1. What is the Elo Probability Formula?

The Elo rating system is a method for calculating the relative skill levels of players in competitor-versus-competitor games like chess. The probability formula predicts the expected outcome between two players based on their Elo ratings.

2. How Does the Calculator Work?

The calculator uses the Elo probability formula:

Where:

• \( P \) — Probability of winning (0 to 1)
• \( R \) — Your Elo rating
• \( R_{opp} \) — Opponent's Elo rating

Explanation: The formula calculates the expected score 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 Elo Probability

Details: Understanding probability helps players assess their chances against opponents, set realistic expectations, and track rating changes after games.

4. Using the Calculator

Tips: Enter both players' Elo ratings. The calculator will show your probability of winning as a percentage. Higher differences in ratings result in more extreme probabilities.

5. Frequently Asked Questions (FAQ)

Q1: What does a 50% probability mean?
A: When both players have equal ratings (difference = 0), each has exactly 50% chance to win.

Q2: How accurate is this prediction?
A: It represents long-term statistical expectation - actual game outcomes may vary due to many factors.

Q3: Why is 400 used in the formula?
A: This is the Elo system's scaling factor - a 400-point difference means 10:1 expected score ratio.

Q4: Does this work for other games?
A: Yes, the Elo system is used in many competitive games, though some may use different scaling factors.

Q5: How are rating changes calculated after a game?
A: The actual score (1 for win, 0.5 for draw, 0 for loss) is compared to the expected score (P) to determine rating adjustments.