How can a number tell whether a football team deserved to win?

Over two matches in 2012, Barcelona had 73% of the possession and 46 shots to Chelsea's 12, and Chelsea went through. Were Barcelona unlucky, or were their shots bad? Expected goals is a way to approach that kind of question.

Expected goals (xG) assigns each shot a probability of being a goal. Adding those up estimates how many goals a team or player would be expected to score given the chances created, independent of whether they were actually converted. An xG of 0.3 means that shots like this one would be scored about 30% of the time over many repetitions; it is not a statement about any single shot.

Where do the numbers come from? From models trained on historical shot data. A 2004 study of 37 matches at the 2002 World Cup, with 930 shots and 93 goals, found five factors that significantly affected whether a shot succeeded: distance, angle, whether the shooter was at least a metre from the nearest defender, whether the shot followed a cross, and how many outfield players stood between shooter and goal.

The payoff is diagnosis. An early write-up of the method suggested that xG could distinguish a lack of quality chances from a finishing problem, and could evaluate defending and goalkeeping. Expected goals against (xGA) adds up the chances a team concedes, and the difference between the two is the expected goal difference.

But a single match is noisy: xG totals from one game are volatile, and gaps between xG and actual goals can come from randomness as well as skill.