Build the rating move one layer at a time

Pick two clubs and a score. The chart shows how each layer of the model builds the rating exchange.

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})

Competition and round weights replace a single base K.

Preliminary

1st Round

2nd Round

3rd Round

Qualifying playoff

Group phase

Early knockout

Late knockout

Historical Fourth Round fixtures use the qualifying-playoff value.

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

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

Home-field edge+60Neutral venue

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

Goal margin scales the move, each extra goal adding less. An extra-time win counts 0.75; a shootout counts as the draw it was.

What the win is worth

G = 1 + \frac{ln ( max ( 1 , g o a l ma r g in ))}{4}

Own uncertainty speeds movement while opponent uncertainty weakens the evidence.

Home team RD60Away team RD60

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})

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})

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}}