Chapter 19 · Worked solutions
Chapter 19 workings: What xG Is Actually For
Chapter nineteen worked: turning xG for and against into attack and defence ratings, then into expected goals and fair match odds.
One exercise, five stages. The trick is matching each team figure with the right league baseline: what a home side scores is compared with what home sides score, and what it concedes is compared with what away sides score.
The exercises
From xG to a fair 1X2
Across the league, home teams average 1.45 xG and away teams 1.15. The home team creates 1.55 and allows 1.20 per home match; the visitors create 1.10 and allow 1.35 per away match. Find the four ratings, both expected-goals figures and fair prices.
Four ratings
Each team figure over its baseline, as in the table.
Home expected goals, λ
League home average × home attack × away defence = 1.45 × 1.0690 × 0.9310 = 1.4431.
Away expected goals, μ
League away average × away attack × home defence = 1.15 × 0.9565 × 1.0435 = 1.1478.
Build the grid and sum it
Poisson for each side, multiply cell by cell, then add up below, on and above the diagonal.
Price it
Home 43.9 per cent, draw 26.1 per cent, away 30.0 per cent. Notice that two fairly even sides produce a draw above a quarter, which is where the plain eye usually underrates it.
| Rating | Team figure | Divided by | Value |
|---|---|---|---|
| Home attack | 1.55 xG for at home | 1.45, league home average | 1.0690 |
| Home defence | 1.20 xG against at home | 1.15, league away average | 1.0435 |
| Away attack | 1.10 xG for away | 1.15, league away average | 0.9565 |
| Away defence | 1.35 xG against away | 1.45, league home average | 0.9310 |
The answer
λ = 1.443, μ = 1.148; home 43.9 per cent, draw 26.1 per cent, away 30.0 per cent, roughly 9/7, 17/6 and 7/3.
| Result | Probability | Fair price |
|---|---|---|
| Home | 43.85% | 2.28, about 5/4 |
| Draw | 26.10% | 3.83, about 11/4 |
| Away | 30.05% | 3.33, about 9/4 |
These are the workings. The argument for them, and the exercises themselves, are in chapter 19 of the book, What xG Is Actually For.
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