Simulate NBA remaining regular season games from standings (#201)
Replace static Basketball-Reference seed probability distributions (p_1..p_10) with dynamic simulation of each team's remaining games based on current standings from the DB. - Load regularSeasonStandings in parallel with participants query - Compute remainingGames = 82 - gamesPlayed per team - Pre-compute per-game win probability (Elo vs average opponent 1500) on TeamEntry at construction time — not inside the hot loop - Sort conference standings by projected wins to assign seeds, replacing the drawSeed() weighted-probability approach - Conference resolved from standings table, falls back to TEAMS_DATA - Strip all p_1..p_10 seed probability data from TEAMS_DATA - Move simulateProjectedWins to module scope (no closure captures) - Remove const N alias; use NUM_SIMULATIONS directly Co-authored-by: Claude Sonnet 4.6 <noreply@anthropic.com>
This commit is contained in:
Chris Parsons
GitHub
parent
618bc57ec1
commit
7093b22726
1 changed files with 134 additions and 202 deletions
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@ -6,11 +6,13 @@
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*
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* Algorithm:
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* 1. Load all participants for the sports season from DB
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* 2. Match participant names to hardcoded team data (Elo + seed probabilities)
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* 3. For each simulation:
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* a. Assign each team a seed based on its weighted probability distribution (p_1..p_10)
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* Teams with no seed probabilities always miss the playoffs (seed = 11)
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* b. Sort each conference by drawn seed + random tiebreaker
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* 2. Load current regular season standings (wins, gamesPlayed, conference)
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* 3. Match participant names to hardcoded team data (Elo ratings)
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* 4. For each simulation:
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* a. For each team, simulate remaining regular season games (82 - gamesPlayed)
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* using Elo win probability vs. an average opponent (Elo 1500)
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* → projectedWins = currentWins + simulatedRemainingWins
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* b. Sort each conference by projected wins (desc) + random tiebreaker → seeds 1–10
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* → Top 6 lock in directly; seeds 7–10 enter the Play-In tournament
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* c. Simulate Play-In (single game each):
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* - Game 1: seed 7 vs seed 8 → winner becomes 7th playoff seed
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@ -21,12 +23,17 @@
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* Round 2: Conference Semis (winners of 1v8/4v5, winners of 2v7/3v6)
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* Round 3: Conference Finals
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* NBA Finals: East champion vs West champion
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* 4. Track placement counts per scoring tier
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* 5. Convert counts to probability distributions
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* 5. Track placement counts per scoring tier
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* 6. Convert counts to probability distributions
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*
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* Win probability (Elo, PARITY_FACTOR = 400):
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* P(A beats B) = 1 / (1 + 10^((eloB - eloA) / 400))
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*
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* Regular season projection:
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* Per-game win probability = eloWinProbability(teamElo, 1500) where 1500 = average opponent.
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* If no standings exist in DB, defaults to 0 wins / 82 remaining games (seeding by Elo only).
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* Conference is read from standings table; falls back to TEAMS_DATA if missing.
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*
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* Placement tiers → SimulationProbabilities mapping:
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* probFirst = NBA champion (1 per sim)
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* probSecond = NBA Finals loser (1 per sim)
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@ -35,9 +42,9 @@
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* Round 1 losers → all 0 (score 0 points)
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* Missed playoffs → all 0
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*
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* Elo ratings and seed probabilities are hardcoded below (March 2026 data).
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* Source: Basketball-Reference Playoff Probabilities + Neil Paine Substack estimates.
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* Update at the start of each season.
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* Elo ratings are hardcoded below (March 2026 data).
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* Source: Neil Paine Substack playoff Elo estimates (last 110 games, no regression,
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* postseason games 3× weight). Update at the start of each season.
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*/
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import { database } from "~/database/context";
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@ -45,6 +52,7 @@ import { eq } 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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import { normalizeTeamName } from "~/lib/normalize-team-name";
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import { getRegularSeasonStandings } from "~/models/regular-season-standings";
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// ─── Simulation parameters ────────────────────────────────────────────────────
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@ -56,158 +64,59 @@ const NUM_SIMULATIONS = 50_000;
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*/
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const PARITY_FACTOR = 400;
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/** Seed probability keys — ordered p_1..p_10 for the drawSeed() inner loop. */
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const SEED_KEYS = ["p_1", "p_2", "p_3", "p_4", "p_5", "p_6", "p_7", "p_8", "p_9", "p_10"] as const;
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/** NBA regular season games per team. */
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const NBA_REGULAR_SEASON_GAMES = 82;
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// ─── Team data (2025-26 season, as of March 6, 2026) ─────────────────────────
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// ─── Team data (2025-26 season, as of March 2026) ─────────────────────────────
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//
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// elo: Estimated Elo rating (higher = stronger).
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// p_1 through p_10: Probability of finishing at each conference seed.
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// Sum of all p_X for a team = probability of making the playoffs.
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// Teams with no p_X entries always miss the playoffs in simulation.
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// elo: Estimated Elo rating (higher = stronger).
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// Source: Playoff rating (last 110 games, no regression to mean, postseason games 3× weight).
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// This is the appropriate signal for simulating both regular season win probability
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// (vs. average opponent) and playoff matchups.
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//
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// Sources:
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// - Elo: Playoff rating (last 110 games, no regression to mean, postseason games 3× weight).
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// This is the appropriate signal for simulating playoff matchups.
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// - Seed probs: Basketball-Reference Playoff Probabilities Report (March 16, 2026).
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//
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// Seed probability methodology:
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// BBRef reports conditional seed probabilities (summing to ~100% per team).
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// We scale each team's values by their Playoffs% to get unconditional probabilities.
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// The drawSeed() function then treats the remainder (1 - sum) as "miss playoffs".
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// Formula: p_X = (BBRef_conditional_X / 100) × (Playoffs% / 100)
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// conference: Used as a fallback when the standings table has no conference data.
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interface NbaTeamData {
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conference: "Eastern" | "Western";
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elo: number;
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p_1?: number;
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p_2?: number;
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p_3?: number;
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p_4?: number;
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p_5?: number;
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p_6?: number;
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p_7?: number;
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p_8?: number;
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p_9?: number;
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p_10?: number;
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}
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const TEAMS_DATA: Record<string, NbaTeamData> = {
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// ── Eastern Conference ──────────────────────────────────────────────────────
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// Elo = playoff rating (last 110 games, no regression, postseason games 3× weight)
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// Seed probs = BBRef conditional × (Playoffs% / 100)
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// Detroit (PO%=100%): locked as 1-seed
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"Detroit Pistons": { conference: "Eastern", elo: 1558,
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p_1: 0.982, p_2: 0.016, p_3: 0.001 },
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// Boston (PO%=100%): clear 2/3 seed
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"Boston Celtics": { conference: "Eastern", elo: 1699,
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p_1: 0.014, p_2: 0.540, p_3: 0.389, p_4: 0.052, p_5: 0.004 },
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// New York (PO%=100%)
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"New York Knicks": { conference: "Eastern", elo: 1626,
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p_1: 0.003, p_2: 0.423, p_3: 0.479, p_4: 0.086, p_5: 0.009, p_6: 0.001 },
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// Cleveland (PO%=99.9%): mostly 4-seed, slight play-in risk
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"Cleveland Cavaliers": { conference: "Eastern", elo: 1628,
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p_2: 0.020, p_3: 0.117, p_4: 0.684, p_5: 0.137, p_6: 0.032, p_7: 0.009, p_8: 0.001 },
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// Orlando (PO%=88.8%): 5/6-seed range, play-in risk
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"Orlando Magic": { conference: "Eastern", elo: 1508,
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p_3: 0.007, p_4: 0.075, p_5: 0.333, p_6: 0.182, p_7: 0.139, p_8: 0.091, p_9: 0.044, p_10: 0.018 },
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// Miami (PO%=78.7%)
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"Miami Heat": { conference: "Eastern", elo: 1530,
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p_3: 0.004, p_4: 0.041, p_5: 0.212, p_6: 0.224, p_7: 0.255, p_8: 0.113, p_9: 0.037, p_10: 0.009 },
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// Toronto (PO%=86.4%)
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"Toronto Raptors": { conference: "Eastern", elo: 1467,
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p_3: 0.001, p_4: 0.038, p_5: 0.165, p_6: 0.324, p_7: 0.192, p_8: 0.103, p_9: 0.041, p_10: 0.011 },
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// Atlanta (PO%=46.7%): mostly play-in range
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"Atlanta Hawks": { conference: "Eastern", elo: 1496,
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p_4: 0.001, p_5: 0.011, p_6: 0.022, p_7: 0.058, p_8: 0.124, p_9: 0.134, p_10: 0.123 },
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// Philadelphia (PO%=52.9%)
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"Philadelphia 76ers": { conference: "Eastern", elo: 1471,
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p_5: 0.011, p_6: 0.039, p_7: 0.079, p_8: 0.116, p_9: 0.134, p_10: 0.091 },
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// Charlotte (PO%=47.1%): deep play-in territory
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"Charlotte Hornets": { conference: "Eastern", elo: 1496,
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p_5: 0.002, p_6: 0.004, p_7: 0.017, p_8: 0.058, p_9: 0.118, p_10: 0.201 },
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// Milwaukee (PO%=0%)
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"Milwaukee Bucks": { conference: "Eastern", elo: 1442 },
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// Chicago (PO%=0%)
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"Chicago Bulls": { conference: "Eastern", elo: 1381 },
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// Brooklyn (PO%=0%)
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"Brooklyn Nets": { conference: "Eastern", elo: 1334 },
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// Indiana (PO%=0%)
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"Indiana Pacers": { conference: "Eastern", elo: 1433 },
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// Washington (PO%=0%)
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"Washington Wizards": { conference: "Eastern", elo: 1255 },
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"Detroit Pistons": { conference: "Eastern", elo: 1558 },
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"Boston Celtics": { conference: "Eastern", elo: 1699 },
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"New York Knicks": { conference: "Eastern", elo: 1626 },
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"Cleveland Cavaliers": { conference: "Eastern", elo: 1628 },
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"Orlando Magic": { conference: "Eastern", elo: 1508 },
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"Miami Heat": { conference: "Eastern", elo: 1530 },
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"Toronto Raptors": { conference: "Eastern", elo: 1467 },
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"Atlanta Hawks": { conference: "Eastern", elo: 1496 },
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"Philadelphia 76ers": { conference: "Eastern", elo: 1471 },
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"Charlotte Hornets": { conference: "Eastern", elo: 1496 },
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"Milwaukee Bucks": { conference: "Eastern", elo: 1442 },
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"Chicago Bulls": { conference: "Eastern", elo: 1381 },
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"Brooklyn Nets": { conference: "Eastern", elo: 1334 },
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"Indiana Pacers": { conference: "Eastern", elo: 1433 },
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"Washington Wizards": { conference: "Eastern", elo: 1255 },
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// ── Western Conference ──────────────────────────────────────────────────────
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// OKC (PO%=100%): dominant 1-seed
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"Oklahoma City Thunder": { conference: "Western", elo: 1731,
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p_1: 0.920, p_2: 0.081 },
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// San Antonio (PO%=100%): locked as 2-seed
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"San Antonio Spurs": { conference: "Western", elo: 1599,
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p_1: 0.081, p_2: 0.919 },
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// Houston (PO%=99.8%): 3/4 seed range
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"Houston Rockets": { conference: "Western", elo: 1564,
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p_3: 0.467, p_4: 0.258, p_5: 0.169, p_6: 0.092, p_7: 0.014, p_8: 0.001 },
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// Denver (PO%=99.8%)
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"Denver Nuggets": { conference: "Western", elo: 1618,
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p_3: 0.222, p_4: 0.270, p_5: 0.277, p_6: 0.181, p_7: 0.043, p_8: 0.001 },
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// LA Lakers (PO%=99.7%)
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"Los Angeles Lakers": { conference: "Western", elo: 1569,
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p_3: 0.219, p_4: 0.267, p_5: 0.242, p_6: 0.172, p_7: 0.079, p_8: 0.003 },
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// Minnesota (PO%=96.2%)
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"Minnesota Timberwolves": { conference: "Western", elo: 1603,
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p_3: 0.072, p_4: 0.154, p_5: 0.222, p_6: 0.340, p_7: 0.173, p_8: 0.007 },
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// Phoenix (PO%=83.4%): mostly 7-seed play-in entry
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"Phoenix Suns": { conference: "Western", elo: 1500,
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p_3: 0.011, p_4: 0.032, p_5: 0.065, p_6: 0.165, p_7: 0.517, p_8: 0.051, p_9: 0.005 },
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// LA Clippers (PO%=71.1%): heavy play-in range
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"LA Clippers": { conference: "Western", elo: 1573,
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p_6: 0.042, p_7: 0.468, p_8: 0.112, p_9: 0.027 },
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// Golden State (PO%=30.3%): longshot play-in
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"Golden State Warriors": { conference: "Western", elo: 1530,
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p_6: 0.003, p_7: 0.053, p_8: 0.160, p_9: 0.147 },
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// Portland (PO%=19.5%): deep longshot
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"Portland Trail Blazers": { conference: "Western", elo: 1426,
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p_7: 0.013, p_8: 0.077, p_9: 0.111 },
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// Dallas (PO%=0%)
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"Dallas Mavericks": { conference: "Western", elo: 1473 },
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// Memphis (PO%=0%)
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"Memphis Grizzlies": { conference: "Western", elo: 1417 },
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// New Orleans (PO%=0%)
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"New Orleans Pelicans": { conference: "Western", elo: 1380 },
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// Sacramento (PO%=0%)
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"Sacramento Kings": { conference: "Western", elo: 1352 },
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// Utah (PO%=0%)
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"Utah Jazz": { conference: "Western", elo: 1334 },
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"Oklahoma City Thunder": { conference: "Western", elo: 1731 },
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"San Antonio Spurs": { conference: "Western", elo: 1599 },
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"Houston Rockets": { conference: "Western", elo: 1564 },
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"Denver Nuggets": { conference: "Western", elo: 1618 },
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"LA Lakers": { conference: "Western", elo: 1569 },
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"Minnesota Timberwolves":{ conference: "Western", elo: 1603 },
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"Phoenix Suns": { conference: "Western", elo: 1500 },
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"LA Clippers": { conference: "Western", elo: 1573 },
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"Golden State Warriors": { conference: "Western", elo: 1530 },
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"Portland Trail Blazers":{ conference: "Western", elo: 1426 },
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"Dallas Mavericks": { conference: "Western", elo: 1473 },
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"Memphis Grizzlies": { conference: "Western", elo: 1417 },
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"New Orleans Pelicans": { conference: "Western", elo: 1380 },
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"Sacramento Kings": { conference: "Western", elo: 1352 },
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"Utah Jazz": { conference: "Western", elo: 1334 },
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};
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// ─── Public helpers (exported for unit testing) ───────────────────────────────
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@ -238,6 +147,13 @@ interface TeamEntry {
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id: string;
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name: string;
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data: NbaTeamData | undefined;
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conference: "Eastern" | "Western";
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/** Actual wins from the standings table (0 if no standings loaded). */
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currentWins: number;
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/** Remaining regular season games = 82 - gamesPlayed (0 if season is complete). */
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remainingGames: number;
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/** Elo win probability vs. average opponent (1500) — constant per team. */
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winProb: number;
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}
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/** Get Elo for a team entry.
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@ -246,17 +162,31 @@ function elo(entry: TeamEntry): number {
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return entry.data?.elo ?? 1400;
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}
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/** Simulate remaining regular season games for a team.
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* Uses the pre-computed per-team winProb (Elo vs. average opponent).
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* Returns projected total wins for the season. */
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function simulateProjectedWins(entry: TeamEntry): number {
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let extra = 0;
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for (let g = 0; g < entry.remainingGames; g++) {
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if (Math.random() < entry.winProb) extra++;
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}
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return entry.currentWins + extra;
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}
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// ─── Simulator ────────────────────────────────────────────────────────────────
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export class NBASimulator implements Simulator {
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async simulate(sportsSeasonId: string): Promise<SimulationResult[]> {
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const db = database();
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// 1. Load all participants for this sports season.
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const participantRows = 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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// 1. Load participants and standings in parallel.
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const [participantRows, standings] = await Promise.all([
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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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getRegularSeasonStandings(sportsSeasonId),
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]);
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if (participantRows.length === 0) {
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throw new Error(
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@ -265,19 +195,35 @@ export class NBASimulator implements Simulator {
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);
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}
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// 2. Match participant names to hardcoded team data.
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// Teams with no match or no seed probabilities will always miss the playoffs.
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// 2. Build standings lookup and construct team entries.
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// Conference, currentWins, remainingGames, and per-game winProb are all
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// resolved once here so nothing is recomputed inside the hot loop.
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const standingsMap = new Map(standings.map((s) => [s.participantId, s]));
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const participantIds = participantRows.map((r) => r.id);
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const teams: TeamEntry[] = participantRows.map((r) => ({
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id: r.id,
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name: r.name,
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data: getTeamData(r.name),
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}));
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const teams: TeamEntry[] = participantRows.map((r) => {
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const standing = standingsMap.get(r.id);
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const data = getTeamData(r.name);
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const gamesPlayed = standing?.gamesPlayed ?? 0;
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const conf = standing?.conference;
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const conference: "Eastern" | "Western" =
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conf === "Eastern" || conf === "Western"
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? conf
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: (data?.conference ?? "Eastern");
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return {
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id: r.id,
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name: r.name,
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data,
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conference,
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currentWins: standing?.wins ?? 0,
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remainingGames: Math.max(0, NBA_REGULAR_SEASON_GAMES - gamesPlayed),
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winProb: eloWinProbability(data?.elo ?? 1400, 1500),
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};
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});
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// Separate by conference for simulation (fall back to Eastern if no data found).
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const easternTeams = teams.filter((t) => (t.data?.conference ?? "Eastern") === "Eastern");
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const westernTeams = teams.filter((t) => t.data?.conference === "Western");
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// 3. Separate by conference for simulation.
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const easternTeams = teams.filter((t) => t.conference === "Eastern");
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const westernTeams = teams.filter((t) => t.conference === "Western");
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// Validate: each conference needs at least 10 teams to fill the bracket + play-in.
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if (easternTeams.length < 10 || westernTeams.length < 10) {
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@ -289,20 +235,6 @@ export class NBASimulator implements Simulator {
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// ─── Helpers (defined once, outside the hot loop) ─────────────────────────
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||||
|
||||
/** Draw a conference seed (1–10) based on a team's probability distribution.
|
||||
* Returns 11 if the draw falls outside all p_X values (team misses playoffs). */
|
||||
const drawSeed = (entry: TeamEntry): number => {
|
||||
const data = entry.data;
|
||||
if (!data) return 11; // Unknown team — always misses playoffs
|
||||
let r = Math.random();
|
||||
for (let i = 0; i < SEED_KEYS.length; i++) {
|
||||
const prob = data[SEED_KEYS[i]] ?? 0;
|
||||
r -= prob;
|
||||
if (r <= 0) return i + 1;
|
||||
}
|
||||
return 11; // Missed playoffs
|
||||
};
|
||||
|
||||
/** Simulate a single playoff game. Returns the winner. */
|
||||
const simGame = (a: TeamEntry, b: TeamEntry): TeamEntry =>
|
||||
Math.random() < eloWinProbability(elo(a), elo(b)) ? a : b;
|
||||
|
|
@ -332,17 +264,18 @@ export class NBASimulator implements Simulator {
|
|||
};
|
||||
|
||||
/** Build an 8-team conference bracket [s1..s8] for one simulation iteration.
|
||||
* Seeds are drawn probabilistically; positions 7–10 go through the Play-In. */
|
||||
* Seeds are determined by simulated projected wins; positions 7–10 go through the Play-In. */
|
||||
const buildConferenceBracket = (confTeams: TeamEntry[]): TeamEntry[] => {
|
||||
const seeded = confTeams.map((t) => ({
|
||||
const projected = confTeams.map((t) => ({
|
||||
team: t,
|
||||
seed: drawSeed(t),
|
||||
projectedWins: simulateProjectedWins(t),
|
||||
tiebreaker: Math.random(),
|
||||
}));
|
||||
seeded.sort((a, b) => a.seed - b.seed || a.tiebreaker - b.tiebreaker);
|
||||
// Higher projected wins = better seed (sort descending; random tiebreaker for ties).
|
||||
projected.sort((a, b) => b.projectedWins - a.projectedWins || b.tiebreaker - a.tiebreaker);
|
||||
|
||||
const top6 = seeded.slice(0, 6).map((x) => x.team);
|
||||
const playIn = seeded.slice(6, 10).map((x) => x.team) as
|
||||
const top6 = projected.slice(0, 6).map((x) => x.team);
|
||||
const playIn = projected.slice(6, 10).map((x) => x.team) as
|
||||
[TeamEntry, TeamEntry, TeamEntry, TeamEntry];
|
||||
const [seed7, seed8] = simPlayIn(playIn);
|
||||
return [...top6, seed7, seed8];
|
||||
|
|
@ -363,13 +296,13 @@ export class NBASimulator implements Simulator {
|
|||
return { winners: [m1.winner, m2.winner], losers: [m1.loser, m2.loser] };
|
||||
};
|
||||
|
||||
// 3. Integer placement count maps — initialized to 0 for all participants.
|
||||
// 4. Integer placement count maps — initialized to 0 for all participants.
|
||||
const championCounts = new Map<string, number>(participantIds.map((id) => [id, 0]));
|
||||
const finalistCounts = new Map<string, number>(participantIds.map((id) => [id, 0]));
|
||||
const confFinalLoserCounts = new Map<string, number>(participantIds.map((id) => [id, 0]));
|
||||
const confSemiLoserCounts = new Map<string, number>(participantIds.map((id) => [id, 0]));
|
||||
|
||||
// 4. Monte Carlo simulation loop.
|
||||
// 5. Monte Carlo simulation loop.
|
||||
for (let s = 0; s < NUM_SIMULATIONS; s++) {
|
||||
// ── Build brackets ───────────────────────────────────────────────────────
|
||||
const eastBracket = buildConferenceBracket(easternTeams);
|
||||
|
|
@ -384,9 +317,9 @@ export class NBASimulator implements Simulator {
|
|||
|
||||
const { winner: champion, loser: finalist } = simSeries(eastChamp, westChamp);
|
||||
|
||||
// ── Record counts (maps are pre-populated so .get() is always defined) ───
|
||||
championCounts.set(champion.id, (championCounts.get(champion.id) ?? 0) + 1);
|
||||
finalistCounts.set(finalist.id, (finalistCounts.get(finalist.id) ?? 0) + 1);
|
||||
// ── Record counts (maps are pre-populated so .get() always returns a number) ───
|
||||
championCounts.set(champion.id, (championCounts.get(champion.id) ?? 0) + 1);
|
||||
finalistCounts.set(finalist.id, (finalistCounts.get(finalist.id) ?? 0) + 1);
|
||||
confFinalLoserCounts.set(eastCFLoser.id, (confFinalLoserCounts.get(eastCFLoser.id) ?? 0) + 1);
|
||||
confFinalLoserCounts.set(westCFLoser.id, (confFinalLoserCounts.get(westCFLoser.id) ?? 0) + 1);
|
||||
for (const loser of [...eastR2Losers, ...westR2Losers]) {
|
||||
|
|
@ -395,12 +328,11 @@ export class NBASimulator implements Simulator {
|
|||
// Round 1 losers are not counted (0 points per scoring rules).
|
||||
}
|
||||
|
||||
// 5. Convert integer counts to probability distributions.
|
||||
// 6. Convert integer counts to probability distributions.
|
||||
// Exact denominators guarantee column sums of 1.0 by construction:
|
||||
// probFirst/Second → N total (1 per sim)
|
||||
// probThird/Fourth → confFinalLoserCounts / (2*N) — 2 conf final losers per sim
|
||||
// probFifth–Eighth → confSemiLoserCounts / (4*N) — 4 conf semi losers per sim
|
||||
const N = NUM_SIMULATIONS;
|
||||
// probFirst/Second → NUM_SIMULATIONS total (1 per sim)
|
||||
// probThird/Fourth → confFinalLoserCounts / (2*N) — 2 conf final losers per sim
|
||||
// probFifth–Eighth → confSemiLoserCounts / (4*N) — 4 conf semi losers per sim
|
||||
const results: SimulationResult[] = participantIds.map((participantId) => {
|
||||
const c = championCounts.get(participantId) ?? 0;
|
||||
const f = finalistCounts.get(participantId) ?? 0;
|
||||
|
|
@ -409,21 +341,21 @@ export class NBASimulator implements Simulator {
|
|||
return {
|
||||
participantId,
|
||||
probabilities: {
|
||||
probFirst: c / N,
|
||||
probSecond: f / N,
|
||||
probThird: cf / (2 * N),
|
||||
probFourth: cf / (2 * N),
|
||||
probFifth: cs / (4 * N),
|
||||
probSixth: cs / (4 * N),
|
||||
probSeventh: cs / (4 * N),
|
||||
probEighth: cs / (4 * N),
|
||||
probFirst: c / NUM_SIMULATIONS,
|
||||
probSecond: f / NUM_SIMULATIONS,
|
||||
probThird: cf / (2 * NUM_SIMULATIONS),
|
||||
probFourth: cf / (2 * NUM_SIMULATIONS),
|
||||
probFifth: cs / (4 * NUM_SIMULATIONS),
|
||||
probSixth: cs / (4 * NUM_SIMULATIONS),
|
||||
probSeventh: cs / (4 * NUM_SIMULATIONS),
|
||||
probEighth: cs / (4 * NUM_SIMULATIONS),
|
||||
},
|
||||
source: "nba_bracket_monte_carlo",
|
||||
};
|
||||
});
|
||||
|
||||
// 6. Per-position normalization — belt-and-suspenders guard against floating-point
|
||||
// division residuals. Columns are already near-exactly 1.0 after step 5.
|
||||
// 7. Per-position normalization — belt-and-suspenders guard against floating-point
|
||||
// division residuals. Columns are already near-exactly 1.0 after step 6.
|
||||
const positionKeys: Array<keyof (typeof results)[0]["probabilities"]> = [
|
||||
"probFirst", "probSecond", "probThird", "probFourth",
|
||||
"probFifth", "probSixth", "probSeventh", "probEighth",
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue