all.
Ground contact time against pace
Three leg lengths taken from the real distribution. The shaded band is the 95% prediction interval for an individual with median legs.
If you want a contact metric that is not contaminated by how tall you are, use duty factor rather than ground contact time. It is the one number here with no detectable stature term, and that holds by four independent routes. Your watch probably does not show it, but it is contact time divided by total step time and you have both.
Vertical oscillation refuses to join the others, and vertical ratio is neutral for a reason nobody says out loud.
Where cadence, step length and contact time all scale with the square root of leg length, vertical oscillation scales almost linearly: exponent +0.974, CI 0.664 to 1.286 A. That is the geometric exponent, and the pendulum value of 0.5 sits outside its interval. So a runner's timings scale like a pendulum while their bounce scales like a length. Same runner, same stride, two different laws. Nothing in either model predicts that split, and this report is not going to pretend it can explain it.
Vertical oscillation rises with height. Vertical ratio does not.
Both computed at the cohort's mean pace from the same regression equations.
Garmin states in its manuals that vertical ratio "is not correlated with height" C. We could find no published source for that claim at all: no sample size, no protocol, no population, no study. So we tested it against the primary data, and it survives. Vertical ratio drifts by about a tenth of a percentage point across the entire 1.60 m to 1.95 m range, which is nothing beside the width of Garmin's own colour bands.
It survives conditionally, though, and this is the part worth knowing. Vertical ratio is flat against height only because two exponents happen to cancel. Hold body mass fixed instead of BMI, so that you are comparing a tall runner with a short runner of the same weight, and the cancellation collapses: the exponent goes to +0.487 and vertical ratio is not neutral in the slightest. Garmin's claim is true of ordinary bodies, where mass rises with height, and false the moment you compare two runners matched for mass. That condition is never stated.
Vertical ratio has the best claim to being anatomy-neutral and, at the same time, the worst evidence base of the four. Pooled against running economy it manages r = 0.20 from two studies and 24 people, with a confidence interval running from −1.00 to +1.00 A. That is not a weak result, it is the absence of one. Raw vertical oscillation, which is not anatomy-neutral, predicts economy better. Normalising appears to strip out real signal along with the body size.
The brief asked about leg length in isolation and leg length as a proportion of height. They are not the same variable and they do not even point the same way.
Everything above concerns absolute leg length, where longer legs mean lower cadence. For relative leg length, legs that are long for your height, exactly one study has looked properly. Swinnen and colleagues, 103 trained runners, leg length measured trochanter to ground, speed handled through the Froude number so absolute size is already divided out. Their finding: individuals with greater relative leg length exhibited higher stride frequencies, P = 0.039 A.
Note the sign. Long legs in absolute terms lower your cadence. Legs that are long for your frame raise it. Those pull in opposite directions, which is exactly why the two questions had to be kept apart, and why "leg length" as a single loose phrase does real damage in most discussions of this.
Against ground contact, relative leg length does nothing: stance time P = 0.710, duty factor P = 0.355 A. Against vertical oscillation, no source exists. Nobody has run that regression, most likely because leg length correlates with height at r ≥ 0.81 and separating them needs either a very large sample or a deliberately stratified one.
In the same models where relative leg length does nothing, relative foot length is highly significant for both stance time and duty factor, P < 0.001 A. The anthropometric ratio that actually predicts your ground contact is the size of your feet relative to your legs. One study, so hold it loosely, but it is a better lead than anything leg length has to offer here.
| Metric | Predictor | r | 95% CI | n | Speed controlled | Grade | Source |
|---|---|---|---|---|---|---|---|
| cadence | leg length | -0.45 | not reported | 82 | no, self-selected | B | Tenforde 2019 |
| stride frequency | relative leg length | 0.20 | not reported | 103 | yes, Froude-normalised | A | Swinnen 2026 |
| stance time | relative leg length | 0.00 | not reported | 103 | yes, Froude-normalised | A | Swinnen 2026 |
| duty factor | relative leg length | 0.00 | not reported | 103 | yes, Froude-normalised | A | Swinnen 2026 |
| duty factor | leg length | 0.00 | not reported | 59 | yes, 8-18 km/h | B | Patoz 2020 |
| stance time | relative FOOT length | 0.45 | not reported | 103 | yes, Froude-normalised | A | Swinnen 2026 |
Where a study reported a model coefficient and a p-value rather than a correlation, the r shown is indicative of an effect of that size at that sample size and is labelled as such. Nulls are listed at zero deliberately: an absence of effect is a finding and it should take up space on the page.
Worth asking before anybody reorganises their running around a number on a watch. One meta-analysis, 51 studies, 1,115 runners, settles it.
| Metric | r with energy cost | 95% CI | n | studies | Grade | Notes |
|---|---|---|---|---|---|---|
| vertical oscillation | +0.35 | +0.19 to +0.49 | 317 | 23 | A | More bounce goes with higher energy cost. The strongest of the four, and still moderate. |
| cadence | -0.20 | -0.35 to -0.05 | 593 | 37 | A | Higher cadence goes with slightly lower energy cost. Real, small. |
| ground contact time | -0.02 | -0.15 to +0.12 | 1115 | — | A | Nothing. The interval sits squarely on zero. |
| duty factor | -0.06 | -0.18 to +0.06 | 1115 | — | A | Nothing. |
| vertical ratio | +0.20 | -1.00 to +1.00 | 24 | 2 | A | Two studies, 24 people, an interval spanning the entire possible range. The metric with the best anatomy-neutrality has the worst evidence behind it. |
Bouncing less is modestly worth having. A higher cadence is worth slightly less than that. Ground contact time and duty factor are worth nothing at all, with intervals sitting squarely on zero. The authors put the realistic ceiling on what technique work can buy at 4 to 12% of explained variance in economy A.
So the practical order is: bounce is worth a look, cadence is worth a nudge, contact time is worth ignoring, and vertical ratio is unevaluated. Which is close to the opposite of the emphasis most watches give them.
Before reading anything into a 0.3 cm change in your vertical oscillation, here is the size of the ruler.
| Device | Metric | Bias | 95% limits of agreement | n | Grade | Source |
|---|---|---|---|---|---|---|
| Garmin HRM-Pro chest strap | vertical oscillation | -1.5 cm | -4.1 to +1.1 cm | 15 | B | Smith 2022 |
| chest sensor vs true centre of mass | vertical oscillation | +16 to +18 mm | systematic, anatomical | 22 | B | Watari 2016 |
| sacral sensor vs true centre of mass | vertical oscillation | 0 to 1.5 mm | 7 mm random, within-subject | 13 | B | Gullstrand 2009 |
| Stryd footpod | ground contact time | -14 ms, about 5% short | heteroscedastic | 49 | B | reported in research/B-gct.md |
The chest-strap problem is not sensor noise, it is anatomy. A strap sits on your sternum and your sternum is not your centre of mass, so it moves more. That gives a systematic overestimate of 16 to 18 mm B, which is larger than the entire effect of height on vertical oscillation across the whole adult range. A sacral or waist-mounted sensor sits within 0 to 1.5 mm of true centre of mass, roughly ten times closer B.
The practical reading: these devices are good at tracking change in one runner, with test-retest error of half a centimetre or less, and bad at absolute values or at comparisons between people on different hardware. Compare yourself with yourself. Comparing your vertical oscillation with a clubmate's, when one of you is on a chest strap and the other on a footpod, is comparing two different measurements that happen to share a name.
An entire genre of coaching content traces back to Jack Daniels counting steps by eye from the stands at the 1984 Olympics. About 47 athletes, across everything from 800 m to the marathon, at racing speed. His actual observation was that only one of them took fewer than 180 steps per minute C. No dataset was ever published. It was a floor observed among elite racers, not a target for recreational runners at 6:00/km, and the population mean in a cohort of 860 real runners is 164 spm. If your watch nags you toward 180, it is nagging you with a number produced by a stopwatch and a pair of eyes.
Three parallel literature passes, one per metric family, each required to return a graded evidence table with sample sizes, protocols, effect sizes and direct links, and each explicitly told to mark gaps as gaps rather than fill them. A fourth pass, done separately, derived the scaling predictions and the attribution mathematics before any results were in, so that the conclusion could not be retrofitted to the evidence. The coefficients underneath every chart were then read directly out of the primary paper's tables rather than taken from anybody's summary.
Three questions hide inside "how much of that gap is anatomy" and they have different answers. If you know both runners' legs, the answer is the regression slope times the difference. If you know only that their cadences differ by 20 spm, the answer works out to something cleaner: the expected share of an observed gap attributable to leg length is exactly R-squared. Not the slope. A large observed gap is far more likely to have come from residual scatter than from an improbably extreme pair of legs. That is where the 20% comes from.
Set in advance: a coefficient steeper than 1.0 spm per cm, an R-squared above 0.4, an adult leg range far wider than assumed, or a measured exponent near 1. The coefficient came in at 0.86 spm per cm, closer to that line than expected. The rest held. The hypothesis survived, but the slope is steeper and more physical than we went in assuming, and saying so is more useful than quietly banking the win.
The primary cohort is recreational, BMI under 27, running at a self-selected 9.9 km/h. Applying its equations to elite runners or to 3:30/km is extrapolation, and the charts deliberately stop where its data stops. Leg length was measured in that study but never reported or entered into any model, so every leg-length coefficient here is a height coefficient converted through the ANSUR II ratio. That is defensible, since 77% of leg-length variance is height, but it is the weakest link in the chain and it is load-bearing.
Beyond that: "leg length" means at least four different measurements across this literature (standing inseam, trochanteric height, subischial length, ASIS to medial malleolus) and they are not interchangeable. Almost nobody reports confidence intervals, so the effect size across studies is uncertain by roughly a factor of three. Everything here is correlational; nobody has lengthened a femur and re-measured. And the speed slope the calculator uses compares different runners, so a single runner speeding themselves up will follow a shallower one, around 7 to 8 spm per m/s rather than 11.