I might be deeply wrong about this, and misunderstand something about the topic. But here are the joint distributions I get from just using both approaches (with a big lambda_common = 4, and lambda1, lambda2 = 1.2, 0.9). The left-side approach considers that the common goals would be same for any given match (which is how I understand the correlation between the home/away goals). It is my understanding that the right-side approach (original approach from this topic) ignores the correlation. I found the correlation essential for football modeling. I don’t think the common lambda is even identifiable without it (well, maybe as an intercept). I probably have misunderstood the code or the approach of the topic, but those are two very different distributions.
