xLosses: expected losses

The headline formula

xLosses = Σ P(loss)

Per-match loss probability

With λ_h = home xG and λ_a = away xG, the joint Poisson probability of a final scoreline of i goals to j goals is:

P(i, j) = ((e^(-λh) · λh^i) / i!) · ((e^(-λa) · λa^j) / j!)

A loss is the mirror of a win. For the home team, a loss happens when the home team scored fewer goals than the away team:

P(loss) = Σ P(i, j)   for all i < j

For the away team, a loss happens when the home team scored more:

P(loss) = Σ P(i, j)   for all i > j

A useful sanity check: the home team's P(loss) always equals the away team's P(win) for the same match, and vice versa.

Worked example

With home xG = 1.80 and away xG = 1.10, summing all (i, j) cells where i < j gives P(home loss) ≈ 0.234. The home team contributes 0.234 to its season xLosses; the away team contributes 0.535 to its xLosses (the home win probability) by symmetry.

Reading xLosses vs actual losses

• Losses > xLosses. Results have been worse than the chance quality predicts. Either the team is being out-finished by opponents or short-term variance has run against them. Expect the gap to close over a longer sample.
• Losses < xLosses. The team has avoided defeats more often than the model expects. That can be elite goalkeeping, defensive over-performance, or simply luck in tight scorelines.
• Losses ≈ xLosses. Defensive results match what the chances created and conceded suggest.

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