[slybot]

More confused,

1) 0.02 * random.random() != N(0, 0.02)

2) The LLM will sample a normal distribution, this only depends on your c parameter, the absolute scale doesn't matter neither in Bradley-Terry nor in Elo. So saying +-4 and claiming LLM reasoning in Standard normal is ridiculous.

3) > then we get a pairwise matrix with virtually identical statistical properties to the observed pairwise matrices. >>> then did you asked yourselves if I have "statistically identical" pair-wise matrix and observed pairwise matrix, the. why you even bother myself? You can simply use observed pairwise matrix...