Machinepower Index / Methodology
How the Index is built.
Three layers, twelve measurements, one number — and an open account of how much that number depends on each choice behind it. If you plan to cite the Index, read this first.
The formula
Potential is the plain average of Watts, Weights and Will. Score combines the twelve measurements beneath them so that one weak number pulls the whole down rather than being averaged away. The gap between the two is what being lopsided costs: nothing if a nation is evenly built, more the further its strengths and weaknesses sit apart. In formal terms the Score is a CES mean of the twelve cells with an elasticity of substitution of one third — explained below.
Why not average
Every comparable index adds its dimensions up or averages them, which lets a strong score in one place cancel out a weak score in another. That is the wrong shape for sovereignty. A world-class model is no use on a grid that cannot power it, and an excellent grid is no use with no models to run on it. A nation needs all three at once.
Economists have a standard dial for how far one input can stand in for another: the elasticity of substitution. Set it to 1 and you get a geometric mean. Set it to 0 and you get a pure minimum — Liebig's law, where output equals the weakest input and nothing else counts. The Index sits at one third: the layers stand in for each other only weakly, without throwing away everything but the worst number. That puts it among the composite indexes built to stop strengths cancelling weaknesses; the Mazziotta–Pareto Index does the same job by a different route.
Why twelve cells rather than three axes
A chokepoint hides inside a layer. Taiwan scores 10.0 on hardware and silicon and 3.0 on frontier models; average those into one Weights figure and both facts vanish, leaving a forgettable middle number. Across the Index, the nations playing Chokepoint Leverage look flatter than average at layer level and spikier one level down. Scoring on the layers would reward them for a balance that averaging invented.
The three layers are still the plain average of their four measurements, and still how the site describes every nation. Only the Score is worked out one level down.
Robustness
The obvious objection to any scoring rule is that the setting was picked to produce the answer we wanted. These tables are the reply. Every figure here is regenerated from the data at each quarterly refresh.
1. Every aggregation rule, from average to pure minimum
| Rule | σ | ρ vs average | Moves | Top five |
|---|---|---|---|---|
| Plain average (no penalty) | — | 1.000 | 18 | United States, China, South Korea, France, Germany |
| Geometric mean | 1.00 | 0.962 | 18 | United States, China, South Korea, France, Germany |
| CES | 0.50 | 0.928 | 12 | United States, China, South Korea, France, Germany |
| CES — published (current) | 0.33 | 0.888 | — | United States, China, South Korea, France, Japan |
| CES | 0.25 | 0.867 | 12 | United States, China, South Korea, France, Japan |
| CES | 0.14 | 0.845 | 15 | United States, China, South Korea, France, Canada |
| Pure minimum (Liebig) | 0.00 | 0.835 | 19 | United States, France, South Korea, China, United Kingdom |
ρ is the Spearman correlation of the resulting ranking against a plain average; lower means the rule genuinely reranks. "Moves" counts nations that would change rank against the published edition. The same four nations — United States, China, South Korea, France — lead the Index under every rule tested, from a plain average to a pure minimum. Their internal order shifts only at the extreme: under a pure minimum, France rises to second and China falls to fourth, because China's weakest single cell is lower than France's. The elasticity does not decide who leads. It decides how the tightly-bunched middle orders itself.
2. Sensitivity to the single weakest cell
Because a low measurement pulls hard, the Score depends more on a nation's weakest judgement than on any other. These are the ten most sensitive cases: what happens to a nation's rank if its lowest measurement were scored a full point higher or lower.
| Jurisdiction | Weakest cell | Rank | −1 | +1 | Swing |
|---|---|---|---|---|---|
| Germany | Frontier Model Output 3.0 | 9 | 19 | 5 | 10 |
| Singapore | Firm Power Capacity 3.5 | 11 | 19 | 6 | 8 |
| Taiwan | Frontier Model Output 3.0 | 13 | 19 | 5 | 8 |
| Japan | Frontier Model Output 4.2 | 5 | 12 | 5 | 7 |
| United Kingdom | Frontier Model Output 4.2 | 7 | 13 | 5 | 6 |
| Canada | Frontier Model Output 4.2 | 6 | 12 | 5 | 6 |
| India | Frontier Model Output 4.0 | 8 | 14 | 5 | 6 |
| Netherlands | Frontier Model Output 3.0 | 15 | 19 | 9 | 6 |
| Israel | Firm Power Capacity 3.9 | 10 | 16 | 7 | 6 |
| Italy | Frontier Model Output 3.0 | 17 | 19 | 12 | 5 |
Median swing across all 25 ranked nations is 5 places; the largest is 10. A full point is a large revision on a one-decimal rubric — most quarterly corrections are a tenth or two — so read this as an outer bound rather than an expected error.
The honest conclusion: an exact rank in the middle of this table is not reliable, and we would rather say so than imply a precision the data cannot support. Twelve nations sit within half a point of each other, so changing one measurement moves several places at once. Treat the leading group and the tiers as findings; treat a mid-table nation's exact position as noise. It is also why the Index gives you a Score, a Potential and a strategic play rather than a bare league position.
3. What is judged rather than measured
116 of 312 measurements (37%) are our own judgement rather than a number taken straight from a published dataset. Each one is flagged on its country page and in the CSV export. They cluster where no dataset measures the thing cleanly — how fast a country permits and builds, how good it is at alignment, how well it is retraining its workforce. This is the honest weak point of the Index, not a rounding detail.
Sources
Every source below was published within the last 12 months. 45 separate sources sit behind this edition, and every country page shows which ones its numbers came from. The main ones are TOP500, Epoch AI, the Stanford AI Index, WIPO, Oxford Insights, OECD.AI, JLL and the Energy Institute.
AI Singapore · ASML · AUKUS (Defence) · CSIS Reports · Council of the EU · DIGITIMES · Data Centre Dynamics · Dept. of Industry, Science and Resources · Ember · Energy Institute Statistical Review · Epoch AI · EuroHPC JU · EuroHPC JU / Forschungszentrum Jülich · EuroHPC Joint Undertaking · European Commission (InvestAI) · GitHub Innovation Graph · IAPP Legislation Tracker · ISED Canada · IndiaAI Mission · Ipsos AI Monitor 2025 · Malaysia Budget 2026 · NIST / IMDA · NVIDIA / HUMAIN · NVIDIA / MSIT Korea · OECD.AI Policy Observatory · OpenAI / G42 · Oxford Insights · Oxford Insights GAIRI 2025 · Public Investment Fund · Rapidus · SDAIA · Sber / Yandex Research · Stanford AI Index 2026 · TOP500.org · TOP500.org / CINECA · TOP500.org / NCHC · TOP500.org / NCI Australia · TSMC · TenneT (Grid Operator) · UK Compute Roadmap · UK Government / MOFA Japan · US State Department · WIPO · White House OSTP · YTL Power / NVIDIA
Known limitations
TOP500 undercounts commercial capacity. It measures disclosed research systems, so Sovereign Compute should be read as a floor rather than a ceiling — particularly for nations whose capacity sits inside hyperscaler estates.
The political layer is measured more kindly than the material one. Watts and Weights rest on hard counts — terawatt-hours, petaflops, notable models. Will rests on surveys and readiness scores, which are gentler. So nations with thin infrastructure tend to look strongest on Will. That is a quirk of the measuring, not a finding about the world.
Documentation is not adoption. Oxford Insights scores internationally documented evidence. China documents little, so its Public Sector Adoption cell likely reflects opacity rather than the actual reach of Chinese state deployment, which is among the most extensive anywhere.
One pair of hands. Every judged measurement is the work of one author, against a published set of rules. The strategic plays are editorial throughout and are never scored at all.
Q3 2026 is the first measured quarter. Country pages carry a direction-only outlook. Numeric quarter-on-quarter movement publishes at the Q4 2026 refresh.