ELF Elo Rankings

The Elo rating system is a method for calculating the relative skill levels of players in zero-sum games such as chess or esports. It is named after its creator Arpad Elo, a Hungarian-American chess master and physics professor.

ELF Elo Ratings

The ELF Elo Ratings are a statistical model used to estimate the relative strength of teams in the European League of Football (ELF). They are based on the classic Elo rating system (originally developed for chess) but adapted to the specific dynamics of American football.

Concept

The model assigns each team a numerical rating representing its current strength. Ratings change only after official games:

• A win increases the winning team’s rating and decreases the losing team’s rating.
• The change depends on the expected win probability before the game and the actual margin of victory (MOV).

Initial Rating

All teams start with the same baseline rating in their first season: $R_{0}=1500$ This value is slightly below the long-term league average, giving established teams a small initial advantage over new entrants.

Expected Win Probability

For two teams A and B with ratings $R_{A}$ and $R_{B}$, the expected probability of team A winning is:

$W_{A}={\frac {1}{1+10^{\frac {R_{B}-R_{A}}{400}}}}$

The probability for team B is: $W_{B}=1-W_{A}$

Margin of Victory Multiplier

We use a capped logarithmic adjustment to prevent blowouts from producing unrealistic rating swings:

$\mathrm {MOV_{mult}} =\ln(\min(\mathrm {MOV} ,35)+1)\cdot {\frac {2.2}{(0.001\cdot |R_{A}-R_{B}|)+2.2}}$

• MOV = absolute point difference in the final score
• Capped at 35 points

Season-to-Season Regression

Between seasons, ratings regress slightly towards the league average to account for off-season roster changes and prevent runaway inflation:

$R_{\text{new}}=R_{\text{old}}+\lambda \cdot (1500-R_{\text{old}})$

Where $\lambda$ is the regression rate.

Playoffs

• Playoff games use a higher K-factor to reflect their importance.
• Playoff results can be included or excluded in displays.

Key Parameters (Default Values)

• Initial rating ($R_{0}$): 1500
• K-factor (Regular Season): 20
• K-factor (Playoffs): 30
• MOV cap: 35 points
• Regression rate per off-season ($\lambda$): 0.33
• League average baseline: 1500
• Exclusions: Walkover games

All-Time Elo

An alternative view calculates Elo ratings across all seasons with light regression between years.

This can be optionally filtered to include only active teams in a given season.

Elo 2025 only

Rank	Team	Elo
1	Vienna Vikings	1633.1
2	Munich Ravens	1618.4
3	Stuttgart Surge	1602.1
4	Nordic Storm	1578.9
5	Madrid Bravos	1571.1
6	Rhein Fire	1569.4
7	Paris Musketeers	1538.3
8	Prague Lions	1518.3
9	Raiders Tirol	1500.6
10	Frankfurt Galaxy	1499.7
11	Panthers Wrocław	1471.6
12	Hamburg Sea Devils	1433.6
13	Berlin Thunder	1408.9
14	Fehérvár Enthroners	1372.8
15	Helvetic Mercenaries	1353.3
16	Cologne Centurions	1329.8

Elo all time 2025 teams only

Rank	Team	All-Time Elo (active in 2025)
1	Vienna Vikings	1750.9
2	Stuttgart Surge	1729.3
3	Rhein Fire	1691.8
4	Munich Ravens	1662.1
5	Paris Musketeers	1634.5
6	Nordic Storm	1619.3
7	Madrid Bravos	1588.2
8	Raiders Tirol	1563.4
9	Frankfurt Galaxy	1522.9
10	Panthers Wrocław	1497.3
11	Prague Lions	1470.8
12	Berlin Thunder	1434.6
13	Hamburg Sea Devils	1424.4
14	Cologne Centurions	1338.4
15	Helvetic Mercenaries	1322.4
16	Fehérvár Enthroners	1322.1

Elo all time

Rank	Team	All-Time Elo
1	Vienna Vikings	1750.9
2	Stuttgart Surge	1729.3
3	Rhein Fire	1691.8
4	Munich Ravens	1662.1
5	Paris Musketeers	1634.5
6	Nordic Storm	1619.3
7	Madrid Bravos	1588.2
8	Raiders Tirol	1563.4
9	Frankfurt Galaxy	1522.9
10	Panthers Wrocław	1497.3
11	Prague Lions	1470.8
12	Leipzig Kings	1441.7
13	Berlin Thunder	1434.6
14	Hamburg Sea Devils	1424.4
15	Helvetic Guards	1414.0
16	Milano Seamen	1393.7
17	Istanbul Rams	1356.1
18	Cologne Centurions	1338.4
19	Helvetic Mercenaries	1322.4
20	Fehérvár Enthroners	1322.1
21	Barcelona Dragons	1322.1