What is ELO?
ELO is a skill-based rating system used to measure player performance. Originally developed for chess, ELO ratings provide a fair and transparent way to rank players based on their actual game results. Every game you play affects your ELO rating, allowing you to track your improvement over time and see how you compare to other players in the community. Learn more about ELO on Wikipedia →
Why ELO Matters
Fair Competition
Your ELO rating reflects your actual skill level. Beat stronger opponents to gain more points, and see your ranking improve as you get better at the game.
Track Progress
Watch your ELO rating change after every game. See your improvement over time and set goals to reach higher ratings.
Leaderboard Ranking
Your ELO rating determines your position on the leaderboard. Compete with players worldwide and see where you stand.
Transparent System
Our ELO system is fully transparent. You can see exactly how your rating changes after each game, with clear explanations of the calculation.
How It Works
Starting Rating
All new players start with an ELO rating of 1500. This is a neutral starting point that represents an average skill level. As you play games, your rating will adjust based on your performance.
Point System
Your ELO change depends on your position and final score in each game:
🥇 First Place
- 5 points if one player finishes with a negative score
- 8 points if both other players finish with negative scores
- + Score bonus: 1 point per 100 final score (capped at 5 points)
- Maximum: 13 points total
🥈 Second Place
- 3 points if you finish with a positive score
- + Score bonus: 1 point per 100 final score (capped at 5 points)
📉 Negative Score Players
Players who finish with negative scores provide the points for positive players. The more negative your score, the more ELO you lose (proportionally).
ELO Scaling
The actual ELO change you receive is scaled based on your opponents' ratings:
- Beat stronger opponents: Gain more ELO points
- Beat weaker opponents: Gain fewer ELO points
- Lose to stronger opponents: Lose fewer ELO points
- Lose to weaker opponents: Lose more ELO points
This ensures that beating a highly-rated player is more rewarding than beating a beginner, making the system fair and skill-based.
Winner Protection
Winners never lose ELO! If you finish in first place, you are guaranteed to gain ELO points (or at least stay the same), regardless of your opponents' ratings. This ensures that winning is always rewarded.
The ELO Formula Explained
Overview
Our ELO system uses a modified version of the standard ELO formula, adapted for three-player Preferans games. The calculation happens in several steps:
- Calculate raw points based on position and final score
- Calculate expected performance based on opponent ELO ratings
- Convert raw points to actual performance (0.0 to 1.0)
- Calculate ELO change using the formula
Step 1: Expected Performance
First, we calculate how well you're expected to perform based on your ELO rating compared to your opponents.
Expected Score Formula
Expected Score = 1 / (1 + 10^((Opponent ELO - Your ELO) / 400))
For each opponent, we calculate your expected score. Then we average these expected scores to get your overall expected performance (ranging from 0.0 to 1.0).
Step 2: Actual Performance
Your actual performance is calculated from the raw points you earned in the game:
Actual Performance Formula
Actual Performance = (Raw Points + 13) / (13 × 2)
This converts your raw points (which can range from -13 to +13) into a performance value between 0.0 and 1.0. For example, 8 points = (8 + 13) / 26 = 0.808, and -5 points = (-5 + 13) / 26 = 0.308.
Step 3: ELO Change
Finally, we calculate how much your ELO rating changes:
ELO Change Formula
ELO Change = K-factor × (Actual Performance - Expected Performance) × 26
The K-factor is fixed at 1 for all players. The multiplier of 26 ensures that when players have equal ELO, the maximum ELO change (13 points) equals the maximum raw points (13). If you perform better than expected, you gain ELO. If you perform worse, you lose ELO.
Detailed Examples
Example 1: Marko, Janko, and Branko (Equal ELO)
Starting ELO: All three players have 1500 ELO
Final Scores: Marko: 200, Janko: 0, Branko: -200
Result: Marko wins (first place), Janko second, Branko third
Calculation:
Marko's Raw Points: 8 (first place with both negative) + 2 (score bonus: 200/100 = 2) = 10 points
Janko's Raw Points: 3 (second place, positive score) + 0 (no score bonus) = 3 points
Branko's Raw Points: -10 (provides points for Marko, proportional to his -200 score)
Expected Performance: Since all players have equal ELO (1500), each player's expected performance = 0.500
Marko's Actual Performance: (10 + 13) / 26 = 0.885
Marko's ELO Change: 1 × (0.885 - 0.500) × 26 = +10.0 ELO
Janko's Actual Performance: (3 + 13) / 26 = 0.615
Janko's ELO Change: 1 × (0.615 - 0.500) × 26 = +3.0 ELO
Branko's Actual Performance: (-10 + 13) / 26 = 0.115
Branko's ELO Change: 1 × (0.115 - 0.500) × 26 = -10.0 ELO
New ELO Ratings: Marko: 1510.0, Janko: 1503.0, Branko: 1490.0
Example 2: Upset Victory
In this scenario Marko is massively underrated compared to Janko and Branko, yet he wins the round and earns an outsized ELO boost.
Calculation:
Marko's Raw Points: 8 (first place with both negative) + 1 (score bonus: 150/100 = 1) = 9 points
Marko's Expected Performance: Against Janko (2000): 1/(1+10^((2000-1000)/400)) = 0.006
Against Branko (2000): 0.006
Average: 0.006 (Marko is heavily expected to lose)
Marko's Actual Performance: (9 + 13) / 26 = 0.846
Marko's ELO Change: 1 × (0.846 - 0.006) × 26 = +21.8 ELO (huge gain for upset!)
Janko's ELO Change: -6.5 ELO (loses less because Marko was much lower rated)
Branko's ELO Change: -15.3 ELO (loses more because his score was worse)
New ELO Ratings: Marko: 1021.8, Janko: 1993.5, Branko: 1984.7
Example 3: High Score Victory
Here Marko posts a perfect 500-point score while opponents go negative, demonstrating the maximum raw-point conversion.
Calculation:
Marko's Raw Points: 8 (first place with both negative) + 5 (score bonus: 500/100 = 5, capped) = 13 points (maximum!)
Marko's Actual Performance: (13 + 13) / 26 = 1.000 (perfect performance)
Marko's ELO Change: 1 × (1.000 - 0.500) × 26 = +13.0 ELO (maximum gain!)
Janko's ELO Change: -5.2 ELO, Branko's ELO Change: -7.8 ELO
New ELO Ratings: Marko: 1513.0, Janko: 1494.8, Branko: 1492.2
ELO Calculator
Enter the ELO ratings and final scores for three players to calculate ELO changes. Perfect for calculating ELO changes from offline Preferans games!
Ready to Compete?
Start playing now and see your ELO rating in action. Every game counts, and every win brings you closer to the top of the leaderboard!