📊 Elo Rating Exchange System
Player ratings dynamically adjust after every match based on relative skill differentials and match outcomes.
🏛️ 1. Origin & Standard
The rating exchange system is directly modeled on the Elo Rating System created by physics professor and chess master Dr. Arpad Elo (1903–1992).
- USCF & FIDE Adoption: Adopted by the US Chess Federation in 1960 and FIDE (World Chess Federation) in 1970 as the gold standard for global player rankings.
- FIFA World Rankings: Adopted by FIFA in 2018 for global national football team rankings.
- Competitive Esports: Foundation for matchmaking rating (MMR) systems in games like League of Legends, CS:GO/CS2, and Rocket League.
- Cue & Racket Sports: Broadly applied across professional billiards, pool, table tennis, and tennis leagues worldwide.
🧮 2. Mathematical Foundation & Formula
Matches are treated as probabilistic events. When two players compete, the algorithm calculates each player's expected win probability based on their current rating difference.
Where RA is Player A's rating and RB is Player B's rating.
The 400 constant scales the logistic curve such that a 400-point rating difference represents a 10:1 ratio in expected win odds (~90.9% vs ~9.1%).
For the match winner (Swinner = 1.0):
ΔR = round( K × ( 1.0 - Ewinner ) )
- Zero-Sum Mechanics: Rating transfers are strictly zero-sum. The winner gains exactly ΔR points while the loser loses ΔR points.
- Minimum Point Transfer: Every win transfers at least 1 point (ΔR ≥ 1), regardless of rating disparity.
- Rating Floor: Player ratings cannot drop below 0 points.
🧮 3. Interactive Elo Exchange Calculator
Test rating exchanges between any two players to preview expected probabilities and point transfers:
Points Exchanged (ΔR)
+16 pts
Player A New Rating
1,216
Player B New Rating
1,184
⚙️ 4. League System Parameters
The system parameters currently configured in Tournament:
Base Starting Rating
1,200
Standard starting score assigned to all newly registered club players.
K-Factor (K)
32
Standard FIDE K-factor balancing rating stability with responsiveness to recent performance.
Scale Constant
400
Logistic scale factor where a 400-point difference equals 10:1 expected win odds.
Minimum Transfer
1 pt
Guarantees every completed match awards at least 1 point to the winner.
Rating Floor
0 pts
Absolute lower boundary preventing negative point values.
💡 5. Practical Match Scenarios
See how ratings shift in common league match outcomes:
Even Matchup
1,200 pts vs 1,200 pts
Both players have equal skill ratings. Win expectation is 50% for each player.
Points Transferred:
+16 pts
Underdog Upset
1,100 pts vs 1,300 pts
Underdog (1,100 pts) defeats Favorite (1,300 pts). Win expectation was only 24.03%.
Points Transferred:
+24 pts
Favorite Expected Win
1,400 pts vs 1,000 pts
Favorite (1,400 pts) defeats Underdog (1,000 pts). Win expectation was 90.91%.
Points Transferred:
+3 pts