Written by Colin+ in ask uncle colin, sport.

Dear Uncle Colin,

What on earth is "expected goals" and why is it supposed to be useful?

- Just Enjoy Football FFS

Hello, JEFF, and thanks for your message!

The first part of your question is simple, although with some subtleties.

'Expected goals' is a statistic that's started to appear in match summaries and flash up on screens and be referred to by losing managers, and it's one I quite like.

Suppose your star striker scores eight out of ten penalties, on average. That means, if you were to be awarded a penalty, you would expect - over the long term - to score 0.8 of a goal. In this hypothetical situation, a penalty would be worth 0.8 expected goals.

The statistic takes all of the chances that your team gets during a match - maybe 0.02 for the ball dropping to the left-back on the volley, 30 yards out, maybe 0.95 for a free header in the box - and adds them up. In a crude sense, it's how many goals you *should* have scored, given the chances you had.

Of course, that's somewhat subjective, and there are problems with it - who decides on the values? If the keeper saves the penalty but flaps the rebound straight to the striker with an open goal, does that count as 1.7 expected goals? But, as we're about to see, it's less problematic than some of the other measures.

"That's football, Mike, Northern Ireland have had several chances and haven't scored but England have had no chances and scored twice."

- Trevor Brooking

On the one hand, only two statistics really matter in a football match: $G_F$, the number of goals you've scored, and $G_A$, the number you've conceded. If $G_F - G_A > 0$, typically you receive three *points* or advance to the next round of the competition1. If $G_F - G_A = 0$, you get one point or may need to replay the match; otherwise you get no points or knocked out of the competition.

That's all well and good, but there's more to football than just the score - there are stories (Benevento 2-2 Milan isn't especially interesting, if you're not a follower of Serie A; Benevento winning their first point of the season with a flying header in the 95th minute, scored by their goalie... that's interesting) and there are statistics.

Football is less of a stats game than, say, cricket or tennis, both of which are made up of discrete events that can be analysed individually. That said, it's still a stats game: you see numbers like "possession" and "yellow cards" and "caught offside" and so on pop up on the screen to give you more of a sense of how the game has been. If it's 0-0 but one side has had 70% of the ball, been caught offside six times and the other has picked up four yellow cards in the first 20 minutes, that gives you an idea of the first team's dominance.

Two of the stats that are always shown - and which are almost completely useless - are "shots on target" and "shots off target". A 30-yard scuff that bobbles pathetically into the goalie's arms counts the same (one shot on target!) as a tremendous point-blank save. Expected goals tries to rectify this uselessness a bit: it quantifies (somewhat arbitrarily) the quality of the chances a team has had as well as their mere existence. It's a measure of a team's luck, or perhaps their ruthlessness in front of goal.

For someone who's not following the game live, expected goals are a useful statistic to judge the story of the game without having to read a report on it. For a losing manager, they are a useful crutch for explaining why defeat was neither their fault, nor their players'.

Hope that helps!

- Uncle Colin

* For more on the maths of sport, you might enjoy Rob Eastaway's How To Take A Penalty. Assuming you already have The Maths Behind, of course; both are available wherever good books are sold.

- except in some competitions where matches are played over two legs. [↩]