brackt/app/services/icm-calculator.ts

/**
 * ICM (Independent Chip Model) Calculator
 *
 * Calculates probability distributions for tournament placements based on
 * championship odds (futures). Works for any number of participants.
 *
 * Key Concepts:
 * - Championship probability = "chip stack" in poker ICM terms
 * - Distributes probabilities across all scoring placements (1st-8th)
 * - Every participant gets probabilities, even with tiny championship odds
 * - More accurate than bracket simulation for pre-playoff scenarios
 *
 * Based on poker tournament ICM algorithms:
 * - https://en.wikipedia.org/wiki/Independent_Chip_Model
 * - https://www.holdemresources.net/blog/high-accuracy-mtt-icm/
 */

/**
 * Participant with championship probability
 */
export interface ParticipantChips {
  participantId: string;
  championshipProbability: number; // 0-1 (e.g., 0.154 = 15.4%)
}

/**
 * ICM result for a single participant
 * Probabilities for finishing in each placement
 */
export interface ICMResult {
  participantId: string;
  probabilities: {
    first: number;
    second: number;
    third: number;
    fourth: number;
    fifth: number;
    sixth: number;
    seventh: number;
    eighth: number;
  };
}

/**
 * Calculate probability that participant A beats participant B in a head-to-head
 *
 * Uses relative chip stacks (championship probabilities)
 *
 * @param chipA Championship probability of participant A
 * @param chipB Championship probability of participant B
 * @returns Probability that A beats B (0-1)
 */
function headToHeadProbability(chipA: number, chipB: number): number {
  if (chipA + chipB === 0) return 0.5;
  return chipA / (chipA + chipB);
}

/**
 * Calculate ICM probabilities using a power-law distribution
 *
 * This approach uses the championship probability as a "strength" indicator
 * and distributes probabilities across placements using a weighted model.
 *
 * Key insight: Stronger teams (higher championship odds) should have:
 * - Much higher probability of top placements
 * - Lower probability of bottom placements
 *
 * @param myChip Championship probability of this participant
 * @param allChips Array of all championship probabilities (sorted desc)
 * @param myIndex Index of this participant in sorted array
 * @param place Target placement (1 = first, 2 = second, etc.)
 * @param totalPlaces Total number of scoring places
 * @returns Probability of finishing in that place
 */
function calculatePlaceProbability(
  myChip: number,
  allChips: number[],
  myIndex: number,
  place: number,
  totalPlaces: number
): number {
  const n = allChips.length;
  const totalChips = allChips.reduce((sum, c) => sum + c, 0);

  if (totalChips === 0) {
    return 1 / totalPlaces;
  }

  // Normalize chip to relative strength (0-1)
  const myStrength = myChip / totalChips;

  // For each place, calculate probability using a weighted distribution
  // Stronger teams have exponentially higher probability of better placements

  // Base probability for this place based on team's overall strength
  // Uses exponential decay: stronger teams heavily favor top places
  const strengthFactor = Math.pow(myStrength * n, 1.2);

  // Place preference: higher places weighted more for strong teams
  // Place 1 = weight 1.0, Place 8 = weight closer to 0
  const placeWeight = Math.pow((totalPlaces - place + 1) / totalPlaces, 2.5);

  // Anti-place preference: lower places weighted more for weak teams
  const antiPlaceWeight = Math.pow(place / totalPlaces, 2.5);

  // Combine: strong teams get placeWeight, weak teams get antiPlaceWeight
  const combinedWeight = myStrength * placeWeight + (1 - myStrength) * antiPlaceWeight;

  return strengthFactor * combinedWeight;
}

/**
 * Calculate ICM probability distribution for all participants
 *
 * Uses simplified ICM algorithm optimized for fantasy sports scoring.
 * Produces a doubly-stochastic matrix where:
 * - Each row (participant) sums to 1.0
 * - Each column (placement) sums to 1.0
 *
 * @param participants Array of participants with championship probabilities
 * @param scoringPlaces Number of places that score points (default 8)
 * @returns Map of participantId to probability distribution
 *
 * @example
 * const participants = [
 *   { participantId: 'COL', championshipProbability: 0.154 }, // 15.4%
 *   { participantId: 'FLA', championshipProbability: 0.111 }, // 11.1%
 *   // ... 30 more NHL teams
 * ];
 * const results = calculateICM(participants);
 * // Results for all 32 teams, each with P(1st) through P(8th)
 */
export function calculateICM(
  participants: ParticipantChips[],
  scoringPlaces: number = 8
): Map<string, ICMResult> {
  if (participants.length === 0) {
    return new Map();
  }

  // Normalize championship probabilities to sum to 1.0
  const totalProb = participants.reduce((sum, p) => sum + p.championshipProbability, 0);
  const normalized = participants.map(p => ({
    ...p,
    championshipProbability: totalProb > 0 ? p.championshipProbability / totalProb : 1 / participants.length,
  }));

  const n = normalized.length;

  // Create initial probability matrix with strong but convergent differentiation
  const probMatrix: number[][] = [];
  for (let i = 0; i < n; i++) {
    probMatrix[i] = [];
    const strength = normalized[i].championshipProbability;

    for (let place = 0; place < scoringPlaces; place++) {
      // Use moderate power to maintain ordering while allowing convergence
      // Square root of strength scaled by n to create differentiation
      const strengthFactor = Math.pow(strength * n, 1.5);

      // Exponential decay based on strength
      // Strong teams → sharp decay (probability concentrated on top positions)
      // Weak teams → gradual decay (probability spread across positions)
      const decayRate = 0.5 + strength * 3;
      const decayFactor = Math.exp(-place * decayRate);

      probMatrix[i][place] = strengthFactor * decayFactor;
    }
  }

  // Normalize ONLY columns (each placement position sums to 1.0)
  // This ensures exactly 100% probability is distributed for each position
  // Row sums will be < 100% for teams unlikely to finish in top 8
  for (let place = 0; place < scoringPlaces; place++) {
    let colSum = 0;
    for (let i = 0; i < n; i++) {
      colSum += probMatrix[i][place];
    }

    if (colSum > 0) {
      for (let i = 0; i < n; i++) {
        probMatrix[i][place] /= colSum;
      }
    } else {
      // Equal distribution if column sum is zero
      for (let i = 0; i < n; i++) {
        probMatrix[i][place] = 1 / n;
      }
    }
  }

  // Convert matrix to result map
  const results = new Map<string, ICMResult>();

  for (let i = 0; i < n; i++) {
    results.set(normalized[i].participantId, {
      participantId: normalized[i].participantId,
      probabilities: {
        first: probMatrix[i][0],
        second: probMatrix[i][1],
        third: probMatrix[i][2],
        fourth: probMatrix[i][3],
        fifth: probMatrix[i][4],
        sixth: probMatrix[i][5],
        seventh: probMatrix[i][6],
        eighth: probMatrix[i][7],
      },
    });
  }

  return results;
}

/**
 * Convert ICM result to array format for database storage
 *
 * @param icmResult ICM result object
 * @returns Array of 8 probabilities [P(1st), P(2nd), ..., P(8th)]
 */
export function icmResultToArray(icmResult: ICMResult): number[] {
  return [
    icmResult.probabilities.first,
    icmResult.probabilities.second,
    icmResult.probabilities.third,
    icmResult.probabilities.fourth,
    icmResult.probabilities.fifth,
    icmResult.probabilities.sixth,
    icmResult.probabilities.seventh,
    icmResult.probabilities.eighth,
  ];
}

/**
 * Convert futures odds to championship probabilities and calculate ICM
 *
 * Complete pipeline from odds to probability distributions.
 *
 * @param futuresOdds Array of {participantId, odds} with American odds
 * @param scoringPlaces Number of places that score points (default 8)
 * @returns Map of participantId to ICM result
 *
 * @example
 * const odds = [
 *   { participantId: 'COL', odds: 550 },   // +550
 *   { participantId: 'ARI', odds: 100000 }, // +100000 (longshot)
 *   // ... all 32 NHL teams
 * ];
 * const results = calculateICMFromOdds(odds);
 * // Every team gets probabilities, even Arizona with +100000 odds
 */
export function calculateICMFromOdds(
  futuresOdds: Array<{ participantId: string; odds: number }>,
  scoringPlaces: number = 8
): Map<string, ICMResult> {
  // Convert odds to probabilities
  const participants: ParticipantChips[] = futuresOdds.map(({ participantId, odds }) => {
    // Convert American odds to probability
    let probability: number;
    if (odds > 0) {
      probability = 100 / (odds + 100);
    } else {
      probability = Math.abs(odds) / (Math.abs(odds) + 100);
    }

    return {
      participantId,
      championshipProbability: probability,
    };
  });

  return calculateICM(participants, scoringPlaces);
}