What a fast shoe is worth
Every published measurement of the same effect, and why they do not agree.
A plated racing shoe is supposed to be worth about 4%. That number came from one study, of one prototype, mass-matched against a racing flat, on a treadmill, at {{proto_speed}} km per hour — and it was measured as metabolic cost, not as time. Every one of those qualifiers moves it. Collect the other published measurements of the same thing and they run from {{lo}}% to {{hi}}%. Look inside the studies that report individual runners rather than group means and the range is {{widest}} percentage points wide, crossing zero in {{n_span}} of the {{n_ind}} studies that publish it.
This page is that collection. It is a table of {{n_rows}} published rows, every one with a named study and a link to it, and some arithmetic over them: what the spread is, how much of it is between studies and how much inside one, and what happens when the economy figures are converted into race time. It does not tell you which shoe to buy, and the reason it cannot is the finding.
What it finds
{{n_aft}} controlled laboratory comparisons of an advanced-footwear shoe against a control shoe have been published with a percentage attached. They range from {{lo}}% to {{hi}}%, a factor of {{ratio}}, with a median of {{median}}%.
Every comparison in the table, ordered by effect size. A bar is the standard deviation the paper published; {{n_without}} of the {{n_aft}} published no dispersion at all and are drawn as a dot alone, because an interval nobody reported is not one this page will draw.
Reading down that figure sorts the comparisons roughly by how artificial the test was. Prototypes on treadmills at elite pace sit at the top; the only measurement made outdoors, an advanced trail shoe at {{trail_speed}} km per hour on real ground, sits at the bottom at {{trail}}% with a standard deviation equal to its mean. That ordering is suggestive and not demonstrated: shoe generation, control shoe, speed, terrain and laboratory all vary together across these rows and nothing here isolates one of them. It is a pattern across studies, not a trend, and it is not drawn as one.
The more useful comparison is between the spread across studies and the spread inside one. Where a study reports what happened to each runner instead of the group mean, the ranges are wider than the entire between-study spread, and most of them include runners the shoe made slower.
The {{n_aft}} study means above the rule, the {{n_ind}} published individual ranges below it, on one axis. Colour names the study: the two Knopp rows are one paper and the two Barnes and Kilding rows another, and Barnes and Kilding's own means carry the same colour above, so one study can be followed from its tight mean to its wide individuals. The widest range, {{widest}} points, is in world-class runners — the group the shoes were built for.
The means huddle. The individuals sprawl. Nothing in the literature predicts which runner falls where in those ranges, and that is the honest answer to what a fast shoe is worth to any particular person: the population mean is {{median}}% and the individual outcome is not the population mean.
What that is worth in a race
Almost every number above is a change in the metabolic or energy cost of running, and no runner is timed in joules. The exchange rate between the two is the subject of Economy is not time, which works it out and reconciles it against the cost-of-running curve: about {{transfer}}, so roughly seven tenths of a metabolic saving reaches the clock. That page owns the derivation and the reason the rate is not one; this one only spends it.
Applying that rate to anything other than added shoe mass is an assumed step and is marked as one wherever it appears. It has never been measured for advanced footwear, and the two interventions need not transfer alike. The rate also has an interval of its own, {{transfer_lo}} to {{transfer_hi}}, which the figure below does not draw. With those caveats, the laboratory range of {{lo}}% to {{hi}}% becomes {{pred_lo}}% to {{pred_hi}}% of race time.
The dashed interval is derived through the transfer coefficient and is drawn differently for that reason alone. The two solid ones are what was observed in {{race_n}} marathons by reading shoes off public race photographs. They overlap, which is consistency and not proof: the race estimates are observational, runners chose their own shoes, and the fastest adopted them first.
This is the one place the page can show agreement rather than disagreement, and it is worth being precise about how weak the agreement is. Three intervals overlapping does not confirm the coefficient; it fails to contradict it.
The mass rule, and the trial that contradicts it
The oldest number in this field is that a shoe costs about 1% of metabolic rate per 100 g per shoe, and it is the number the {{transfer}} ratio above depends on. It was measured at {{mass_rule}}%, with a 95% confidence interval of {{mass_ci}} — the only confidence interval published anywhere in this table.
A later trial performed the same manipulation and measured {{mass_alt_lo}}% and {{mass_alt_hi}}%.
The founding constant and the trial that contradicts it, on a linear axis. A log axis would compress a gap of {{mass_ratio_lo}} to {{mass_ratio_hi}} times into something that looks like ordinary disagreement, and the size of the gap is why the figure exists. Both are peer-reviewed and neither is retracted.
No one has reconciled them. That matters beyond the mass question, because the 1% figure is load-bearing: it is the basis of the transfer coefficient, and it is the reason the industry treats shoe weight as a design constraint at all.
What the mechanism is not
The popular explanation is the carbon plate. The evidence does not support that as a standalone claim. A meta-analysis of {{stephen_studies}} studies covering {{stephen_n}} runners found that neither longitudinal bending stiffness alone nor midsole energy return alone significantly affected oxygen consumption — only their interaction did. A separate meta-analysis found that a curved plate improved economy while a flat plate did not, and a narrative review puts the bending-stiffness literature at about 3% deterioration to about 3% improvement.
Two independent meta-analyses, one over {{xiao_studies}} trials and one over {{stephen_studies}}, both arrive at a standardised mean difference of {{smd}} for oxygen consumption. That agreement is real. It is also not a percentage, which is why no meta-analysis appears as a row in the figures above: a standardised mean difference and a per cent change do not share an axis, and putting them on one would be the conflation this page argues against.
Method
The laboratory comparisons come from Hoogkamer and colleagues in 2018, Hunter and colleagues in 2019, Barnes and Kilding in 2019, Whiting and colleagues in 2021, Joubert and colleagues in 2024, and Joubert and Sanders in 2026. The added-mass rows come from Hoogkamer and colleagues in 2016 and from Rodrigo-Carranza and colleagues in 2020, the individual ranges from Knopp and colleagues in 2023, and the race estimates from Guinness and colleagues in 2020.
The data is a declared table of {{n_rows}} rows in
data/studies.py, each read out of the paper it comes from and
carrying the sample, the test speed, the setting, a note, and a DOI. There is
no download step, because no public dataset reports these numbers. The
inclusion rule for the laboratory comparisons is every controlled comparison of
an advanced-footwear shoe against a control shoe reporting running economy or
metabolic cost as a percentage that the Stage 1 literature search found. That
is a collected table and not a systematic review, and where a study reported
two arms both are in — dropping the smaller of a study's two spikes is how a
collection starts flattering itself.
Everything else is arithmetic over that table: the extremes, the median, the ratio between them, the width of each individual range and whether it crosses zero, the counts of what was and was not published, and the transfer coefficient, which is one published row divided by another and is recomputed here rather than read from the sibling project's payload, so neither page can break the other. Nothing is fitted, smoothed or regressed. A standard deviation and a confidence interval are held in separate fields and neither is ever derived from the other.
The sign convention is that a positive number means the energy cost of running fell. Advanced-footwear rows are therefore positive and added-mass rows negative, and the build refuses to run if any row breaks that.
Limits
Nothing here predicts an individual. The published ranges say the individual response varies by more than the mean effect; no study offers a variable that predicts where a given runner lands, and this page does not offer one either.
The samples are narrow. Of {{n_rows}} rows, {{n_female}} include women at all, and {{n_outdoor}} was measured outside a laboratory. {{n_time}} rows measure time; the rest measure oxygen or energy.
There is no shoe database. No free, comprehensive source gives shoe mass, stack height, foam type or plate geometry by model. World Athletics publishes a list of approved shoes, and it is an eligibility list — brand, model, and which events a shoe may be worn in, with no specifications. So this page cannot compare shoes, only studies.
The table is a collection, not a review. It was assembled by one search rather than by a registered protocol, and a systematic review would apply quality weighting this does not.
The code
Three Python files and the table. data/studies.py declares every
published row with its source and DOI; build_shoes.py computes the
spreads, the counts and the transfer coefficient and writes the payload;
fig_shoes.py draws the four figures from it. The page's numbers are
written from the payload by update_page.py, and
test_shoes.py checks the failure modes this project is exposed to —
chiefly that no interval is drawn that nobody published.