brackt/app/services/simulations/mlb-simulator.ts

/**
 * MLB Playoff Simulator
 *
 * Monte Carlo simulation of the MLB season and playoffs including seeding
 * projection for the current season (2026).
 *
 * Algorithm:
 *   1. Load all participants for the sports season from DB
 *   2. Load current standings (wins, gamesPlayed) from regularSeasonStandings
 *   3. Load sourceElo ratings from seasonParticipantExpectedValues
 *   4. Match participant names to hardcoded team data (RDif + league/division)
 *   5. For each simulation:
 *      a. For each league (AL/NL), simulate remaining regular season games for
 *         every team using Binomial sampling, giving final projected wins.
 *      b. Division winner = best record in each division (3 per league).
 *         Wild card = next 3 best records among non-division-winners per league.
 *      c. Seed division winners 1–3 by final wins (best = seed 1);
 *         WC teams 4–6 by final wins.
 *      d. Run the playoff bracket per league:
 *         - Wildcard Round (best-of-3): 3 vs 6, 4 vs 5 (seeds 1 & 2 get byes)
 *         - Division Series (best-of-5): 1 vs lowest WC survivor, 2 vs other
 *         - League Championship Series (best-of-7)
 *      e. World Series (best-of-7): AL champ vs NL champ
 *   6. Track placement counts per scoring tier
 *   7. Convert counts to probability distributions
 *
 * Win probability (log5 formula):
 *   Step 1 — convert projected RDif to win rate for playoff matchups:
 *     winRate = clamp(0.5 + rdif / RDIF_DIVISOR, 0.01, 0.99)
 *     RDIF_DIVISOR compresses team strengths toward .500 for playoff parity.
 *   Step 2 — Bill James log5 head-to-head probability:
 *     P(A beats B) = (wA - wA·wB) / (wA + wB - 2·wA·wB)
 *
 * Regular season simulation (seeding):
 *   Each team's raw per-game win rate is derived from sourceElo (if set) or
 *   from the hardcoded RDif using SEEDING_RDIF_SCALE ≈ 10 runs/win × 162 games.
 *   Remaining games = TOTAL_SEASON_GAMES − gamesPlayed are drawn from a
 *   Binomial distribution.  This makes playoff seeding respond to both current
 *   standings and user-entered projected wins.
 *
 * Futures blending:
 *   If sourceOdds are stored in participantExpectedValues for this season,
 *   the per-game win probability for playoff series is blended:
 *     P(game) = RDIF_WEIGHT * rdifProb + ODDS_WEIGHT * oddsProb
 *   RDIF_WEIGHT = 0.7, ODDS_WEIGHT = 0.3.
 *
 * Placement tiers → SimulationProbabilities mapping:
 *   probFirst              = World Series champion (1 per sim)
 *   probSecond             = World Series loser (1 per sim)
 *   probThird / probFourth = LCS losers (2 per sim — AL + NL, split evenly)
 *   probFifth–probEighth   = Division Series losers (4 per sim, split evenly)
 *   Wildcard Round losers  → all 0 (score 0 points, same as non-playoff teams)
 *   Missed playoffs        → all 0
 *
 * Team data keys:
 *   rdif:  FanGraphs Depth Charts projected run differential for 2026.
 *          Used as fallback for seeding win rate and for playoff series win probability.
 *   league/division: Static MLB structure — does not change season-to-season.
 *
 * Sources:
 *   rdif: https://www.fangraphs.com/standings/projected-standings
 * Update rdif at the start of each season.
 *
 * Divisions:
 *   AL East:    Yankees, Orioles, Red Sox, Rays, Blue Jays
 *   AL Central: Royals, Guardians, Twins, Tigers, White Sox
 *   AL West:    Astros, Mariners, Rangers, Angels, Athletics
 *   NL East:    Phillies, Braves, Mets, Nationals, Marlins
 *   NL Central: Brewers, Cubs, Cardinals, Reds, Pirates
 *   NL West:    Dodgers, Padres, Diamondbacks, Giants, Rockies
 */

import { database } from "~/database/context";
import { eq } from "drizzle-orm";
import * as schema from "~/database/schema";
import type { Simulator, SimulationResult } from "./types";
import { positiveConfigNumber } from "./config-access";
import { logger } from "~/lib/logger";
import { getRegularSeasonStandings } from "~/models/regular-season-standings";

// ─── Simulation parameters ────────────────────────────────────────────────────

const DEFAULT_NUM_SIMULATIONS = 50_000;
const TOTAL_SEASON_GAMES = 162;

/**
 * Controls how much projected run differential spreads teams away from .500
 * for single-game playoff matchups.
 *
 * Effect on Dodgers (RDif +137):
 *   1620 → win rate 0.585 (raw Pythagorean — too dominant for playoff matchups)
 *   8000 → win rate 0.517 (current — near coin-flip vs any playoff team)
 */
const RDIF_DIVISOR = 8000;

/**
 * Scale for converting RDif to a raw per-game win rate for regular-season
 * seeding simulation.  Unlike RDIF_DIVISOR (which compresses for playoff
 * parity), this uses ~10 runs/win × 162 games to give realistic season win%.
 */
const SEEDING_RDIF_SCALE = 1620;

// ─── Team data (2026 pre-season — FanGraphs Depth Charts) ────────────────────
//
// rdif: Projected run differential from FanGraphs Depth Charts.
//       Source: https://www.fangraphs.com/standings/projected-standings
//
// league/division: Static MLB structure — update only if teams change leagues.
//
// Update rdif at the start of each season.

interface MlbTeamData {
  league: "AL" | "NL";
  division: "AL East" | "AL Central" | "AL West" | "NL East" | "NL Central" | "NL West";
  rdif: number;  // 2026 FanGraphs Depth Charts projected run differential
}

const TEAMS_DATA: Record<string, MlbTeamData> = {
  // ── American League East ───────────────────────────────────────────────────
  "New York Yankees":   { league: "AL", division: "AL East",    rdif:  67 },
  "Baltimore Orioles":  { league: "AL", division: "AL East",    rdif:  23 },
  "Boston Red Sox":     { league: "AL", division: "AL East",    rdif:  48 },
  "Tampa Bay Rays":     { league: "AL", division: "AL East",    rdif:   2 },
  "Toronto Blue Jays":  { league: "AL", division: "AL East",    rdif:  37 },

  // ── American League Central ────────────────────────────────────────────────
  "Kansas City Royals":    { league: "AL", division: "AL Central", rdif:   8 },
  "Cleveland Guardians":   { league: "AL", division: "AL Central", rdif: -38 },
  "Minnesota Twins":       { league: "AL", division: "AL Central", rdif: -15 },
  "Detroit Tigers":        { league: "AL", division: "AL Central", rdif:  26 },
  "Chicago White Sox":     { league: "AL", division: "AL Central", rdif: -112 },

  // ── American League West ───────────────────────────────────────────────────
  "Houston Astros":      { league: "AL", division: "AL West",    rdif:  -1 },
  "Seattle Mariners":    { league: "AL", division: "AL West",    rdif:  66 },
  "Texas Rangers":       { league: "AL", division: "AL West",    rdif:  20 },
  "Los Angeles Angels":  { league: "AL", division: "AL West",    rdif: -65 },
  "Athletics":           { league: "AL", division: "AL West",    rdif: -17 },

  // ── National League East ───────────────────────────────────────────────────
  "Philadelphia Phillies": { league: "NL", division: "NL East",    rdif:  51 },
  "Atlanta Braves":        { league: "NL", division: "NL East",    rdif:  67 },
  "New York Mets":         { league: "NL", division: "NL East",    rdif:  71 },
  "Washington Nationals":  { league: "NL", division: "NL East",    rdif: -113 },
  "Miami Marlins":         { league: "NL", division: "NL East",    rdif: -48 },

  // ── National League Central ────────────────────────────────────────────────
  "Milwaukee Brewers":   { league: "NL", division: "NL Central", rdif:   9 },
  "Chicago Cubs":        { league: "NL", division: "NL Central", rdif:  23 },
  "St. Louis Cardinals": { league: "NL", division: "NL Central", rdif: -55 },
  "Cincinnati Reds":     { league: "NL", division: "NL Central", rdif: -31 },
  "Pittsburgh Pirates":  { league: "NL", division: "NL Central", rdif:  13 },

  // ── National League West ───────────────────────────────────────────────────
  "Los Angeles Dodgers":    { league: "NL", division: "NL West",    rdif: 137 },
  "San Diego Padres":       { league: "NL", division: "NL West",    rdif:  -9 },
  "Arizona Diamondbacks":   { league: "NL", division: "NL West",    rdif:   5 },
  "San Francisco Giants":   { league: "NL", division: "NL West",    rdif:   3 },
  "Colorado Rockies":       { league: "NL", division: "NL West",    rdif: -173 },
};

// ─── Public helpers (exported for unit testing) ───────────────────────────────

/** Normalize a team name for lookup (lowercase, trimmed, collapsed whitespace). */
export function normalizeTeamName(name: string): string {
  return name.toLowerCase().trim().replace(/\s+/g, " ");
}

/** Look up team data by participant name (case-insensitive). */
export function getTeamData(name: string): MlbTeamData | undefined {
  const normalized = normalizeTeamName(name);
  for (const [teamName, data] of Object.entries(TEAMS_DATA)) {
    if (normalizeTeamName(teamName) === normalized) return data;
  }
  return undefined;
}

/**
 * Convert projected run differential to a compressed win rate for playoff matchup probability.
 * Uses RDIF_DIVISOR to control how much team strength spreads away from .500.
 * Clamped to [0.01, 0.99] to avoid degenerate log5 values.
 * Exported for unit testing.
 */
export function winRateFromRDif(rdif: number): number {
  return Math.min(0.99, Math.max(0.01, 0.5 + rdif / RDIF_DIVISOR));
}

/**
 * Convert projected run differential to a raw per-game win rate for regular-season
 * seeding simulation.  Uses SEEDING_RDIF_SCALE (~10 runs/win × 162 games) which
 * gives a realistic season win percentage rather than the playoff-compressed value.
 * Exported for unit testing.
 */
export function rawWinRateFromRDif(rdif: number): number {
  return Math.min(0.99, Math.max(0.01, 0.5 + rdif / SEEDING_RDIF_SCALE));
}

/**
 * Derive a raw per-game win rate directly from an Elo rating.
 * This is the inverse Elo formula, returning the same win probability
 * that was originally used to compute the Elo from projected wins.
 * Exported for unit testing.
 */
export function rawWinRateFromElo(elo: number): number {
  return 1 / (1 + Math.pow(10, (1500 - elo) / 400));
}

/**
 * Convert an Elo rating to an equivalent projected run differential.
 * Uses the standard Elo win probability formula (parity factor 400, average Elo 1500),
 * then inverts the winRateFromRDif formula: rdif = (winRate − 0.5) × RDIF_DIVISOR.
 * Exported for unit testing.
 */
export function eloToRDif(elo: number): number {
  return (rawWinRateFromElo(elo) - 0.5) * RDIF_DIVISOR;
}

/**
 * Bill James log5 head-to-head win probability for team A over team B,
 * given their projected run differentials.
 *   P(A beats B) = (wA - wA·wB) / (wA + wB - 2·wA·wB)
 * Exported for unit testing.
 */
export function rdifWinProbability(rdifA: number, rdifB: number): number {
  const wA = winRateFromRDif(rdifA);
  const wB = winRateFromRDif(rdifB);
  // Denominator is always > 0 when wA and wB are in (0,1).
  return (wA - wA * wB) / (wA + wB - 2 * wA * wB);
}

/**
 * Sample the number of wins from n independent Bernoulli trials each with
 * probability p.  Used to project remaining regular-season wins per team.
 *
 * For n ≥ 30 (where CLT applies well: n·p ≥ 5 and n·(1-p) ≥ 5 for any
 * realistic win rate), uses a Box-Muller normal approximation — 2 Math.random()
 * calls per team instead of n, cutting the seeding phase from ~243M to ~3M
 * Math.random() calls per 50K-simulation run.  For small n the exact Bernoulli
 * loop is used.  Both paths produce integer output clamped to [0, n].
 * Exported for unit testing.
 */
export function sampleBinomial(n: number, p: number): number {
  if (n <= 0) return 0;
  if (p <= 0) return 0;
  if (p >= 1) return n;

  if (n >= 30) {
    // Normal approximation via Box-Muller transform.
    // Guard u1 > 0 to avoid log(0) = -Infinity.
    const u1 = Math.max(Number.EPSILON, Math.random());
    const u2 = Math.random();
    const z = Math.sqrt(-2 * Math.log(u1)) * Math.cos(2 * Math.PI * u2);
    return Math.round(Math.min(n, Math.max(0, n * p + Math.sqrt(n * p * (1 - p)) * z)));
  }

  // Exact Bernoulli trials for small n.
  let wins = 0;
  for (let i = 0; i < n; i++) {
    if (Math.random() < p) wins++;
  }
  return wins;
}

// ─── Internal types ───────────────────────────────────────────────────────────

interface TeamEntry {
  id: string;
  name: string;
  data: MlbTeamData | undefined;
  originalSeed?: number;
  currentWins: number;    // from regularSeasonStandings (0 pre-season)
  remainingGames: number; // TOTAL_SEASON_GAMES - gamesPlayed
}

/** Get projected RDif for a team entry. Fallback 0 (league-average) for unknown teams. */
function getEntryRDif(entry: TeamEntry): number {
  return entry.data?.rdif ?? 0;
}

// ─── Series simulators ─────────────────────────────────────────────────────────

type SeriesResult = { winner: TeamEntry; loser: TeamEntry };

/** Simulate a series where the winner must reach `winsNeeded` wins. */
function simSeries(
  a: TeamEntry,
  b: TeamEntry,
  winsNeeded: number,
  gameWinProb: (a: TeamEntry, b: TeamEntry) => number
): SeriesResult {
  const prob = gameWinProb(a, b);
  let winsA = 0;
  let winsB = 0;
  while (winsA < winsNeeded && winsB < winsNeeded) {
    if (Math.random() < prob) winsA++; else winsB++;
  }
  return winsA === winsNeeded ? { winner: a, loser: b } : { winner: b, loser: a };
}

/** Wildcard Round: best-of-3 (first to 2 wins). */
export function simBo3(
  a: TeamEntry,
  b: TeamEntry,
  gameWinProb: (a: TeamEntry, b: TeamEntry) => number
): SeriesResult {
  return simSeries(a, b, 2, gameWinProb);
}

/** Division Series: best-of-5 (first to 3 wins). */
export function simBo5(
  a: TeamEntry,
  b: TeamEntry,
  gameWinProb: (a: TeamEntry, b: TeamEntry) => number
): SeriesResult {
  return simSeries(a, b, 3, gameWinProb);
}

/** League Championship + World Series: best-of-7 (first to 4 wins). */
export function simBo7(
  a: TeamEntry,
  b: TeamEntry,
  gameWinProb: (a: TeamEntry, b: TeamEntry) => number
): SeriesResult {
  return simSeries(a, b, 4, gameWinProb);
}

// ─── League bracket builder ───────────────────────────────────────────────────

/**
 * Draws the 6-team playoff field for one league (AL or NL) by simulating the
 * remaining regular season for each team.
 *
 * Steps:
 *   1. For each team, sample remaining wins from Binomial(remainingGames, seedingWinRate).
 *      A tiny uniform noise [0, 0.001) is added to break integer ties randomly.
 *   2. Division winner = team with highest final wins in each division (3 per league).
 *   3. Wild card = next 3 highest final wins among non-division-winners.
 *   4. Seed division winners 1–3 by final wins descending (best = seed 1).
 *   5. Seed WC teams 4–6 by final wins descending.
 *
 * Returns an array of 6 TeamEntry objects in seed order [1..6], each annotated
 * with originalSeed, or undefined if the league has fewer than 3 eligible WC teams.
 */
function drawLeaguePlayoffField(
  leagueTeams: TeamEntry[],
  getSeedingWinRate: (t: TeamEntry) => number
): TeamEntry[] | undefined {
  // Group by division
  const divMap = new Map<string, TeamEntry[]>();
  for (const t of leagueTeams) {
    const div = t.data?.division ?? "Unknown";
    if (!divMap.has(div)) divMap.set(div, []);
    divMap.get(div)?.push(t);
  }

  // Simulate remaining games for each team; tiny noise breaks integer win ties
  const finalWins = new Map<string, number>();
  for (const t of leagueTeams) {
    finalWins.set(
      t.id,
      t.currentWins + sampleBinomial(t.remainingGames, getSeedingWinRate(t)) + Math.random() * 0.001
    );
  }

  // Division winners: best record per division
  const divisionWinners: TeamEntry[] = [];
  const divWinnerSet = new Set<TeamEntry>();

  for (const divTeams of divMap.values()) {
    const winner = divTeams.reduce((best, t) =>
      (finalWins.get(t.id) ?? 0) > (finalWins.get(best.id) ?? 0) ? t : best
    );
    divisionWinners.push(winner);
    divWinnerSet.add(winner);
  }

  // Wild card: top 3 non-division-winners by final wins
  const wcTeams = leagueTeams
    .filter((t) => !divWinnerSet.has(t))
    .toSorted((a, b) => (finalWins.get(b.id) ?? 0) - (finalWins.get(a.id) ?? 0))
    .slice(0, 3);

  if (wcTeams.length < 3) return undefined;

  // Seed: div winners 1–3 and WC teams 4–6, both by final wins descending
  const sortedDivWinners = divisionWinners.toSorted(
    (a, b) => (finalWins.get(b.id) ?? 0) - (finalWins.get(a.id) ?? 0)
  );
  const sortedWcTeams = wcTeams.toSorted(
    (a, b) => (finalWins.get(b.id) ?? 0) - (finalWins.get(a.id) ?? 0)
  );

  const seeds = [...sortedDivWinners, ...sortedWcTeams];
  return seeds.map((t, i) => ({ ...t, originalSeed: i + 1 }));
}

/**
 * Simulate the full playoff bracket for one league.
 *
 * Bracket structure:
 *   Wildcard Round (best-of-3): seeds 3v6, 4v5 — seeds 1 & 2 get byes
 *   Division Series (best-of-5): 1 vs lowest-seeded WC survivor; 2 vs other
 *   League Championship Series (best-of-7)
 *
 * Returns { lcWinner, lcLoser, dsLosers[2], wcLosers[2] }
 */
function simLeagueBracket(
  seeds: TeamEntry[],
  gameWinProb: (a: TeamEntry, b: TeamEntry) => number
): {
  lcWinner: TeamEntry;
  lcLoser: TeamEntry;
  dsLosers: [TeamEntry, TeamEntry];
  wcLosers: [TeamEntry, TeamEntry];
} {
  const [s1, s2, s3, s4, s5, s6] = seeds;

  // Wildcard Round (best-of-3)
  const wc1 = simBo3(s3, s6, gameWinProb);
  const wc2 = simBo3(s4, s5, gameWinProb);

  // Division Series: re-seed — seed 1 plays the worse WC survivor, seed 2 plays the better one.
  // Sort by originalSeed ascending: [0] = lower seed number = better team, [1] = worse team.
  const survivors = [wc1.winner, wc2.winner].toSorted(
    (a, b) => (a.originalSeed ?? 0) - (b.originalSeed ?? 0)
  );
  const ds1 = simBo5(s1, survivors[1], gameWinProb); // 1 vs worse remaining (higher seed number)
  const ds2 = simBo5(s2, survivors[0], gameWinProb); // 2 vs better remaining (lower seed number)

  // League Championship Series (best-of-7)
  const lcs = simBo7(ds1.winner, ds2.winner, gameWinProb);

  return {
    lcWinner: lcs.winner,
    lcLoser: lcs.loser,
    dsLosers: [ds1.loser, ds2.loser],
    wcLosers: [wc1.loser, wc2.loser],
  };
}

// ─── Simulator ────────────────────────────────────────────────────────────────

export class MLBSimulator implements Simulator {
  async simulate(sportsSeasonId: string, config: Record<string, unknown> = {}): Promise<SimulationResult[]> {
    const numSimulations = Math.round(positiveConfigNumber(config, "iterations", DEFAULT_NUM_SIMULATIONS));
    const db = database();

    // 1. Load all participants for this sports season.
    const participantRows = await db
      .select({ id: schema.seasonParticipants.id, name: schema.seasonParticipants.name })
      .from(schema.seasonParticipants)
      .where(eq(schema.seasonParticipants.sportsSeasonId, sportsSeasonId));

    if (participantRows.length === 0) {
      throw new Error(
        `No participants found for sports season ${sportsSeasonId}. ` +
          `Add MLB teams as participants before running simulation.`
      );
    }

    const participantIds = participantRows.map((r) => r.id);
    const participantIdSet = new Set(participantIds);

    // 2. Load current standings (wins + games played) to seed the regular-season simulation.
    const standings = await getRegularSeasonStandings(sportsSeasonId);
    const standingsByParticipantId = new Map(standings.map((s) => [s.participantId, s]));

    const teams: TeamEntry[] = participantRows.map((r) => {
      const standing = standingsByParticipantId.get(r.id);
      const gamesPlayed = standing?.gamesPlayed ?? 0;
      return {
        id: r.id,
        name: r.name,
        data: getTeamData(r.name),
        currentWins: standing?.wins ?? 0,
        remainingGames: Math.max(0, TOTAL_SEASON_GAMES - gamesPlayed),
      };
    });

    // Warn about participants that don't match any hardcoded team.
    const unrecognized = teams.filter((t) => !t.data);
    if (unrecognized.length > 0) {
      logger.warn(
        `[MLBSimulator] ${unrecognized.length} participant(s) not found in TEAMS_DATA and will be excluded: ` +
          unrecognized.map((t) => t.name).join(", ")
      );
    }

    // Warn when standings exist for some teams but not all recognized ones — this
    // usually means a partial sync.  Missing teams fall back to 0 wins / 162
    // remaining games (league-average strength), which distorts mid-season seeding.
    if (standings.length > 0) {
      const missingStandings = teams.filter(
        (t) => t.data && !standingsByParticipantId.has(t.id)
      );
      if (missingStandings.length > 0) {
        logger.warn(
          `[MLBSimulator] ${missingStandings.length} recognized team(s) have no standings row — ` +
            `seeding will use 0 wins / 162 remaining games for: ` +
            missingStandings.map((t) => t.name).join(", ")
        );
      }
    }

    const alTeams = teams.filter((t) => t.data?.league === "AL");
    const nlTeams = teams.filter((t) => t.data?.league === "NL");

    if (alTeams.length < 6 || nlTeams.length < 6) {
      throw new Error(
        `Each league needs at least 6 recognized participants (3 division winners + 3 wild cards) ` +
          `(got AL: ${alTeams.length}, NL: ${nlTeams.length}). ` +
          `Add MLB teams before running simulation.`
      );
    }

    // ─── Strength from the resolved Elo ────────────────────────────────────────
    // sourceElo is the single Elo produced by the input policy — already a blend
    // of any raw Elo / projections / futures odds — so the simulator just reads it
    // and no longer blends odds itself.

    const evRows = await db
      .select({
        participantId: schema.seasonParticipantExpectedValues.participantId,
        sourceElo: schema.seasonParticipantExpectedValues.sourceElo,
      })
      .from(schema.seasonParticipantExpectedValues)
      .where(eq(schema.seasonParticipantExpectedValues.sportsSeasonId, sportsSeasonId));

    // Build a map of sourceElo-derived RDif values (overrides hardcoded TEAMS_DATA.rdif)
    // for playoff series win probability.
    const sourceEloRDifMap = new Map<string, number>();
    // Build a map of raw (uncompressed) win rates from sourceElo for regular-season seeding.
    const rawWinRateMap = new Map<string, number>();
    for (const r of evRows) {
      if (r.sourceElo !== null && r.sourceElo !== undefined && participantIdSet.has(r.participantId)) {
        sourceEloRDifMap.set(r.participantId, eloToRDif(r.sourceElo));
        rawWinRateMap.set(r.participantId, rawWinRateFromElo(r.sourceElo));
      }
    }

    // ─── Helpers ──────────────────────────────────────────────────────────────

    /** Effective RDif for playoff series: prefer sourceElo-derived value over hardcoded rdif. */
    const effectiveRDif = (entry: TeamEntry): number =>
      sourceEloRDifMap.get(entry.id) ?? getEntryRDif(entry);

    /**
     * Raw per-game win rate for regular-season seeding simulation.
     * Uses sourceElo-derived rate if available; falls back to hardcoded rdif
     * with SEEDING_RDIF_SCALE (Pythagorean approximation).
     */
    const seedingWinRate = (entry: TeamEntry): number =>
      rawWinRateMap.get(entry.id) ?? rawWinRateFromRDif(getEntryRDif(entry));

    /**
     * Per-game win probability for team A over team B in a playoff series, from
     * the (resolved-Elo-derived) run differential.
     */
    const gameWinProb = (a: TeamEntry, b: TeamEntry): number =>
      rdifWinProbability(effectiveRDif(a), effectiveRDif(b));

    // ─── Placement count maps ──────────────────────────────────────────────────

    const championCounts = new Map<string, number>(participantIds.map((id) => [id, 0]));
    const finalistCounts = new Map<string, number>(participantIds.map((id) => [id, 0]));
    const lcsLoserCounts = new Map<string, number>(participantIds.map((id) => [id, 0]));
    const dsLoserCounts  = new Map<string, number>(participantIds.map((id) => [id, 0]));
    // WC losers are not tracked — they score 0 points

    // ─── Monte Carlo simulation loop ───────────────────────────────────────────

    let effectiveN = 0;

    for (let s = 0; s < numSimulations; s++) {
      const alField = drawLeaguePlayoffField(alTeams, seedingWinRate);
      const nlField = drawLeaguePlayoffField(nlTeams, seedingWinRate);
      if (!alField || !nlField) continue; // degenerate draw — skip

      effectiveN++;

      // Simulate both league brackets
      const alResult = simLeagueBracket(alField, gameWinProb);
      const nlResult = simLeagueBracket(nlField, gameWinProb);

      // LCS losers (3rd/4th tier)
      lcsLoserCounts.set(alResult.lcLoser.id, (lcsLoserCounts.get(alResult.lcLoser.id) ?? 0) + 1);
      lcsLoserCounts.set(nlResult.lcLoser.id, (lcsLoserCounts.get(nlResult.lcLoser.id) ?? 0) + 1);

      // DS losers (5th–8th tier)
      for (const loser of [...alResult.dsLosers, ...nlResult.dsLosers]) {
        dsLoserCounts.set(loser.id, (dsLoserCounts.get(loser.id) ?? 0) + 1);
      }

      // World Series (best-of-7)
      const ws = simBo7(alResult.lcWinner, nlResult.lcWinner, gameWinProb);
      championCounts.set(ws.winner.id, (championCounts.get(ws.winner.id) ?? 0) + 1);
      finalistCounts.set(ws.loser.id,  (finalistCounts.get(ws.loser.id) ?? 0)  + 1);
    }

    if (effectiveN === 0) {
      throw new Error(
        "All simulations produced degenerate brackets. " +
          "Check that each division has teams with non-degenerate RDif values."
      );
    }

    // ─── Convert counts to probability distributions ───────────────────────────
    //
    //   probFirst/Second  → count / N           (1 team per sim)
    //   probThird/Fourth  → count / (2 * N)     (2 LCS losers per sim: AL + NL)
    //   probFifth–Eighth  → count / (4 * N)     (4 DS losers per sim: 2 per league)
    //   WC losers         → 0 (all probs zero)

    const N = effectiveN;
    const results: SimulationResult[] = participantIds.map((participantId) => {
      const c   = championCounts.get(participantId) ?? 0;
      const f   = finalistCounts.get(participantId) ?? 0;
      const lcs = lcsLoserCounts.get(participantId) ?? 0;
      const ds  = dsLoserCounts.get(participantId) ?? 0;
      return {
        participantId,
        probabilities: {
          probFirst:   c   / N,
          probSecond:  f   / N,
          probThird:   lcs / (2 * N),
          probFourth:  lcs / (2 * N),
          probFifth:   ds  / (4 * N),
          probSixth:   ds  / (4 * N),
          probSeventh: ds  / (4 * N),
          probEighth:  ds  / (4 * N),
        },
        source: "mlb_bracket_monte_carlo",
      };
    });

    // ─── Per-position normalization ────────────────────────────────────────────

    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;
  }
}