Elo Rating System Calculator

Elo Rating System Calculator

The Elo rating system is a method for calculating the relative skill levels of players in competitor-versus-competitor games such as chess. It was invented by Arpad Elo, a Hungarian-American physics professor. This calculator helps you determine the new ratings for two players after a match, based on their current ratings and a K-factor.

(Common K-factors: 10 for highly experienced players, 20 for intermediate, 40 for new/junior players)

Player A Wins Player B Wins Draw

Calculation Results:

Enter the details above and click "Calculate New Ratings" to see the results.

Understanding the Elo Rating System

The Elo rating system is a zero-sum system, meaning that when one player gains points, another loses an equivalent amount. It's designed to predict the outcome of a match: a higher-rated player is expected to win against a lower-rated player. The magnitude of the rating change depends on the difference in ratings between the two players and the K-factor.

How it Works:

  1. Expected Score (E): This is the probability of a player winning the match. It's calculated based on the rating difference between the two players. If two players have the same rating, each has an expected score of 0.5 (50% chance of winning).
  2. Actual Score (S): This is 1 for a win, 0 for a loss, and 0.5 for a draw.
  3. K-Factor: This constant determines the maximum possible adjustment per game. A higher K-factor means ratings will change more dramatically after each game, making the system more responsive to recent performance but also more volatile. Lower K-factors lead to slower, more stable rating changes.
  4. New Rating (R'): The new rating is calculated using the formula: R' = R + K * (S - E). This means if a player performs better than expected (S > E), their rating increases. If they perform worse than expected (S < E), their rating decreases.

Example Scenario:

Let's say Player A has a rating of 1600 and Player B has a rating of 1400. The K-factor is 32.

  • If Player A wins: Player A, being the higher-rated player, was expected to win. Their rating will increase, but by a smaller amount than if they had beaten a much higher-rated opponent. Player B's rating will decrease.
  • If Player B wins: Player B, being the lower-rated player, pulled off an upset. Their rating will increase significantly, while Player A's rating will decrease significantly.
  • If it's a Draw: Player A, the higher-rated player, was expected to win. A draw would be considered an underperformance for Player A, so their rating might slightly decrease. For Player B, a draw against a higher-rated opponent is an overperformance, so their rating might slightly increase.

This calculator automates these calculations, providing immediate insights into how ratings shift after a match.

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Match Details:

'; resultHtml += 'Player A Current Rating: ' + playerARating.toFixed(0) + "; resultHtml += 'Player B Current Rating: ' + playerBRating.toFixed(0) + "; resultHtml += 'K-Factor: ' + kFactor.toFixed(0) + "; resultHtml += 'Match Result: ' + (matchResult === 'A_wins' ? 'Player A Wins' : (matchResult === 'B_wins' ? 'Player B Wins' : 'Draw')) + "; resultHtml += '

Expected Scores:

'; resultHtml += 'Player A Expected Score: ' + Ea.toFixed(3) + "; resultHtml += 'Player B Expected Score: ' + Eb.toFixed(3) + "; resultHtml += '

New Ratings:

'; resultHtml += 'Player A New Rating: ' + newPlayerARating.toFixed(0) + ' (Change: ' + (ratingChangeA > 0 ? '+' : ") + ratingChangeA.toFixed(1) + ')'; resultHtml += 'Player B New Rating: ' + newPlayerBRating.toFixed(0) + ' (Change: ' + (ratingChangeB > 0 ? '+' : ") + ratingChangeB.toFixed(1) + ')'; document.getElementById('eloResult').innerHTML = resultHtml; }

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