问估计一场足球比赛中每一场比赛的平均持续时间，给出主队和客场队的隐含进球。

EN

from dataclasses import dataclass
import random
from statistics import mean

from numpy import cumsum

MATCH_LENGTH = 95
TRIALS = 100_000

@dataclass
class MatchGameState:
    """
    Represents for how many minutes of a particular game:
      - home team was ahead
      - teams were drawing
      - away team was ahead
    """
    home_ahead: int
    draw: int
    away_ahead: int
    
MatchGameStates = list[MatchGameState]

def mean_game_state(home_implied_goals: float, 
                    away_implied_goals: float, 
                    match_length: int=MATCH_LENGTH, 
                    trials: int=TRIALS) -> tuple[float, float, float]:
    """
    Given match length in minutes and implied goals for home and away teams, 
    calculates for how many minutes per match in average home team will be ahead,
    there will be a draw and away team will be ahead.
    """
    random.seed()
    sims = [single_match_game_state(home_implied_goals, away_implied_goals, match_length) for _ in range(trials)]
    home_ahead_mean = round(mean(s.home_ahead for s in sims), 2)
    draw_mean = round(mean(s.draw for s in sims), 2)
    away_ahead_mean = round(mean(s.away_ahead for s in sims), 2)
    return home_ahead_mean, draw_mean, away_ahead_mean

def single_match_game_state(home_implied_goals: float, 
                            away_implied_goals: float, 
                            match_length: int=95) -> MatchGameState:
    """
    Given match length in minutes and implied goals for home and away teams,
    simulates teams scoring minute by minute for a particular game.
    Returns MatchGameState for the game.
    """
    # Probability to score in a given minute
    home_goals_per_min = home_implied_goals / match_length
    away_goals_per_min = away_implied_goals / match_length
    # For every minute in a game, 1 if a team scored in that minute, 0 otherwise
    home_outcomes = [random.random() for _ in range(match_length)]
    away_outcomes = [random.random() for _ in range(match_length)]
    home_goals_by_minute = [int(home_outcome < home_goals_per_min) for home_outcome in home_outcomes]
    away_goals_by_minute = [int(away_outcome < away_goals_per_min) for away_outcome in away_outcomes]
    # How many goals a team scored by a particular minute of the game
    home_cumulative_goals = cumsum(home_goals_by_minute)
    away_cumulative_goals = cumsum(away_goals_by_minute)
    home_ahead, draw, away_ahead = 0, 0, 0
    for home_cumulative_score, away_cumulative_score in zip(home_cumulative_goals, away_cumulative_goals):
        if home_cumulative_score > away_cumulative_score:
            home_ahead += 1
        elif home_cumulative_score == away_cumulative_score:
            draw += 1
        else:
            away_ahead += 1
    assert home_ahead + draw + away_ahead == match_length 
    return MatchGameState(home_ahead, draw, away_ahead)

if __name__ == '__main__':
    print(mean_game_state(2.15, 1.20))