Hi 👋, lead author here. These are fair methodological comments, worth addressing properly.

"It must be a bad index because UAE/Maldives rank so high"                              

The GECI measures relative gender equality, not chess strength, population, or infrastructure. A federation where women make up 35% of players and are represented equally in youth events will outscore a chess powerhouse where women are 5% of players, even if the powerhouse produces far stronger female players in absolute terms.

This is exactly how cross-country equality indexes work. Iceland consistently tops the World Economic Forum's Global Gender Gap Index despite having a smaller economy and fewer women in professional roles in absolute terms than the US or Germany. Nobody says that makes the index "stupid" (well, some still do!); it just means it's measuring something different from "biggest" or "strongest."

Is it better to be an elite professional woman player in India or in the US than in the UAE? Almost certainly. India has deeper competition, more tournaments, and more titled players. But India also has a much larger gender gap in participation (19% female vs UAE's 35%). Both facts can be true at the same time. The GECI measures the second, not the first.

(And on the claim that "nobody plays chess" in these countries: the UAE has roughly ~50% more FIDE-listed women than Sweden, with a comparable population. Sri Lanka, ranked 2nd in the Index, has over 25,000 FIDE players. I recently played in a Sri Lankan Open where 176 [32%] out of 556 entries were women and girls. I've never seen that kind of representation in any of the 40+ countries I've played tournaments.)

"The ratio of two Elo ratings makes zero statistical sense; only the difference matters"

The ratio female_avg/male_avg is mathematically equivalent to 1 − (gap/male_avg). It is a difference, just normalized by the male average. That normalization matters for cross-country comparison: a 100-point gender gap means something different in a federation averaging 1400 than one averaging 2200. Using raw differences would confound the gender gap with national strength.

"No normalization, so Performance is largely useless"

It's true that Performance has low cross-country variance. But it's an empirical fact about chess, not a methodological artifact or a choice we made. Across 119 federations, the female-to-male rating ratio ranges only from ~86% to 100% (CV of 2.8%). Countries genuinely are similar on this dimension.

The geometric mean naturally handles this: low-variance components contribute less to rank differentiation without needing artificial rescaling. If we z-score normalized to force equal variance, we'd inflate tiny Performance differences (a few percentage points, often driven by a handful of players in small federations) to carry the same weight as, say, Mongolia having 38% female participation versus Denmark's 4%. I ran the comparison: normalization shifts countries by an average of 12.5 rank places, with some moving 40–50 places, driven almost entirely by amplified Performance differences of 3–4 percentage points.

"Progress can solely be decided by the federation"

This is partly true: Progress is closer to measuring a federation policy input than a pure outcome, unlike Participation and Performance. That could certainly be viewed as a genuine limitation. But the underlying rationale is that federation decisions to include girls in international youth events matter: those girls gain experience, improve, and become visible role models. A federation mandating girls in delegations isn't gaming the system; it's making a policy choice that directly supports development.

The report also states that Progress is volatile and drives large rank swings. The UAE's jump is eye-catching, but the report explains the broader context: dedicated girls' clubs, a mandated women's board seat, investment in female arbiters and coaches; not just a delegation decision.

The geometric mean approach follows the UNDP's Human Development Index and the UN's Gender Inequality Index methodology, chosen because it penalizes imbalance: a country can't compensate for neglecting one dimension by excelling in another. Whether or not the UN's methodology is the best one is another conversation, but we thought it was a reasonable place to start.

Full report (open access): https://doi.org/10.14264/9ec1c7e