/**
 * Normal CDF using rational approximation (Abramowitz & Stegun).
 */
function normalCDF(x, mean = 0, stddev = 1) {
  if (stddev <= 0) return x >= mean ? 1 : 0;
  const z = (x - mean) / stddev;
  const t = 1 / (1 + 0.2316419 * Math.abs(z));
  const d = 0.3989422804014327; // 1/sqrt(2*pi)
  const p = d * Math.exp(-z * z / 2) *
    (t * (0.3193815 + t * (-0.3565638 + t * (1.781478 + t * (-1.8212560 + t * 1.3302744)))));
  return z > 0 ? 1 - p : p;
}

/**
 * Calculate model probability for a prop line using normal distribution.
 * @param {number} mean - Projected mean
 * @param {number} stddev - Standard deviation
 * @param {number} line - The prop line
 * @param {string} direction - 'over' or 'under'
 * @returns {number} Probability 0-1
 */
function calculateModelProbability(mean, stddev, line, direction) {
  if (stddev <= 0) {
    if (direction === 'over') return mean > line ? 1 : 0;
    return mean < line ? 1 : 0;
  }

  const cdf = normalCDF(line, mean, stddev);
  return direction === 'over' ? 1 - cdf : cdf;
}

/**
 * Convert American odds to implied probability.
 * @param {number} odds - American odds (e.g. -110, +150)
 * @returns {number} Implied probability 0-1
 */
function americanToImplied(odds) {
  if (odds < 0) return Math.abs(odds) / (Math.abs(odds) + 100);
  return 100 / (odds + 100);
}

/**
 * Compare model probability to book implied probability.
 *
 * EDGE IS RETIRED AS A DECISION (2026-08-01). `value_detected: edge > 0` used to
 * declare that a line had value. It cannot: measured on n=200 settled MLB rows,
 * corr(edge, outcome) = -0.010 under the incumbent ruler and -0.022 under the
 * consensus ruler, while corr(p_win, outcome) = +0.26. A quantity that does not
 * predict the outcome must not decide anything the user sees.
 *
 * `edge` is STILL COMPUTED AND RETURNED — losing the record would be worse than
 * mis-using it, and it stays in the ledger as a diagnostic. What is gone is the
 * verdict derived from it. `value_detected` is now null with an explicit reason,
 * so a caller that reads it gets an honest absence instead of a false boolean.
 *
 * @returns {object} { model_prob, book_implied, edge, value_detected, value_basis }
 */
function compareToBookImplied(modelProb, bookOdds) {
  const bookImplied = americanToImplied(bookOdds);
  const edge = modelProb - bookImplied;

  return {
    model_prob: Math.round(modelProb * 1000) / 1000,
    book_implied: Math.round(bookImplied * 1000) / 1000,
    // DIAGNOSTIC ONLY — never a ranking, gate or quality signal.
    edge: Math.round(edge * 1000) / 1000,
    value_detected: null,
    value_basis: 'retired:edge_does_not_predict',
  };
}

/**
 * Rank the rungs of an alt-line ladder by the model-vs-price gap.
 *
 * ⚠️ THIS MODULE HAS NO CALLERS (verified 2026-08-01) — it is unwired, like
 * mlbGrader.js. Left in place, made honest, not deleted.
 *
 * EDGE IS NO LONGER A VERDICT HERE. This used to `filter(e => e.value_detected)`
 * and call the survivor `optimal_line`. Both were quality claims that edge
 * cannot support (n=200 settled MLB: corr(edge, outcome) = -0.010 / -0.022).
 *
 * A HONEST NOTE ON WHY THIS ONE IS DIFFERENT. Ranking props AGAINST EACH OTHER
 * must not use edge — p_win is the measured predictor. But choosing between
 * RUNGS OF THE SAME PROP is inherently price-relative: every rung has a
 * different price, and ranking rungs by model probability alone would always
 * pick the lowest line (P(over 0.5) > P(over 2.5) by construction). So the gap
 * is kept as the ordering key here — and labelled as an UNVALIDATED price
 * diagnostic, because we have no evidence it predicts rung outcomes either.
 *
 * @returns {object|null} { ranked_lines, ranking_basis, top_by_price_gap, ... }
 */
function scanAltLines(prop, oddsData) {
  if (!prop || !oddsData || oddsData.length === 0) return null;

  const { projected_mean, projected_stddev } = prop;
  const direction = prop.direction || 'over';

  const evaluated = oddsData.map(alt => {
    const modelProb = calculateModelProbability(projected_mean, projected_stddev, alt.line, direction);
    const comparison = compareToBookImplied(modelProb, alt.odds);

    return {
      line: alt.line,
      odds: alt.odds,
      book: alt.book,
      model_probability: comparison.model_prob,
      book_implied: comparison.book_implied,
      edge: comparison.edge,
    };
  });

  if (evaluated.length === 0) return null;

  // No value FILTER: a negative gap is a real observation about a rung, not a
  // reason to hide it. The whole ladder is returned, ranked, and labelled.
  const ranked = [...evaluated].sort((a, b) => b.edge - a.edge);
  const top = ranked[0];

  return {
    ranking_basis: 'price_gap_diagnostic_unvalidated',
    top_by_price_gap: top.line,
    odds: top.odds,
    book: top.book,
    model_probability: top.model_probability,
    book_implied: top.book_implied,
    edge: top.edge,
    ranked_lines: ranked,
  };
}

module.exports = {
  scanAltLines,
  calculateModelProbability,
  compareToBookImplied,
  normalCDF,
  americanToImplied,
};