The headline formula
xDraws = Ξ£ P(draw)
Per-match draw probability
With Ξ»h = home xG and Ξ»a = away xG, the joint Poisson probability of any final scoreline (i, j) is:
P(i, j) = ((e^(-Ξ»h) Β· Ξ»h^i) / i!) Β· ((e^(-Ξ»a) Β· Ξ»a^j) / j!)
The draw probability is the sum of all level scorelines:
P(draw) = Ξ£ P(i, j) for all i = j
In practice this is the diagonal of the 0..10 by 0..10 scoreline grid: 0-0, 1-1, 2-2, 3-3, 4-4, and so on. For typical league xG values the mass is concentrated in 0-0, 1-1, and 2-2; everything past 4-4 is statistically negligible.
Worked example
With home xG = 1.80 and away xG = 1.10, the diagonal probabilities are approximately:
- P(0-0) β 0.0550
- P(1-1) β 0.1089
- P(2-2) β 0.0540
- P(3-3) β 0.0119
- P(4-4) β 0.0015
Summing the diagonal gives P(draw) β 0.231. Both sides accumulate 0.231 xDraws from this match.
Why xDraws is symmetric
A draw is a single outcome that affects both teams identically (1 point each). In contrast, a win for the home team is a loss for the away team, so home xWins equals away xLosses (and vice versa). The xDraws value for both teams in any given match is by construction the same number. Across the season, two clubs that have played each other once will each have that match's P(draw) added to their xDraws total once.