Germany

Each pairing is scored by the ensemble (Dixon-Coles bivariate-Poisson, the Bayesian hierarchical model and the global LightGBM-Poisson, log-pooled), producing an 11×11 scoreline grid that is marginalised into win/draw/loss, expected goals (λ), over/under 2.5 and both-teams-to-score. These are the same distributions the tournament simulator consumes, oriented here to Germany. Knockout fixtures are not shown — their occupants are still probabilistic, so there is no single pairing to forecast yet.

g is the residual from regressing a team’s current squad market value on its history-based strength in the Bayesian hierarchical model. Positive g means the squad is valued above what the team’s record predicts; negative means the record outruns the squad’s price (the side achieves more than its market value implies). Regressed on out-of-sample success the slope is positive — squad-rich sides go a touch further — but not statistically significant at n = 3 tournaments, so treat a single team’s g as a descriptive read, not a hard prediction. The full decoupling essay →

This line is the public eloratings.net series (year-end ratings), which terminates exactly at the current rating and world rank shown on the marker. It is a different number from the Elo shown in the header band (a panel-normalised rating used inside the forecast); the two are ~0.99 correlated but on different scales. We keep them distinct rather than blend them.