c58cfb2d2f
- Remove hardcoded SEEDINGS_2026 name→seed map from snooker-simulator.ts - Load worldRanking from participantExpectedValues (same column darts uses) - Top 16 by worldRanking get seeded; fallback to Elo order if none stored - Add /admin/sports-seasons/:id/snooker-elo route with bulk import (name, Elo, world ranking format) and per-player Elo + Rank # form, matching darts-elo UX - Update snooker simulator tests: remove name-based ranking fixtures, add tests for DB-driven rankings and Elo fallback https://claude.ai/code/session_01Fz54vdsLjDVintFguH32To
586 lines
25 KiB
TypeScript
586 lines
25 KiB
TypeScript
/**
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* Snooker World Championship Simulator
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*
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* Monte Carlo simulation of the World Snooker Championship (Crucible, Sheffield).
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* The tournament is a 32-player single-elimination bracket with 5 rounds, using
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* best-of frame formats that increase in length each round.
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*
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* Algorithm:
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* 1. Load the bracket scoring event and all playoff matches from DB.
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* 2. Load Elo ratings and world rankings from participantExpectedValues.
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* 3. Compute per-match win probability using the Bernoulli frame model:
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* p_frame = 1 / (1 + e^(-(Elo1 - Elo2) / ELO_DIVISOR))
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* P(win match) = sum_{w2=0}^{F-1} C(F-1+w2, w2) * p^F * (1-p)^w2
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* where F = frames to win, which varies by round.
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* 4. Two simulation paths:
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* a. Bracket populated: simulate from actual draw, respecting completed matches.
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* b. No bracket: sort players by worldRanking (fallback: Elo order), place top 16
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* as seeds, randomly draw the rest into seed slots 17-32 each simulation.
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* 5. Track integer placement counts per tier across 50,000 simulations.
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* 6. Convert to probability distributions using exact denominators (column sums = 1.0).
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*
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* Round format (Crucible main draw):
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* First Round (R32): best-of-19, first to 10
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* Second Round (R16): best-of-25, first to 13
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* Quarter-Finals (QF): best-of-25, first to 13
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* Semi-Finals (SF): best-of-33, first to 17
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* Final: best-of-35, first to 18
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*
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* Placement bucketing (8-slot probability model):
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* probFirst → Champion
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* probSecond → Finalist
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* probThird/Fourth → SF losers (2/sim)
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* probFifth–Eighth → QF losers (4/sim)
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* R16 losers → all 0
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* R32 losers → all 0
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*
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* World rankings (for pre-bracket path): loaded from participantExpectedValues.worldRanking.
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* Set via the snooker-elo admin page. Falls back to Elo order if no rankings are stored.
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*/
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import { database } from "~/database/context";
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import { eq, and } from "drizzle-orm";
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import * as schema from "~/database/schema";
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import type { Simulator, SimulationResult } from "./types";
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// ─── Simulation parameters ────────────────────────────────────────────────────
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const NUM_SIMULATIONS = 50000;
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/**
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* Controls how much Elo gaps affect per-frame win probability.
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* Higher = softer probabilities (more randomness, less Elo dominance).
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* Lower = sharper probabilities (Elo differences matter more).
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*
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* Standard chess Elo uses 400. Snooker frames are more random than chess
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* games, so a higher value is appropriate. Tune this until tournament win
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* probabilities for the top seed feel realistic (~15% for a clear favourite
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* in a 32-player field).
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*
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* Reference calibration points at ELO_DIVISOR=700:
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* 100-pt gap → 53.5% per frame
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* 300-pt gap → 60.6% per frame
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* At ELO_DIVISOR=400 (standard chess):
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* 100-pt gap → 56.2% per frame
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* 300-pt gap → 67.9% per frame
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*/
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const ELO_DIVISOR = 700;
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/**
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* Frames needed to win per round, indexed by round order (most matches first).
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* Index 0 = R32 (16 matches, best-of-19, need 10)
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* Index 1 = R16 (8 matches, best-of-25, need 13)
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* Index 2 = QF (4 matches, best-of-25, need 13)
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* Index 3 = SF (2 matches, best-of-33, need 17)
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* Index 4 = Final (1 match, best-of-35, need 18)
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*/
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const FRAMES_TO_WIN = [10, 13, 13, 17, 18] as const;
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/**
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* Standard seeded R32 bracket for 32-player single-elimination.
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* Each entry is [seedA, seedB] for one R32 match, in bracket order.
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* Consecutive pairs of R32 winners form R16 matches (bracket structure preserved).
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* Ensures seed 1 and seed 2 can only meet in the Final.
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*
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* Structure (seeds 1-16 are fixed; seeds 17-32 are randomly drawn qualifiers):
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* Top half: 1v32, 16v17, 9v24, 8v25, 5v28, 12v21, 13v20, 4v29
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* Bottom half: 3v30, 14v19, 11v22, 6v27, 7v26, 10v23, 15v18, 2v31
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*/
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const R32_BRACKET: Array<[number, number]> = [
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[1, 32], [16, 17],
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[9, 24], [8, 25],
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[5, 28], [12, 21],
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[13, 20], [4, 29],
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[3, 30], [14, 19],
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[11, 22], [6, 27],
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[7, 26], [10, 23],
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[15, 18], [2, 31],
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];
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// ─── Math helpers ──────────────────────────────────────────────────────────────
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/**
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* Per-frame win probability for player 1 vs player 2 based on their Elo ratings.
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*
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* Uses the logistic sigmoid: p = 1 / (1 + e^(-(R1 - R2) / ELO_DIVISOR))
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*
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* ELO_DIVISOR is set higher than standard chess (400) to reflect the greater
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* randomness of snooker frames vs chess games. At ELO_DIVISOR=700:
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* 100-pt gap → ~53.5% per frame
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* 300-pt gap → ~60.6% per frame
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*
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* Exported for unit testing.
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*/
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export function frameWinProb(elo1: number, elo2: number): number {
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return 1 / (1 + Math.exp(-(elo1 - elo2) / ELO_DIVISOR));
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}
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/**
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* Match win probability for player 1 using the Bernoulli frame model.
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*
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* For a best-of-(2F-1) match (first to F frames wins):
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* P(win) = sum_{w2=0}^{F-1} C(F-1+w2, w2) * p^F * (1-p)^w2
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*
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* where p = per-frame win probability and F = framesToWin.
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* This sums over all winning score combinations (F-0, F-1, ..., F-(F-1)).
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* Exported for unit testing.
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*/
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export function matchWinProb(p: number, framesToWin: number): number {
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const F = framesToWin;
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let prob = 0;
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for (let w2 = 0; w2 < F; w2++) {
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prob += binomialCoeff(F - 1 + w2, w2) * Math.pow(p, F) * Math.pow(1 - p, w2);
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}
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return prob;
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}
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/** Binomial coefficient C(n, k) using iterative multiplication to avoid overflow. */
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function binomialCoeff(n: number, k: number): number {
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if (k === 0) return 1;
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if (k > n - k) k = n - k; // Symmetry: C(n,k) = C(n, n-k)
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let result = 1;
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for (let i = 0; i < k; i++) {
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result = (result * (n - i)) / (i + 1);
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}
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return result;
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}
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/** Fisher-Yates shuffle (in-place). */
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function shuffle<T>(arr: T[]): T[] {
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for (let i = arr.length - 1; i > 0; i--) {
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const j = Math.floor(Math.random() * (i + 1));
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[arr[i], arr[j]] = [arr[j], arr[i]];
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}
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return arr;
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}
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// ─── Simulator ────────────────────────────────────────────────────────────────
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export class SnookerSimulator implements Simulator {
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async simulate(sportsSeasonId: string): Promise<SimulationResult[]> {
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const db = database();
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// 1. Find the bracket scoring event for this sports season.
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const bracketEvent = await db.query.scoringEvents.findFirst({
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where: and(
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eq(schema.scoringEvents.sportsSeasonId, sportsSeasonId),
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eq(schema.scoringEvents.eventType, "playoff_game")
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),
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});
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// 2. Load playoff matches (may be empty if bracket hasn't been drawn yet).
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const allMatches = bracketEvent
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? await db.query.playoffMatches.findMany({
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where: eq(schema.playoffMatches.scoringEventId, bracketEvent.id),
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orderBy: (m, { asc }) => [asc(m.matchNumber)],
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})
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: [];
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// 3. Load Elo ratings and world rankings from participantExpectedValues.
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const evRows = await db
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.select({
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participantId: schema.participantExpectedValues.participantId,
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sourceElo: schema.participantExpectedValues.sourceElo,
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worldRanking: schema.participantExpectedValues.worldRanking,
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})
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.from(schema.participantExpectedValues)
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.where(eq(schema.participantExpectedValues.sportsSeasonId, sportsSeasonId));
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// Build Elo and ranking maps; fall back to 1500 for any participant with no stored rating.
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const eloMap = new Map<string, number>();
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const rankingMap = new Map<string, number>();
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for (const r of evRows) {
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if (r.sourceElo !== null && r.sourceElo !== undefined) {
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eloMap.set(r.participantId, r.sourceElo);
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} else if (!eloMap.has(r.participantId)) {
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eloMap.set(r.participantId, 1500);
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}
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if (r.worldRanking !== null && r.worldRanking !== undefined) {
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rankingMap.set(r.participantId, r.worldRanking);
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}
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}
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// Determine which simulation path to take.
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const bracketPopulated =
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allMatches.some((m) => m.participant1Id && m.participant2Id);
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if (bracketPopulated) {
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return this.simulateBracket(allMatches, eloMap);
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} else {
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return this.simulatePreBracket(sportsSeasonId, eloMap, rankingMap, db);
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}
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}
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// ─── Path A: Full bracket simulation ────────────────────────────────────────
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private async simulateBracket(
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allMatches: Awaited<ReturnType<ReturnType<typeof database>["query"]["playoffMatches"]["findMany"]>>,
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eloMap: Map<string, number>
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): Promise<SimulationResult[]> {
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// Group matches by round, sorted by match count descending (R32 first).
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const byRound = new Map<string, typeof allMatches>();
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for (const m of allMatches) {
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if (!byRound.has(m.round)) byRound.set(m.round, []);
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byRound.get(m.round)?.push(m);
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}
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const sortedRounds = [...byRound.values()]
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.toSorted((a, b) => b.length - a.length)
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.map((matches) => matches.sort((a, b) => a.matchNumber - b.matchNumber));
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if (sortedRounds.length !== 5) {
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throw new Error(
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`Expected 5 rounds for World Snooker Championship, found ${sortedRounds.length}. ` +
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`Rounds: ${[...byRound.keys()].join(", ")}`
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);
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}
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const [r32Matches, r16Matches, qfMatches, sfMatches, finalMatches] = sortedRounds;
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if (r32Matches.length !== 16) {
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throw new Error(
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`Expected 16 First Round matches, found ${r32Matches.length}.`
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);
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}
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// Collect all 32 participant IDs from R32.
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const participantIds: string[] = [];
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for (const m of r32Matches) {
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if (!m.participant1Id || !m.participant2Id) {
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throw new Error(
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`First Round match ${m.matchNumber} is missing participants. ` +
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`Assign all 32 players to the bracket before running simulation.`
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);
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}
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participantIds.push(m.participant1Id, m.participant2Id);
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}
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// Build lookup maps by matchNumber for O(1) access in the hot loop.
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const r32ByNum = new Map(r32Matches.map((m) => [m.matchNumber, m]));
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const r16ByNum = new Map(r16Matches.map((m) => [m.matchNumber, m]));
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const qfByNum = new Map(qfMatches.map((m) => [m.matchNumber, m]));
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const sfByNum = new Map(sfMatches.map((m) => [m.matchNumber, m]));
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const finalMatch = finalMatches[0];
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const fallbackElo = 1500;
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// Cache matchWinProb results — the Elo values and framesToWin are fixed across
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// all simulations, so the same (elo1, elo2, framesToWin) triple always yields
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// the same probability. Avoids recomputing the Bernoulli sum ~2M times per run.
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const matchProbCache = new Map<string, number>();
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const simMatch = (p1: string, p2: string, framesToWin: number): { winner: string; loser: string } => {
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const elo1 = eloMap.get(p1) ?? fallbackElo;
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const elo2 = eloMap.get(p2) ?? fallbackElo;
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const cacheKey = `${elo1},${elo2},${framesToWin}`;
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let winProb = matchProbCache.get(cacheKey);
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if (winProb === undefined) {
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winProb = matchWinProb(frameWinProb(elo1, elo2), framesToWin);
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matchProbCache.set(cacheKey, winProb);
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}
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const winner = Math.random() < winProb ? p1 : p2;
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return { winner, loser: winner === p1 ? p2 : p1 };
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};
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// Integer placement counts.
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const championCounts = new Map<string, number>(participantIds.map((id) => [id, 0]));
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const finalistCounts = new Map<string, number>(participantIds.map((id) => [id, 0]));
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const sfLoserCounts = new Map<string, number>(participantIds.map((id) => [id, 0]));
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const qfLoserCounts = new Map<string, number>(participantIds.map((id) => [id, 0]));
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for (let s = 0; s < NUM_SIMULATIONS; s++) {
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// ── First Round (R32) ──────────────────────────────────────────────────
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const r32Winners: string[] = [];
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for (let i = 1; i <= 16; i++) {
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const m = r32ByNum.get(i);
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if (!m) continue;
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if (m.isComplete && m.winnerId) {
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r32Winners.push(m.winnerId);
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} else {
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const { winner } = simMatch(m.participant1Id ?? "", m.participant2Id ?? "", FRAMES_TO_WIN[0]);
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r32Winners.push(winner);
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}
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}
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// ── Second Round (R16) ────────────────────────────────────────────────
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// R16 losers score 0 — only the winner is tracked.
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const r16Winners: string[] = [];
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for (let i = 1; i <= 8; i++) {
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const dbMatch = r16ByNum.get(i);
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let winner: string;
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if (dbMatch?.isComplete && dbMatch.winnerId) {
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winner = dbMatch.winnerId;
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} else {
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const p1 = r32Winners[(i - 1) * 2];
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const p2 = r32Winners[(i - 1) * 2 + 1];
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({ winner } = simMatch(p1, p2, FRAMES_TO_WIN[1]));
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}
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r16Winners.push(winner);
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}
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// ── Quarter-Finals ────────────────────────────────────────────────────
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const qfWinners: string[] = [];
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for (let i = 1; i <= 4; i++) {
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const dbMatch = qfByNum.get(i);
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let winner: string;
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let loser: string;
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if (dbMatch?.isComplete && dbMatch.winnerId && dbMatch.loserId) {
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winner = dbMatch.winnerId;
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loser = dbMatch.loserId;
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} else {
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const p1 = r16Winners[(i - 1) * 2];
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const p2 = r16Winners[(i - 1) * 2 + 1];
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({ winner, loser } = simMatch(p1, p2, FRAMES_TO_WIN[2]));
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}
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qfWinners.push(winner);
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qfLoserCounts.set(loser, (qfLoserCounts.get(loser) ?? 0) + 1);
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}
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// ── Semi-Finals ───────────────────────────────────────────────────────
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const sfWinners: string[] = [];
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for (let i = 1; i <= 2; i++) {
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const dbMatch = sfByNum.get(i);
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let winner: string;
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let loser: string;
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if (dbMatch?.isComplete && dbMatch.winnerId && dbMatch.loserId) {
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winner = dbMatch.winnerId;
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loser = dbMatch.loserId;
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} else {
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const p1 = qfWinners[(i - 1) * 2];
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const p2 = qfWinners[(i - 1) * 2 + 1];
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({ winner, loser } = simMatch(p1, p2, FRAMES_TO_WIN[3]));
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}
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sfWinners.push(winner);
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sfLoserCounts.set(loser, (sfLoserCounts.get(loser) ?? 0) + 1);
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}
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// ── Final ─────────────────────────────────────────────────────────────
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let champion: string;
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let finalist: string;
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if (finalMatch?.isComplete && finalMatch.winnerId && finalMatch.loserId) {
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champion = finalMatch.winnerId;
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finalist = finalMatch.loserId;
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} else {
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({ winner: champion, loser: finalist } = simMatch(sfWinners[0], sfWinners[1], FRAMES_TO_WIN[4]));
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}
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championCounts.set(champion, (championCounts.get(champion) ?? 0) + 1);
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finalistCounts.set(finalist, (finalistCounts.get(finalist) ?? 0) + 1);
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}
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return buildResults(participantIds, NUM_SIMULATIONS, {
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championCounts,
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finalistCounts,
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sfLoserCounts,
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qfLoserCounts,
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});
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}
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// ─── Path B: Pre-bracket simulation ─────────────────────────────────────────
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// Players beyond the top 16 seeds haven't been drawn yet. Each simulation:
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// 1. Randomly pairs qualifiers (seeds 17+) and simulates best-of-19 matches if >16.
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// 2. The 16 remaining qualifiers are shuffled and drawn into seed slots 17-32.
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// 3. The full 32-player bracket is then simulated using the proper seeded structure.
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//
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// Seeding is determined by worldRanking from participantExpectedValues (ascending).
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// Falls back to Elo order (descending) for players with no ranking stored.
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private async simulatePreBracket(
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sportsSeasonId: string,
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eloMap: Map<string, number>,
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rankingMap: Map<string, number>,
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db: ReturnType<typeof database>
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): Promise<SimulationResult[]> {
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const allParticipants = await db
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.select({ id: schema.participants.id, name: schema.participants.name })
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.from(schema.participants)
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.where(eq(schema.participants.sportsSeasonId, sportsSeasonId));
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if (allParticipants.length < 17) {
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throw new Error(
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`Pre-bracket simulation requires at least 17 participants (got ${allParticipants.length}). ` +
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`Add players to this sports season first.`
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);
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}
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// Sort by world ranking (ascending). Unranked players fall back to Elo order (descending).
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const fallbackElo = 1500;
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const ranked = allParticipants.toSorted((a, b) => {
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const rankA = rankingMap.get(a.id);
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const rankB = rankingMap.get(b.id);
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if (rankA !== undefined && rankB !== undefined) return rankA - rankB;
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if (rankA !== undefined) return -1;
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if (rankB !== undefined) return 1;
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return (eloMap.get(b.id) ?? fallbackElo) - (eloMap.get(a.id) ?? fallbackElo);
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});
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const topSeeds = ranked.slice(0, 16); // Fixed seed positions 1-16
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const qualifiers = ranked.slice(16); // Randomly drawn into positions 17-32
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const matchProbCache = new Map<string, number>();
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const simMatch = (p1Id: string, p2Id: string, framesToWin: number): string => {
|
||
const elo1 = eloMap.get(p1Id) ?? fallbackElo;
|
||
const elo2 = eloMap.get(p2Id) ?? fallbackElo;
|
||
const cacheKey = `${elo1},${elo2},${framesToWin}`;
|
||
let winProb = matchProbCache.get(cacheKey);
|
||
if (winProb === undefined) {
|
||
winProb = matchWinProb(frameWinProb(elo1, elo2), framesToWin);
|
||
matchProbCache.set(cacheKey, winProb);
|
||
}
|
||
return Math.random() < winProb ? p1Id : p2Id;
|
||
};
|
||
|
||
// Pre-extract qualifier IDs once — reused (with a fresh shuffle) each iteration.
|
||
const qualifierIds = qualifiers.map((p) => p.id);
|
||
|
||
const allParticipantIds = allParticipants.map((p) => p.id);
|
||
const championCounts = new Map<string, number>(allParticipantIds.map((id) => [id, 0]));
|
||
const finalistCounts = new Map<string, number>(allParticipantIds.map((id) => [id, 0]));
|
||
const sfLoserCounts = new Map<string, number>(allParticipantIds.map((id) => [id, 0]));
|
||
const qfLoserCounts = new Map<string, number>(allParticipantIds.map((id) => [id, 0]));
|
||
|
||
// Whether qualifying needs to be simulated (>16 players competing for 16 bracket slots).
|
||
// If exactly 16 qualifiers are already loaded (the common case when only 32 total players
|
||
// are in the DB), skip the qualifying simulation and use them directly as seeds 17-32.
|
||
const needsQualifying = qualifiers.length > 16;
|
||
|
||
for (let s = 0; s < NUM_SIMULATIONS; s++) {
|
||
// ── Qualifying: run elimination rounds until exactly 16 qualifiers remain ──
|
||
let drawnQualifiers: string[];
|
||
if (!needsQualifying) {
|
||
// All 16 qualifiers go straight through — just shuffle the draw order.
|
||
drawnQualifiers = shuffle([...qualifierIds]);
|
||
} else {
|
||
// Multiple qualifying rounds (best-of-19 each) to whittle down to 16.
|
||
let pool = shuffle([...qualifierIds]);
|
||
while (pool.length > 16) {
|
||
const winners: string[] = [];
|
||
for (let i = 0; i + 1 < pool.length; i += 2) {
|
||
winners.push(simMatch(pool[i], pool[i + 1], FRAMES_TO_WIN[0]));
|
||
}
|
||
// Odd player out gets a bye.
|
||
if (pool.length % 2 !== 0) {
|
||
winners.push(pool[pool.length - 1]);
|
||
}
|
||
pool = shuffle(winners);
|
||
}
|
||
drawnQualifiers = pool;
|
||
}
|
||
|
||
// Seeds 5-16: randomly swap adjacent pairs to reflect uncertainty in
|
||
// mid-tier seedings (top 4 are locked in).
|
||
const midSeeds = topSeeds.slice(4).map((p) => p.id);
|
||
for (let i = 0; i < midSeeds.length - 1; i++) {
|
||
if (Math.random() < 0.5) {
|
||
[midSeeds[i], midSeeds[i + 1]] = [midSeeds[i + 1], midSeeds[i]];
|
||
}
|
||
}
|
||
|
||
// Map seed number (1-indexed) → participant ID.
|
||
const seedToId = new Map<number, string>();
|
||
topSeeds.slice(0, 4).forEach((p, i) => seedToId.set(i + 1, p.id));
|
||
midSeeds.forEach((id, i) => seedToId.set(i + 5, id));
|
||
drawnQualifiers.forEach((id, i) => seedToId.set(i + 17, id));
|
||
|
||
// ── First Round (R32) — proper seeded bracket ─────────────────────────
|
||
// R32_BRACKET defines which seeds meet in each match, in bracket order so
|
||
// consecutive R32 winner pairs form the correct R16 matchups.
|
||
const r32Winners: string[] = [];
|
||
for (const [s1, s2] of R32_BRACKET) {
|
||
const p1 = seedToId.get(s1) ?? "";
|
||
const p2 = seedToId.get(s2) ?? "";
|
||
r32Winners.push(simMatch(p1, p2, FRAMES_TO_WIN[0]));
|
||
}
|
||
|
||
// ── Second Round (R16) ────────────────────────────────────────────────
|
||
const r16Winners: string[] = [];
|
||
for (let i = 0; i < r32Winners.length; i += 2) {
|
||
r16Winners.push(simMatch(r32Winners[i], r32Winners[i + 1], FRAMES_TO_WIN[1]));
|
||
}
|
||
|
||
// ── Quarter-Finals ────────────────────────────────────────────────────
|
||
const qfWinners: string[] = [];
|
||
for (let i = 0; i < r16Winners.length; i += 2) {
|
||
const p1 = r16Winners[i], p2 = r16Winners[i + 1];
|
||
const winner = simMatch(p1, p2, FRAMES_TO_WIN[2]);
|
||
qfWinners.push(winner);
|
||
qfLoserCounts.set(winner === p1 ? p2 : p1, (qfLoserCounts.get(winner === p1 ? p2 : p1) ?? 0) + 1);
|
||
}
|
||
|
||
// ── Semi-Finals ───────────────────────────────────────────────────────
|
||
const sfWinners: string[] = [];
|
||
for (let i = 0; i < qfWinners.length; i += 2) {
|
||
const p1 = qfWinners[i], p2 = qfWinners[i + 1];
|
||
const winner = simMatch(p1, p2, FRAMES_TO_WIN[3]);
|
||
sfWinners.push(winner);
|
||
sfLoserCounts.set(winner === p1 ? p2 : p1, (sfLoserCounts.get(winner === p1 ? p2 : p1) ?? 0) + 1);
|
||
}
|
||
|
||
// ── Final ─────────────────────────────────────────────────────────────
|
||
const champion = simMatch(sfWinners[0], sfWinners[1], FRAMES_TO_WIN[4]);
|
||
const finalist = champion === sfWinners[0] ? sfWinners[1] : sfWinners[0];
|
||
championCounts.set(champion, (championCounts.get(champion) ?? 0) + 1);
|
||
finalistCounts.set(finalist, (finalistCounts.get(finalist) ?? 0) + 1);
|
||
}
|
||
|
||
return buildResults(allParticipantIds, NUM_SIMULATIONS, {
|
||
championCounts,
|
||
finalistCounts,
|
||
sfLoserCounts,
|
||
qfLoserCounts,
|
||
});
|
||
}
|
||
}
|
||
|
||
// ─── Shared result builder ─────────────────────────────────────────────────────
|
||
|
||
function buildResults(
|
||
participantIds: string[],
|
||
N: number,
|
||
counts: {
|
||
championCounts: Map<string, number>;
|
||
finalistCounts: Map<string, number>;
|
||
sfLoserCounts: Map<string, number>;
|
||
qfLoserCounts: Map<string, number>;
|
||
}
|
||
): SimulationResult[] {
|
||
const { championCounts, finalistCounts, sfLoserCounts, qfLoserCounts } = counts;
|
||
|
||
const results: SimulationResult[] = participantIds.map((participantId) => {
|
||
const c = championCounts.get(participantId) ?? 0;
|
||
const f = finalistCounts.get(participantId) ?? 0;
|
||
const sf = sfLoserCounts.get(participantId) ?? 0;
|
||
const qf = qfLoserCounts.get(participantId) ?? 0;
|
||
return {
|
||
participantId,
|
||
probabilities: {
|
||
probFirst: c / N,
|
||
probSecond: f / N,
|
||
probThird: sf / (2 * N),
|
||
probFourth: sf / (2 * N),
|
||
probFifth: qf / (4 * N),
|
||
probSixth: qf / (4 * N),
|
||
probSeventh: qf / (4 * N),
|
||
probEighth: qf / (4 * N),
|
||
},
|
||
source: "snooker_world_championship_monte_carlo",
|
||
};
|
||
});
|
||
|
||
// Per-position column normalization — ensures sums are exactly 1.0.
|
||
const positionKeys: Array<keyof typeof results[0]["probabilities"]> = [
|
||
"probFirst", "probSecond", "probThird", "probFourth",
|
||
"probFifth", "probSixth", "probSeventh", "probEighth",
|
||
];
|
||
for (const key of positionKeys) {
|
||
const colSum = results.reduce((s, r) => s + r.probabilities[key], 0);
|
||
const residual = 1.0 - colSum;
|
||
if (residual !== 0) {
|
||
const maxResult = results.reduce((best, r) =>
|
||
r.probabilities[key] > best.probabilities[key] ? r : best
|
||
);
|
||
maxResult.probabilities[key] += residual;
|
||
}
|
||
}
|
||
|
||
return results;
|
||
}
|