*29.04.2021 • Author: Maximilian Wensch*

The graph shows the average number of scores in a match in the respective sports. A score describes any action that increases the score of one’s own team, i.e. a successful goal in soccer, handball and ice hockey. In basketball this means 2 and 3 point shots and free throws, and in American football a touchdown, field goal, extra point or safety.

From the graph, the increased influence of chance in football can be deduced. A score achieved “by chance”, such as a deflected goal kick, has a much more significant influence on the outcome of the game than in other sports. In soccer, trivial analyses often talk about unearned or earned victories. These terms are heard much less often in other sports, as chance plays a minor role due to much higher scores scored.

**The Expected Goals method adjusts the game results from chance and objectively states how the game would have turned out based on the value of the scoring chances created.**

In the beginning, the Expected Goals metric was only used in insider forums and had little media attention. In 2001, the English company Opta Sports (now Stats Perform) was founded. The company set out to create a database that could be used as a basis for new approaches to analysis in football. Through the Expected Goals method, a way should be found to separate luck and chance from the teams’ abilities. The idea is not to describe what actually happened, but what should have happened according to expectations. For this purpose, Opta Sports has documented goal chances over many years with respect to the position of the goal shot and the position of the defenders. Even today, the goal chances of games are documented and added to the constantly growing database.

But back to the Expected Goals method. The Expected Goals value of a goal chance is thus calculated on the basis of all historical goal chances under the same conditions.

The following figure shows the conditions considered in the Expected Goals method in the Bundesliga.

*4 Conditions in the calculation of the xG value of a goal chance (source)*

Using mathematical principles, it is easy to calculate the expected value of the chance. If the chance was a goal, it is assigned the value 1, if not the value 0. If you add up all historical goal chances under the same conditions and divide them by the number, you get the expected value of this specific goal chance.

However, before the method became popular with clubs in the professional soccer business, it was mainly used by professional gamblers and betting syndicates. The founder of the sports statistics provider SmartOdds, Matthew Benham, was also the owner of the Brentford FC football club in the second English league. He introduced the Expected Goals method to professional football for the first time and used it specifically in scouting. The metric achieved its breakthrough in the 2017/18 season when it was first presented on platforms such as Sky Sports and BBC.

For those familiar with the Moneyball concept or have seen the movie “Moneyball – The Art of Winning”: The English club Brentford FC is the equivalent in football to the Oakland Athletics in baseball.

For all those who haven’t heard of this before: These are clubs with financial possibilities far below the league average. Following the Moneyball concept, these clubs have attempted to sign unknown talent through new data-based approaches to scouting. Using objective statistical approaches such as the Expected Goals method, among others, they have signed young talent that has remained under the radar of the financially strong clubs and their scouts.

A look at Brentford FC’s transfer record shows that the club has not been entirely unsuccessful with this approach. Over the last 6 years, the club has generated a transfer surplus of almost 120 million euros, which is quite exceptional for English professional clubs.

But now back to the Expected Goals metric. The most common and intuitive representation of the metric is the so-called Expected Goals Map. On the left, you can see the map for the Champions League Quarter Finals 2021 (FC Bayern vs. Paris Saint-Germain).

The rectangles represent all goal chances of both teams with the corresponding shot position. The green rectangles are scoring chances that were converted into a goal in the match. The size of the rectangles is determined by the Expected Goals value. If you remember the quarterfinal first leg between FC Bayern and Paris Saint Germain, you might even recognize one or the other goal based on the positions and sizes of the rectangles. For example, the small green rectangle on the edge of the penalty area was Kylian Mbappé’s goal when he tunneled Jerome Boateng off the dribble. The rectangle is relatively small, as the Expected Goals value of a goal shot from this position with the defender directly in the line of fire is still very small at 0.11 xG.

But the Expected Goals method can do a lot more! From the individual Expected Goals values of the goal kicks, the Expected Points values can be calculated for the teams for each game, i.e. how many points the team expects to take home from a game. To be able to understand this a bit better, we will calculate the Expected Points step by step using an example. For this purpose, we will take the upcoming match between Borussia Dortmund and RB Leipzig on 08.05.2021.

We first look at both the Expected Goals of the teams and the values of their opponents, the so-called Expected Goals against. To make the calculation as realistic as possible, we subdivide all values into certain shot zones in which the goal chances were created.

Borussia Dortmund | RB Leipzig | League average | |||
---|---|---|---|---|---|

xGoals for (xGF) | xGoals against (xGA) | xGoals for (xGF) | xGoals against (xGA) | xGoals for (xGF) | |

Outside penalty area | 0,17 | 0,13 | 0,20 | 0,06 | 0,14 |

Within penalty area | 1,37 | 0,73 | 1,34 | 0,59 | 0,98 |

Within 6 yard box | 0,58 | 0,28 | 0,40 | 0,19 | 0,30 |

*Average expected goals values per shot zone*

All readers with a slight allergy to math will have to stay strong for the next few lines, because we need to do some calculations to calculate the expected point output.

First, the Expected Goals per Zone are calculated for both teams for this game. Using the league average, the defensive performances (xGA) of both teams can be put into perspective.

For both teams, the values for each shooting zone are as follows:

Borussia Dortmund | RB Leipzig | |
---|---|---|

Outside penalty area | 0,07 | 0,19 |

Within penalty area | 0,82 | 0,99 |

Within 6 yard box | 0,37 | 0,37 |

Sum | 1,26 | 1,55 |

*Game-specific expected goals*

Based on the summed xG values from the upper table, the probabilities for the number of goals scored by both teams can now be calculated using the Poisson distribution:

Number of goals | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|---|

Dortmund | 28,37% | 35,74% | 22,52% | 9,46% | 2,98% | 0,75% | 0,16% |

Leipzig | 21,22% | 32,89% | 25,49% | 13,17% | 5,10% | 1,58% | 0,41% |

*Predicted probabilities for certain number of goals*

Die Wahrscheinlichkeiten für die einzelnen Spielresultate können nun mittels Multiplikation der Wahrscheinlichkeiten der Toranzahlen beider Teams berechnet werden.

Das Endergebnis mit der höchsten Wahrscheinlichkeit sind die jeweiligen Maximalwerte beider Teams, also ein 1:1 Unentschieden. Dafür wäre die Wahrscheinlichkeit das Produkt der zwei Einzelwahrscheinlichkeiten, also etwa 11,7 Prozent. Berechnet man alle Werte ergibt sich folgende Matrix.

Number of goals Dortmund | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|---|

Dortmund wins by 0 | 7,58% | 4,78% | 2,01% | 0,63% | 0,15% | 0,03% | |

Dortmund wins by 1 | 7,40% | 3,11% | 0,98% | 0,25% | 0,05% | ||

Dortmund wins by 2 | 2,41% | 0,76% | 0,19% | 0,04% | |||

Dortmund wins by 3 | 0,39% | 0,09% | 0,03% | ||||

Dortmund wins by 4 | 0,04% | 0,01% | |||||

Dortmund wins by 5 | 0,01% |

Number of goals Leipzig | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|---|

Leipzig wins by 0 | 9,33% | 7,23% | 3,73% | 1,44% | 0,44% | 0,11% | |

Leipzig wins by 1 | 9,11% | 4,70% | 1,82% | 0,56% | 0,15% | ||

Leipzig wins by 2 | 2,96% | 1,15% | 0,36% | 0,09% | |||

Leipzig wins by 3 | 0,48% | 0,15% | 0,04% | ||||

Leipzig wins by 4 | 0,05% | 0,02% | |||||

Leipzig wins by 5 | 0,01% |

Tie | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|---|

6,02% | 11,75% | 5,74% | 1,25% | 0,15% | 0,02% | 0,00% |

Place | Team | xG | xA | xP |
---|---|---|---|---|

1 | RB Leipzig | 57,56 | 24,97 | 64,08 |

2 | Borussia Dortmund | 63,19 | 34,98 | 60,08 |

3 | FC Bayern München | 65,56 | 35,36 | 59,01 |

4 | VFL Wolfsburg | 47,27 | 35,09 | 50,99 |

*Bundesliga table based on Expected Points*

Players with a high outperformance value have effectively used their scoring opportunities and scored more goals than would be expected based on scoring chances. The player with the highest effectiveness in the top 5 European leagues is – who would have expected it – Robert Lewandowski. Lewandowski surpassed his Expected Goals value of 26.27 with 35 actual goals scored.

During the Champions League quarterfinal between FC Bayern and Paris Saint Germain, there was a lot of discussion about the loss of Lewandowski and his replacement Eric Maxim Choupo-Mouting. Despite Choupo-Mouting’s two goals, many agreed that with Lewandowski in the squad, Bayern would have scored at least one more goal, which would have been enough to reach the semifinals.

Compared to Robert Lewandowski, Choupo-Moting has under-performed his Expected Goals value by 1.1 goals this season. However, due to comparatively fewer minutes of action, this statistic is not particularly meaningful. But even over his entire career, the goals he has actually scored are lower than his total Expected Goals value (-2.26). We will probably never know whether Lewandowski could have actually helped FC Bayern to progress in the Champions League. However, one thing is certain: Lewa’s ability to convert his chances this season is extremely good and may even help him break Gerd Müller’s goal record from 1971/72 with 40 goals in one season.

It is also remarkable that, in addition to the Bundesliga players Lewandowski, Andre Silva and Erling Haaland, there are 3 ex-Bundesliga players in Kevin Volland, Son Heung Min and Ilkay Gündogan.

In this article you already got to know some fields of application of the Expected Goals metric. If you still don’t have enough of the Expected Goals method or are looking for general Expected Goals statistics for the European football leagues, you can find them here.

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