课程作业：基于Python实现疯狂三月蒙特卡洛赛事预测模型问询

Hey Cole, great call going with Python for your March Madness bracket model—it’s way more scalable and customizable than Excel for this kind of simulation. Let’s turn your rough idea into working code, step by step.

Step 1: Store Your Team Data #

First, you’ll need to organize each team’s key stats: average field goal attempts per game (x) and field goal percentage (y). A Python dictionary is ideal here because it lets you quickly look up teams by name:

# Example team data: Team Name -> (Average Attempts, Shooting Percentage)
teams = {
    "Duke Blue Devils": (65, 0.47),
    "UNC Tar Heels": (62, 0.45),
    "Kansas Jayhawks": (68, 0.46),
    "Villanova Wildcats": (63, 0.48),
    # Add all the teams in your bracket here!
}

Step 2: Write a Function to Simulate a Team’s Score #

Your core idea is spot-on: generate x random numbers, count how many are ≤ the shooting percentage (since a number > y means a miss). Let’s wrap this in a reusable function:

import random

def calculate_team_score(attempts, shooting_pct):
    made_shots = 0
    for _ in range(attempts):
        # Generate a random number between 0 and 1
        shot_outcome = random.random()
        # If the number is <= shooting percentage, the shot goes in
        if shot_outcome <= shooting_pct:
            made_shots += 1
    # Assume all made shots are 2-pointers for simplicity (we can expand this later!)
    return made_shots * 2

Step 3: Simulate a Single Game #

Now, let’s pit two teams against each other by calculating their simulated scores and comparing them:

def simulate_single_game(team_a, team_b):
    # Pull stats from our teams dictionary
    a_attempts, a_pct = teams[team_a]
    b_attempts, b_pct = teams[team_b]
    
    # Calculate each team's score
    a_score = calculate_team_score(a_attempts, a_pct)
    b_score = calculate_team_score(b_attempts, b_pct)
    
    # Determine the winner
    if a_score > b_score:
        return f"{team_a} wins! Final Score: {a_score} - {b_score}"
    elif b_score > a_score:
        return f"{team_b} wins! Final Score: {b_score} - {a_score}"
    else:
        return f"OT Bound! Tie Score: {a_score} - {b_score}"

# Test it out!
print(simulate_single_game("Duke Blue Devils", "UNC Tar Heels"))

Step 4: Run Multiple Simulations for Better Accuracy #

A single simulation is just luck—run 1000+ simulations to get a realistic win probability for each team:

def simulate_multiple_games(team_a, team_b, num_simulations=1000):
    a_wins = 0
    b_wins = 0
    ties = 0
    
    for _ in range(num_simulations):
        a_attempts, a_pct = teams[team_a]
        b_attempts, b_pct = teams[team_b]
        
        a_score = calculate_team_score(a_attempts, a_pct)
        b_score = calculate_team_score(b_attempts, b_pct)
        
        if a_score > b_score:
            a_wins += 1
        elif b_score > a_score:
            b_wins += 1
        else:
            ties += 1
    
    # Calculate percentages
    a_win_pct = (a_wins / num_simulations) * 100
    b_win_pct = (b_wins / num_simulations) * 100
    tie_pct = (ties / num_simulations) * 100
    
    # Print results
    print(f"After {num_simulations} simulations:")
    print(f"{team_a} wins {a_win_pct:.1f}% of the time")
    print(f"{team_b} wins {b_win_pct:.1f}% of the time")
    print(f"Ties happen {tie_pct:.1f}% of the time")

# Try it with 5000 simulations for more precision
simulate_multiple_games("Kansas Jayhawks", "Villanova Wildcats", 5000)

Optional Enhancements (For When You’re Comfortable) #

Once you’ve got the basics down, you can make your model more realistic:

• Add 3-Pointers: Split attempts into 2-point and 3-point, with separate shooting percentages for each.
• Free Throws: Factor in free throw attempts and percentage (you can tie this to fouls, or use average free throw attempts per game).
• Use Pandas for Data: If you have a CSV of all team stats, use pandas to load and manage the data instead of a dictionary—way easier for large datasets.
• Bracket Simulation: Write a function to run through an entire bracket, simulating each round until you have a champion.

内容的提问来源于stack exchange，提问作者Cole Ragone