Each of 9 underlying sustainability metrics (3 Environmental, 3 Social, 3 Governance) has a true performance value m_i â [0,100] for the simulated company. A rating agency never observes m_i perfectly â disclosure gaps and differing estimation methods add noise Îĩ_i â and, more importantly, each agency counts a different subset of those 9 metrics and weights them differently, not just at the E/S/G pillar level but metric by metric (an environment-focused rater over-weights carbon intensity specifically, not "environment" in general):
estimate_i = clamp(m_i + Îĩ_i, 0, 100)
composite = ÎŖ w_i ¡ estimate_i, ÎŖ w_i = 1
Because w_i genuinely differs by agency methodology, the same company can land in wildly different score brackets â this is a documented, real phenomenon called "ratings divergence" or "aggregate confusion" in ESG research (major raters have historically shown pairwise correlations as low as ~0.3, versus >0.9 for credit ratings). Four agency profiles are compared:
- EnviroFirst â heavily over-weights Carbon Intensity and Water Stewardship
- SocialTrust â heavily over-weights Labor Practices and Diversity & Inclusion
- GovCore â heavily over-weights Board Independence and Anti-Corruption Controls
- Custom â your own E/S/G pillar mix, split evenly within each pillar
The correlation study re-runs this scoring process on 400 freshly simulated companies (independent random metrics each time), records each agency's composite score for every company, and computes the real Pearson correlation coefficient between every pair of agencies' score series:
r(A,B) = ÎŖ(a_k â Ä)(b_k â bĖ) / â[ÎŖ(a_k â Ä)² ¡ ÎŖ(b_k â bĖ)²]
The headline stat averages the three pairs among EnviroFirst / SocialTrust / GovCore â the fixed, independently-designed methodologies, comparable to how researchers benchmark real ESG raters against each other. Because their per-metric weights genuinely diverge, this settles in the ~0.3â0.5 band actually measured between real-world ESG raters (versus >0.9 for credit ratings scoring the same bonds). The scatter plot below the bar chart shows EnviroFirst vs GovCore directly â the wide, weakly-correlated cloud is the divergence.