Methodology story

Build the rating move one layer at a time

Pick two clubs, choose a result, then walk through the rating update from the simplest Elo version to the full beyondELO match adjustment.

Methodology follows the selected rating system

After every layerParis Saint-Germain +12.7

62.7% Paris Saint-Germain / 37.3% Bayern Munich

Home teamParis Saint-Germain#1

ELO rating

Away teamBayern Munich#2

ELO rating

Paris Saint-Germain

2-1

Bayern Munich

Step 1

Start with only the two ratings

The two ELO ratings set the win probability before the result moves points.

R_{n e w} = R_{o l d} + K (W - W_{e})

Learn more about this step

Calculation at this pointParis Saint-Germain +9.8

Paris Saint-Germain51.0%

Bayern Munich49.0%

Paris Saint-Germain2006 -> 2016+9.8

Bayern Munich1999 -> 1989-9.8

This is the clean baseline before match context is added.

Only the two starting ratings and the chosen result are active here. Every later step changes this same exchange.

Step 2

Add match importance with adaptive K

Competition and round weights replace a single base K.

K_{ba se} = f (co m p e t i t i o n, s t a g e)

Learn more about this step

Calculation at this pointParis Saint-Germain +14.7

Paris Saint-Germain51.0%

Bayern Munich49.0%

Paris Saint-Germain2006 -> 2021+14.7

Bayern Munich1999 -> 1984-14.7

This layer changes Paris Saint-Germain by +4.9 Elo compared with the previous step.

Qualification

Main competition

CompetitionsPreliminary1st Round2nd Round3rd RoundQualifying playoff

UCL

UEL

UECL

Historical Fourth Round fixtures use the qualifying-playoff value.

CompetitionsGroup phaseEarly knockoutLate knockout

UCL

UEL

UECL

Step 3

Give the home team its venue edge

Home advantage is added before probability, and removed at neutral venues.

W_{e} = \frac{1}{1 + 1 0 ^{(R_{a w a y} - (R_{h o m e} + H F A)) /400}}

Learn more about this step

Calculation at this pointParis Saint-Germain +11.2

Paris Saint-Germain62.7%

Bayern Munich37.3%

Paris Saint-Germain2006 -> 2017+11.2

Bayern Munich1999 -> 1988-11.2

This layer changes Paris Saint-Germain by -3.5 Elo compared with the previous step.

Home-field edgeNeutral venue

Step 4

Let the scoreline describe the result

Goal margin scales the move while extra time and penalties soften it.

G = 3 max (1, g o a l ma r g in)

Learn more about this step

Calculation at this pointParis Saint-Germain +11.2

Paris Saint-Germain62.7%

Bayern Munich37.3%

Paris Saint-Germain2006 -> 2017+11.2

Bayern Munich1999 -> 1988-11.2

This layer changes Paris Saint-Germain by 0.0 Elo compared with the previous step.

Paris Saint-GermainBayern Munich

Step 5

Move uncertain teams faster

Own uncertainty speeds movement while opponent uncertainty weakens the evidence.

K_{t e am} = K_{ba se} \times G \times R D_{o w n} \times R e l iabi l i t y (R D_{o pp})

Learn more about this step

Calculation at this pointParis Saint-Germain +12.7

Paris Saint-Germain62.7%

Bayern Munich37.3%

Paris Saint-Germain2006 -> 2019+12.7

Bayern Munich1999 -> 1986-13.3

This layer changes Paris Saint-Germain by +1.5 Elo compared with the previous step.

Paris Saint-Germain uncertaintyBayern Munich uncertainty

Paris Saint-Germain move x1.15 / x0.99 own uncertainty / opponent reliability

Bayern Munich move x1.20 / x0.99 own uncertainty / opponent reliability

Step 6

Put the full model together

The final exchange combines importance, venue, scoreline, and rating certainty.

R_{n e w} = R_{o l d} + K_{t e am} (W - W_{e})

K_{t e am} = K_{ba se} \times G \times R D_{o w n} \times R e l iabi l i t y (R D_{o pp})

W_{e} = \frac{1}{1 + 1 0 ^{(R_{a w a y} - (R_{h o m e} + H F A)) /400}}

R D_{o w n} = min (3, (\frac{max ( R D , 60 )}{60})^{0.6})

R e l iabi l i t y (R D_{o pp}) = \frac{g ( R D _{o pp} )}{g ( 60 )}, g (R D) = \frac{1}{1 + 3 ( R D /173.7178 ) ^{2} / π ^{2}}

Learn more about this step

Loading the latest UCL example from full match history.

Build the rating move one layer at a time

Start with any two teams

Start with only the two ratings

Add match importance with adaptive K

Give the home team its venue edge

Let the scoreline describe the result

Move uncertain teams faster

Put the full model together