Did we deserve to win?
The final score is one roll of the dice. Enter the shots each side took, as expected goals, and see what the chances they created were really worth.
Try an example
One xG value per shot, between 0 and 1, separated by commas or spaces. Most match reports and shot maps list them.
- Home win
- Draw
- Away win
- Home points deserved
- Away points deserved
- Most likely score
Home goals: how many?
Away goals: how many?
How it works
Every shot is treated as its own Bernoulli trial: it goes in with probability equal to its xG, or it doesn't. A side fails to score only if every shot misses:
$$\begin{aligned} &P(\text{no goals}) \\ &= (1 - p_1)(1 - p_2)\cdots(1 - p_n) \end{aligned}$$Working through every combination of shots gives the chance of each goal total, and pairing the two sides gives every scoreline. The points each side deserved are then
$$\begin{aligned} &\text{points deserved} \\ &= 3 \times P(\text{win}) + 1 \times P(\text{draw}) \end{aligned}$$In plain football
- \(p_1, p_2, \ldots\) are the xG values of each shot, one per chance.
- \((1 - p)\) is the chance a shot misses. Multiply them all and you get the chance of a blank.
- Points deserved is what the side would average if the match were replayed from the same chances many times.
Why the number of shots matters
Try the first example. Both sides create about 1.3 xG, yet the side with one big chance is more likely to win than the side with thirteen small ones. A single 0.76 chance scores three times in four; thirteen 0.1 chances fail completely a quarter of the time. The Bernoulli article works through the same two teams.
Assumptions
- Each shot's xG is its true chance of scoring. xG models differ, so the same match can look different on different sites.
- Shots are independent. A save followed by a rebound is really one moment, and counting both overstates the chance of a goal.
Where it goes wrong
- It ignores game state. A side that goes ahead often stops shooting, so its shot count understates what it could have created.
- Chances that never became shots, such as a cut-back nobody reached, don't appear in xG at all.
These probabilities come from a statistical model and are for analysis and education. Football remains uncertain, and "deserved" is a statement about chances, not about who played better.