Knockout Elo & odds

Tournament Elo (default) - instead of replaying matches one at a time, the engine fits every completed result simultaneously (maximum-likelihood Bradley-Terry on the Elo scale): it finds the one set of ratings where each team's expected score We = 1/(1+10^(-Delta/400)) best matches what actually happened across all of its games, goal-difference weighted, shootouts counted as draws. Because everything is solved together, results propagate through common opponents - beating a side that goes on to beat everyone else counts for more than beating a struggler, and the order matches were played in no longer matters. Each team is also anchored by 3 virtual draws against its starting rating (1500 in this mode), so a small sample can't run away. Hosts get the home boost in their own venues. It measures only in-tournament form, so odds stay upset-friendly.

World Elo - tournament-start World Football Elo snapshot. In this mode the same joint fit anchors each team to its snapshot rating instead of 1500.

Hybrid - anchors each team at 1500 + 0.4*(World Elo - 1500), then runs the same joint fit over the completed matches. It gives pre-tournament strength a vote without letting it fully dominate tournament form.

Odds propagate exactly up the tree (no simulation): each round's number accounts for every possible opponent path. Win chances are uncertainty-aware: the fit also knows how settled each rating is (fewer or noisier games = wobblier), and every matchup's probability is pulled toward 50/50 in proportion to both sides' uncertainty (Glicko-style). Ratings are held fixed during projection. Market is de-vigged and normalised across live teams.