Elo Rating System Guide

This guide outlines the rules and features of the Elo rating system designed for your ranking structure.

1. Overview of the System

This Elo rating system is used to determine player skill levels based on match outcomes. Players are assigned a rating and categorized into one of ten ranks, which represent their skill level. Over time, ratings adjust as players compete, allowing for promotions and demotions between ranks.

2. Starting Conditions

  • Default Starting Rating: 1000 (Novice rank).
  • New players begin their journey in the Novice rank and climb the ranks based on their performance.

3. Ranking Structure

Players are categorized into the following ranks based on their rating:

Rank

Rating Range

Super

2800+

King

2400–2799

Prince

2000–2399

Duke

1800–1999

Lord

1600–1799

Master

1400–1599

Soldier

1200–1399

Fellow

1100–1199

Apprentice

1001–1099

Novice

≤ 1000

4. Rating Adjustments

After every match, a player's rating is updated using the following formula:

R' = R + K * (S - E)

  • R: Current rating.
  • R′: Updated rating.
  • K: The adjustment factor (varies by rank and conditions).
  • S: Actual score (1 for a win, 0.5 for a draw, 0 for a loss).
  • E: Expected score, calculated by: E = 1 / (1 + 10^((Opponent_Rating - Player_Rating) / 400))

5. K-Factor (Adjustment Speed)

The K-factor determines how quickly a player's rating changes after a match.

  • Standard K-Factors by Rank:

Rank

K-Factor

Novice–Master

40

Master–Prince

24

King–Super

16

6. Promotions and Demotions

  • Promotions:
    Players are promoted to the next rank as soon as their rating surpasses the upper limit of their current rank. No buffer is required.
    Example: A "Novice" with a rating of 1001 is promoted to "Apprentice."
  • Demotions:
    Players are demoted if their rating drops 50 points below the lower limit of their current rank.
    Example: A "Master" falls below 1350 (threshold for demotion to "Soldier").

7. Expected Match Outcome

Before each match, the system calculates the expected score (E) for both players based on their ratings. A higher-rated player is expected to win, so they gain fewer points for a victory and lose more points for a loss.

8. Example Match Calculation

A "Novice" (rating 1000) plays against a "Fellow" (rating 1100):

  • Step 1: Calculate Expected Score
    E = 1 / (1 + 10^((1100 - 1000) / 400)) ≈ 0.36
  • Step 2: Update Rating (Win Result) S = 1

R' = 1000 + 40 * (1 - 0.36) ≈ 1014

  • Step 3: Update Rating (Loss Result) S = 0

            R' = 1000 + 40 * (0 - 0.36) ≈ 985

9. Special Rules

Demotion Buffer

  • A 50-point buffer prevents immediate demotion, ensuring stability in ranks.

11. How to Use This System

  1. Assign Ratings: Start all new players at 1000 (Novice).
  2. Track Match Results: Record match outcomes (win/loss/draw).
  3. Update Ratings: Apply the formula to adjust ratings and determine promotions/demotions.
  4. Apply Enhancements: Consider the buffer zones as needed.