Phase 2: predictive model — Elo + Dixon-Coles + Monte Carlo

- buildRatings.ts: walks 49k historical results → World-Football-Elo per team,
  data-calibrated goals model (goals-per-Elo slope, mean goals) + MLE-fit
  Dixon-Coles rho. Top: Spain/Argentina/France (the real 2026 favourites)
- src/lib/model: elo, poisson/dixon-coles, predict, host-advantage, monteCarlo
  (full 48-team sim — group sampling, best-third bipartite allocation, knockout
  advance probs). 20 vitest cases incl. exact per-round count invariants
- Server ModelEngine: live Elo re-rating after each result, per-match W/D/L,
  20k-sim odds, odds-over-time history; broadcast on finished-result changes
- Client: championship board, heat-shaded odds table, lazy-loaded title-race
  chart (Recharts split to its own chunk), match-prediction bars, bracket
  advance overlay
- Verified: odds render, chart populates as injected results re-rate teams live

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

src/lib/types.ts

@@ -69,9 +69,61 @@ export interface Snapshot {
   tables: Record<string, StandingRow[]>;
 }
 
+// ---- model / predictions ----
+
+/** Per-team tournament odds from the Monte Carlo simulation. */
+export interface TeamOdds {
+  team: string;
+  winGroup: number;
+  qualify: number;
+  reachR16: number;
+  reachQF: number;
+  reachSF: number;
+  reachFinal: number;
+  champion: number;
+}
+
+export interface MatchProbs {
+  home: number;
+  draw: number;
+  away: number;
+}
+
+/** A single per-match prediction (group + resolved knockout games). */
+export interface MatchPrediction {
+  num: number;
+  home: string;
+  away: string;
+  probs: MatchProbs;
+  lambdaHome: number;
+  lambdaAway: number;
+  topScore: { home: number; away: number; p: number };
+}
+
+/** A point on the championship-odds-over-time chart. */
+export interface OddsHistoryPoint {
+  t: string;
+  label: string;
+  top: { team: string; champion: number }[];
+}
+
+export interface ModelSnapshot {
+  generatedAt: string;
+  /** Date the underlying ratings reflect (advances as results re-rate teams). */
+  asOf: string;
+  iterations: number;
+  matches: MatchPrediction[];
+  odds: TeamOdds[];
+  history: OddsHistoryPoint[];
+}
+
 // ---- WebSocket protocol ----
 // The snapshot is small (~104 fixtures), so the server simply re-pushes the full
-// snapshot on every change — no diffing, no client-side merge races.
+// snapshot on every change — no diffing, no client-side merge races. Predictions
+// are heavier to compute, so they ride a separate message sent only when the set
+// of finished results changes.
 
 /** Server → client. */
-export type ServerMessage = { t: 'snapshot'; snapshot: Snapshot };
+export type ServerMessage =
+  | { t: 'snapshot'; snapshot: Snapshot }
+  | { t: 'predictions'; model: ModelSnapshot };