Value of the combined Bernoulli negative log-likelihood (Eq. (18)) in the comparison of the SPT-ECS sample (reference) and the eRASS1 cosmology sample (test) for various values of the correlation coefficient ρ. This coefficient expresses the level of covariance between lnL_X and lnζ at fixed halo mass and redshift. Assuming all other model parameters are correct, the constraint obtained from the catalogue comparison exercise depicted in this paper is relatively loose: ρ ≃ 0.2 ± 0.6 (68% confidence level) as deduced from $(B-B_{\text{min}})~{\chi }_1^2$.