1. What is the Elo Rating System?

The Elo rating system is a method for calculating the relative skill levels of players in competitor-versus-competitor games. It was originally developed for chess but is now used in many other games and sports.

2. How Does the Calculator Work?

The calculator uses the Elo win probability formula:

Where:

• \( P \) — Probability that Player A wins (0-1)
• \( E_a \) — Elo rating of Player A
• \( E_b \) — Elo rating of Player B

Explanation: The formula calculates the expected outcome between two players based on their rating difference. A 400-point difference means the higher-rated player is 10 times more likely to win.

3. Importance of Win Probability

Details: Understanding win probabilities helps in matchmaking, tournament predictions, and analyzing player performance. It's also used for calculating rating changes after games.

4. Using the Calculator

Tips: Enter both players' Elo ratings. The calculator will show the probability that Player A wins and Player B wins. Ratings must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What does a 400-point rating difference mean?
A: A 400-point difference means the higher-rated player is expected to win about 90.9% of the time (10:1 odds).

Q2: What's considered a significant rating difference?
A: Differences of 200+ points are significant (about 75% win probability). Differences under 100 points are relatively small (about 64% win probability).

Q3: How are rating changes calculated after a game?
A: The winner gains points equal to K×(1 - expected win probability), while the loser loses the same amount (K is typically 16-32 for established players).

Q4: Does this work for team games?
A: Yes, the same formula can be used by averaging team ratings, though some variations use different formulas for team calculations.

Q5: What's the origin of the 400 constant?
A: The 400 value determines how quickly win probability changes with rating difference. It was chosen to provide meaningful rating scales in chess.