114 lines
4.0 KiB
Python
114 lines
4.0 KiB
Python
"""Poisson 分佈賽果預測模組。"""
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from __future__ import annotations
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import numpy as np
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from scipy.stats import poisson
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class PoissonMatchPredictor:
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"""基於攻守強度的雙方進球機率預測器。"""
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def __init__(
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self,
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home_attack_strength: float,
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home_defense_strength: float,
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away_attack_strength: float,
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away_defense_strength: float,
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league_avg_home_goals: float,
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) -> None:
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for value, name in [
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(home_attack_strength, 'home_attack_strength'),
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(home_defense_strength, 'home_defense_strength'),
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(away_attack_strength, 'away_attack_strength'),
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(away_defense_strength, 'away_defense_strength'),
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(league_avg_home_goals, 'league_avg_home_goals'),
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]:
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if value <= 0:
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raise ValueError(f'{name} 必須大於 0')
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self.home_attack_strength = float(home_attack_strength)
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self.home_defense_strength = float(home_defense_strength)
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self.away_attack_strength = float(away_attack_strength)
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self.away_defense_strength = float(away_defense_strength)
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self.league_avg_home_goals = float(league_avg_home_goals)
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def calculate_expected_goals(self) -> tuple[float, float]:
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"""根據攻守強度與聯盟均值估算預期進球數（λ 值）。
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使用比值校正避免極端值放大風險：
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- 主隊 λ = 聯盟主場均值 × (主攻 / 客守)
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- 客隊 λ = 聯盟客場均值 × (客攻 / 主守)
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"""
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league_avg_away_goals = self.league_avg_home_goals * 0.95
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home_lambda = self.league_avg_home_goals * (self.home_attack_strength / self.away_defense_strength)
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away_lambda = league_avg_away_goals * (self.away_attack_strength / self.home_defense_strength)
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home_lambda = max(0.01, min(home_lambda, 8.0))
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away_lambda = max(0.01, min(away_lambda, 8.0))
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return home_lambda, away_lambda
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def predict_exact_score_matrix(self, max_goals: int = 5) -> np.ndarray:
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"""輸出 0~max_goals 間所有比分組合的機率矩陣。
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回傳 shape = (max_goals+1, max_goals+1)，
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index [i,j] 代表主隊 i 球、客隊 j 球的機率。
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"""
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if max_goals < 0:
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raise ValueError('max_goals 必須大於等於 0')
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home_lambda, away_lambda = self.calculate_expected_goals()
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goals = np.arange(max_goals + 1)
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home_prob = poisson.pmf(goals, home_lambda)
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away_prob = poisson.pmf(goals, away_lambda)
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matrix = np.outer(home_prob, away_prob)
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matrix = matrix.astype(float)
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matrix /= matrix.sum() if matrix.sum() > 0 else 1.0
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return matrix
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def predict_1x2_probabilities(self) -> dict[str, float]:
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"""由波膽矩陣匯總 1x2（主勝/平/客勝）機率。"""
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matrix = self.predict_exact_score_matrix(max_goals=8)
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draw = float(np.trace(matrix))
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home_win = float(np.tril(matrix, -1).sum())
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away_win = float(np.triu(matrix, 1).sum())
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total = home_win + draw + away_win
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if total <= 0:
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return {'home_win': 0.0, 'draw': 0.0, 'away_win': 0.0}
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return {
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'home_win': home_win / total,
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'draw': draw / total,
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'away_win': away_win / total,
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}
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def predict_over_under_prob(self, line: float = 2.5, max_goals: int = 8) -> tuple[float, float]:
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"""回傳（Under 機率, Over 機率）。"""
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if line < 0:
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raise ValueError('line 必須大於等於 0')
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matrix = self.predict_exact_score_matrix(max_goals=max_goals)
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goals = np.arange(max_goals + 1)
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home, away = np.meshgrid(goals, goals)
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total = home + away
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under_mask = total <= line
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under = float(matrix[under_mask].sum())
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over = float(matrix[~under_mask].sum())
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normalizer = under + over
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if normalizer <= 0:
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return 0.0, 0.0
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return under / normalizer, over / normalizer
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