FAQ

Elo Rating System (Mellon League)

Starting point: Everyone begins at 1000 Elo.

A) First 5 games (per player)

To stabilise new players, the first five games use fixed scoring:

• Win: +25
• Draw: 0
• Loss: −25

No army multipliers or opponent adjustments apply during these first five games. Each player exits this phase independently after their fifth recorded game.

B) Expected score (after 5 games)

After the first five games, Elo uses an expected-score formula based on rating difference:

For Player A vs Player B:

EA = 1 / (1 + 10^((RB − RA)/300))
EB = 1 − EA

We use a divisor of 300, making upsets more impactful than standard Elo.

C) K-factor

After the first five games, the system uses:

• K = 25

This controls how quickly ratings change.

D) Army & opponent multipliers

Elo changes are adjusted based on: (1) your army’s league winrate and (2) your opponent’s army winrate. All winrates are taken before the match is played.

1) Base army multiplier (capped)

Let w be your army winrate (0–100%).

Mbase = 1 + 0.25 × (1 − w)

• 100% army: ×1.00
• 50% army: ×1.125
• 0% army: ×1.25

For losses, the inverse is used:

MlossBase = 1 / Mbase

So weaker armies lose less, but only modestly (max 20% protection). Unknown armies (no data yet) are treated as 50% winrate.

2) Opponent army difficulty factor

If your opponent is using a much stronger (or weaker) army, the result is adjusted slightly. Let:

• wa = your army winrate
• wb = opponent’s army winrate

Mopp = 1 + 0.10 × |wb − wa|

• Maximum adjustment: +10%
• Applies to both wins and losses

This rewards beating strong lists and softens losses against them.

3) Final multiplier used

• On a win: M = Mbase × Mopp
• On a loss: M = MlossBase × Mopp

E) Independent rating updates

Ratings are updated independently for each player:

ΔRA = K × (SA − EA) × MA
ΔRB = K × (SB − EB) × MB

Where:

• S = actual result (1 = win, 0.5 = draw, 0 = loss)
• M depends on the player’s army and opponent’s army
• Players may still be in their first five games (fixed scoring)

Because multipliers are applied per player, rating gains and losses do not need to sum to zero. This is intentional.

F) Rounding and caps

• Final Elo changes are rounded to the nearest integer
• A non-zero result is never rounded to 0
• Maximum change per game is capped at ±60 Elo

Example

Peppe (1000 Elo, army WR 20%) vs Richard (1200 Elo, army WR 60%). Peppe wins.

Expected scores:

• EPeppe ≈ 0.24
• ERichard ≈ 0.76

Base Elo change (K = 25):

• Peppe: 25 × (1 − 0.24) ≈ +19.0
• Richard: 25 × (0 − 0.76) ≈ −19.0

Multipliers:

• Peppe base army multiplier: 1 + 0.25 × (1 − 0.20) = 1.20
• Opponent factor: 1 + 0.10 × |0.60 − 0.20| = 1.04
• Peppe total multiplier: 1.20 × 1.04 ≈ 1.25
• Richard loss base multiplier: 1 / (1 + 0.25 × (1 − 0.60)) ≈ 0.91
• Richard total multiplier: 0.91 × 1.04 ≈ 0.95

Final Elo changes:

• Peppe: +19.0 × 1.25 ≈ +24
• Richard: −19.0 × 0.95 ≈ −18

Summary:

• Upsets are rewarded
• Weak armies get recognition, not immunity
• Strong armies cannot farm Elo safely
• Losing to weaker players hurts appropriately