Upstream · a pre-registered test that failed

Grinding-ball imports failed as a yearly mining gauge

Mills grind ore with steel balls that wear away as the rock passes through, so a country that mills more ore should use more balls. If customs data could see that, it would be a public, near-real-time measure of mining activity. We wrote the rules of the test down first and then ran it. In the 10 countries where imports cover at least half of what the mills need, imports did not pass as a year-by-year gauge of ore milled: the estimated response was 0.35 against an expected one-for-one, with a 95% interval from −0.10 to 0.79. That interval takes in zero and most of the range the rules would have accepted, so the test could neither confirm the link nor rule it out.

Result FAIL

Year-to-year growth in forged-ball imports (customs code 7326.11, tonnes, imports minus exports) against growth in ore milled, with country and year effects, 2003–2024. Every threshold below was committed before the test ran.

Check	Rule set in advance	Result
Imports follow ore milled	response between 0.4 and 1.5, p < 0.05	response 0.35 (95% interval -0.10 to 0.79), p = 0.11	fail
Not driven by one country	dropping any one country keeps it between 0.3 and 1.7	ranges 0.19 to 0.42	fail
Not cement	still in band with cement output added, and stronger than cement	response 0.34; cement shows no link (t = 0.16)	fail
Placebo: screws and bolts	no link to ore milled	response -0.29, p = 0.26	pass
Australia: iron ore	iron ore, which is not milled, shows no link	failed on only 7 years: Australia exported more balls than it imported until 2017	fail

In levels, a link shows up. Comparing levels rather than yearly changes, with country and year effects, a country imports more balls in the years it mills more ore (response 1.19, p = 0.003). That is an association that shared trends alone can produce, and the rules said in advance that a relationship visible only in levels does not count, because it says nothing about whether imports follow mining from one year to the next, which is what a gauge has to do. The same rules discount a link that appears only when cast balls (customs code 7325.91, which cement mills also use) are pooled in: pooled, the response is 0.397, p = 0.04, still below the 0.4 floor.

What this does not say

Not that balls are unrelated to mining. Errors in measured ore milled pull a year-to-year estimate toward zero. Ore milled has to be estimated from metal output with fixed global ore grades, so changes in grade, recovery or the share of ore that is leached rather than milled show up as noise. For a true one-for-one response to appear as 0.35, that noise would need to be about twice the real variation in ore growth, which is plausible for annual data. Noise on the import side (mines buy balls in lumps and hold stock; customs tonnages are noisy) does not bias the estimate in that way, but it widens the interval.
Nothing about Chile, Peru or Canada. Their net imports cover well under half of what their mills are estimated to need (Chile, for one, has large domestic ball plants), so imports cannot stand for their mills, and they were never in the test. Australia is in the same position and appears only as the negative control above.
Ore grades: not testable from public data. The planned grade test needs a public series of the grade of ore entering the mills for one of the ten countries. None was located (the search was not exhaustive), so it was not run.

Where imports could be the input

Before any regression, a coverage check: could a country’s net ball imports physically supply its mills? Ball demand is ore milled times a consumption rate taken from 12 mine technical reports (copper 0.33–0.88, gold 0.46–1.01, lead-zinc 0.36–0.74 kg of steel per tonne of ore). Countries milling more than 20 Mt of ore in 2024; imports and demand averaged over 2022–24. A country enters the test if net imports cover at least half of mid-range demand.

Country	ore milled 2024	ball demand	net imports	coverage	group
Brazil	128 Mt	78 kt	122 kt	158%	imports cover half or more
Ecuador	35 Mt	24 kt	31 kt	128%	imports cover half or more
Mongolia	80 Mt	46 kt	47 kt	101%	imports cover half or more
Saudi Arabia	27 Mt	17 kt	15 kt	90%	imports cover half or more
Kazakhstan	217 Mt	145 kt	124 kt	85%	imports cover half or more
Bolivia	30 Mt	30 kt	22 kt	73%	imports cover half or more
Ghana	114 Mt	72 kt	48 kt	67%	imports cover half or more
Burkina Faso	46 Mt	33 kt	21 kt	63%	imports cover half or more
Philippines	34 Mt	24 kt	14 kt	57%	imports cover half or more
Côte d’Ivoire	39 Mt	28 kt	16 kt	55%	imports cover half or more
Serbia	64 Mt	33 kt	17 kt	49%	imports cover under half
Tanzania	49 Mt	33 kt	16 kt	49%	imports cover under half
Mali	50 Mt	39 kt	17 kt	42%	imports cover under half
Guinea	55 Mt	43 kt	14 kt	33%	imports cover under half
Zimbabwe	32 Mt	22 kt	7.1 kt	32%	imports cover under half
Mexico	248 Mt	177 kt	50 kt	28%	imports cover under half
Türkiye	54 Mt	36 kt	8.1 kt	22%	imports cover under half
Papua New Guinea	56 Mt	35 kt	7.9 kt	22%	imports cover under half
Chile	1,109 Mt	655 kt	140 kt	21%	imports cover under half
Peru	649 Mt	388 kt	73 kt	18%	imports cover under half
Venezuela	23 Mt	17 kt	2.8 kt	16%	imports cover under half
Australia	396 Mt	275 kt	43 kt	15%	imports cover under half
Canada	254 Mt	172 kt	25 kt	14%	imports cover under half
Colombia	44 Mt	33 kt	4.7 kt	14%	imports cover under half
Bulgaria	23 Mt	15 kt	2.1 kt	14%	imports cover under half
Argentina	31 Mt	23 kt	3.0 kt	13%	imports cover under half
DR Congo	649 Mt	372 kt	39 kt	10%	imports cover under half
India	27 Mt	16 kt	1.0 kt	6%	imports cover under a tenth
Sudan	49 Mt	25 kt	1.6 kt	6%	imports cover under a tenth
Zambia	163 Mt	93 kt	4.9 kt	5%	imports cover under a tenth
Sweden	25 Mt	17 kt	0.5 kt	3%	imports cover under a tenth
Uzbekistan	118 Mt	78 kt	1.3 kt	1%	imports cover under a tenth
Poland	79 Mt	52 kt	0.7 kt	1%	imports cover under a tenth
Indonesia	279 Mt	165 kt	2.1 kt	1%	imports cover under a tenth
China	762 Mt	493 kt	0.0 kt	0%	imports cover under a tenth
Spain	26 Mt	16 kt	0.0 kt	0%	imports cover under a tenth
Iran	74 Mt	47 kt	0.0 kt	0%	imports cover under a tenth
Russia	457 Mt	291 kt	0.0 kt	0%	imports cover under a tenth
United States	349 Mt	240 kt	0.0 kt	0%	imports cover under a tenth
South Africa	82 Mt	60 kt	0.0 kt	0%	imports cover under a tenth

Two known weak spots. Brazil’s balls also grind iron ore, which is not counted, so Brazil looks better covered than it is. DR Congo’s ore is rich and much of its copper is leached, not milled, so a fixed global grade overstates the rock it mills.

How it was done, and reviewed

The design was drafted with two independent language models acting as advisors, and the rules, bands and controls were committed to the repository before any result existed: the pre-registration, with a dated log of every change made afterwards. Consumption rates come from primary mine reports, each with page and quotation (sources); cement output from seven editions of the USGS Minerals Yearbook.

Reviewed by two engines, one before and one after publication. This atlas’s studies are reviewed adversarially by two independent language models run separately, each given the rules, the code and every number. When this result was first published (15 Sep 2026), only the first was available. It found three errors; none changed the verdict:

A failed control (Australia) had been written up as “not counted” after the result was seen. It is now reported as failed, with the reason it was unusable.
The coverage check set net imports to zero after averaging three years instead of before, as the rules said. Corrected: Bulgaria moves up a group; the ten test countries are unchanged.
Pass/fail was judged on rounded numbers. It now uses exact values; nothing changes.

The second review (17 Sep 2026) found no error in the code or the verdict, but found that this page said more than the test shows. Corrected:

The title and opening said imports “don’t track” mining. The test only failed to validate them as a gauge; the opening now gives both ends of the interval.
A levels association was headed “in the long run the link is real”. It is an association, and is now described as one; the pooled cast-ball result is now shown.
Noise in imports was said to pull the estimate toward zero. It widens the interval instead; only noise in measured ore milled pulls toward zero.
Australia was said never to have been in the test. It was the negative control.
In the pre-registration’s result section, two countries fell below 0.3 when one was left out, not three, and the pooled estimate, shown as 0.40, is 0.397, below the 0.4 floor.

Sources. Trade: CEPII BACI HS 2002, V202601 (Etalab Open Licence 2.0), with flows priced outside 0.4–3× the year’s median dropped. Mine production: BGS World Mineral Statistics. Cement: USGS Minerals Yearbook, Cement, table 22. Consumption rates: mine technical reports listed in the sources file. Built by build_grinding_balls.py from out/grinding_balls.json, which holds every figure on this page.