I think you really should be looking at Trueskill for this task, it is better suited for multi contested events
A starter, some Python code perhaps each horse would start with its initial allotted handicap mark
import trueskill
# 1. Initialize the TrueSkill environment
# By default, mu=25, sigma=8.333, beta=4.166, tau=0.083
env = trueskill.TrueSkill(draw_probability=0.0) # Set draws to 0% since horses rarely tie
print("--- INITIAL HORSE RATINGS ---")
# 2. Define our 5 horses
# We will give them names and standard starting ratings
horses = {
"Thunderbolt": env.Rating(), # New horse
"Storm Dancer": env.Rating(), # New horse
"Silver Bullet": env.Rating(), # New horse
"Midnight Run": env.Rating(), # New horse
"Pegasus": env.Rating() # New horse
}
def display_ratings(horse_dict):
"""Helper function to print current mu, sigma, and the displayed score (mu - 3*sigma)"""
print(f"{'Horse Name':<15} | {'Mu (μ)':<10} | {'Sigma (σ)':<10} | {'Displayed Score':<15}")
print("-" * 60)
for name, rating in horse_dict.items():
# TrueSkill conservative score formula: mu - 3 * sigma
score = rating.mu - (3 * rating.sigma)
print(f"{name:<15} | {rating.mu:<10.3f} | {rating.sigma:<10.3f} | {score:<15.3f}")
print("\n")
display_ratings(horses)
# 3. Define the Race Outcome
# Let's say the final finishing positions are:
# 1st: Pegasus
# 2nd: Thunderbolt
# 3rd: Storm Dancer
# 4th: Midnight Run
# 5th: Silver Bullet
print("--- RACE FINISH POSITION ---")
print("1st: Pegasus | 2nd: Thunderbolt | 3rd: Storm Dancer | 4th: Midnight Run | 5th: Silver Bullet\n")
# TrueSkill expects groups of teams. Because it's a Free-For-All,
# each horse is placed inside its own single-element tuple.
rating_groups = [
(horses["Pegasus"],),
(horses["Thunderbolt"],),
(horses["Storm Dancer"],),
(horses["Midnight Run"],),
(horses["Silver Bullet"],)
]
# Ranks correspond to the order of the rating_groups above.
# Since we already ordered our list from 1st to 5th, the ranks are simply 0, 1, 2, 3, 4.
# (0 means 1st place, 1 means 2nd place, etc.)
ranks = [0, 1, 2, 3, 4]
# 4. Calculate the new ratings
new_rating_groups = env.rate(rating_groups, ranks=ranks)
# 5. Assign the updated ratings back to our horses
horses["Pegasus"] = new_rating_groups[0][0]
horses["Thunderbolt"] = new_rating_groups[1][0]
horses["Storm Dancer"] = new_rating_groups[2][0]
horses["Midnight Run"] = new_rating_groups[3][0]
horses["Silver Bullet"] = new_rating_groups[4][0]
print("--- UPDATED RATINGS AFTER RACE 1 ---")
display_ratings(horses)
