Liverpool’s Premier League unbeaten streak of over a year has been incredible. Currently sitting atop the table with 73 of a possible 75 points, Liverpool is on pace to set a record-breaking total of 110 points, 10 more than City’s record of 100 from 2 years ago.
As a fan, while I am glad Liverpool continues to win, sometimes I feel uneasy when Liverpool steals 3 points after yet another late from Roberto Firmino. It is impossible to win every game in a calendar year without at least some good fortune. Naturally, I began to wonder if there was a way to quantify this. What is the probability that Liverpool actually deserves to be where they are in the table?
Fortunately, this question is not limited to soccer. For example, a hockey website called MoneyPuck.com features a ‘Deserve to Win O’Meter’, which strips out the luck inherent in each game and spits out the probability that either team will win based on their quality of play. Inspired by this idea, I wanted to quantify just how likely it is for Liverpool to currently be sitting at 73 points given the team’s expected goals generation relative to opponents.
xGoals in soccer
Similar to other sports, expected goals, or xGoals, measures the percent chance a specific shot will find the back of the net given the quality of shot. In soccer, this takes into account factors such as shot location, whether the shot was taken with a player’s dominant foot or head, or whether or not the shot came from a cross, corner, foul, or open play.
Notably, a penalty shot is converted upon 76% of the time and thus, if a team takes a penalty, they gain 0.76 xGoals. If a team was to miss on this chance, the actual score would lie at 0-0, while the xGoals score of the game would be 0.76-0. If another penalty is taken by the same team and they miss, again, the actual score would still be 0-0, while the xGoals score would jump to 1.52-0.
Knowing how xG works for penalty shots, we can calculate them for all shots by accounting for the factors mentioned earlier. This makes them useful on a game by game basis because every shot has an xG value, which lets us calculate a projected score given quality of chances.
Over the course of a game and even more a season, the expectation is for expected goals and actual goals to even out. Say a team takes 20 penalty shots throughout a season. While in one game they may fail to score on 2 such as the example above, over the course of the season, they will likely eventually regress towards expectation which is 15.2 goals off of penalties. However, teams such as Liverpool who are experiencing such a phenomenally unlikely season, likely can be deemed as “lucky” and will have actual goals higher than their expected goals.
Calculating the probabilities
To find the percent chance that Liverpool was to win each match they played, I found that the probability of variance between xGoals and actual goals scored for teams could be estimated using a normal distribution by conducting a Chi Squares Test. Through finding the variance between actual goals and xGoals for every Premier League game over the past 3 seasons, I was able to find the standard deviation for both home and away teams, and use this to build my normal distribution for both team’s scores.
The plan was to declare team A the winner when they had a higher distribution at a particular score, and team B the winner when they had the higher distribution. Additionally, recognizing the potential for draws, I created a range around the point of intersection between the two distributions in which games would be called an expected draw by the model. To calculate the width of the “draw range”, I found the average difference in expected goals between teams in which the game ended in a draw over the past 3 Premier League seasons. To validate this number, I compared sum of the odds a game ended in a draw to the actual draws this season and found results to be very similar. Once this “draw range” was found, I ran a script in excel using solver to find the point of intersection between the two distributions before applying the range and assigning probabilities that each team wins as demonstrated in the graphic below. Note probabilities of each result are calculated using the cumulative area under the normal distribution graph of whichever team has the highest xGoals in the game.
Results
Calculating the probability of Liverpool holding a record of 24 wins, 1 draw and 0 losses this season in 23 games played reveals there is a great deal of luck associated with a winning sort of such. In fact, the odds of holding this record based on the calculation process above is only 0.00001067% or roughly 1 in 9.37 million. This low percentage is largely in part to Liverpool only deserving to win (win over 50%) 13 games and having been out chanced according to xGoals in 4 of their games.
These 4 games include games against Southampton (deserve to win 22% of the time), Chelsea (30%), Manchester City (31%) and Wolves (23%). In week 2, Liverpool allowed only 1 goal despite giving up 9 shots from within 12 yards and 3 from within 6 yards in a 2-1 victory over Southampton. Against Chelsea, Liverpool scored 2 before the 30th minute before letting score effects take over, only registering 1 shot in the second half to Chelsea’s onslaught of 9. However, Liverpool held on for a 2-1 victory. In a highly anticipated clash at Anfield against Manchester City, Liverpool again came away with a victory in a game where they had a lower xGoals. After a controversial handball was turned up the field leading to an early goal, Liverpool scored a quick second within 12 minutes before holding on to win 3-1. Finally, last week at Wolves, Liverpool gave up 5 chances from within 12 yards including three with a 0.3 xGoals or higher but were once again bailed out by a late Roberto Firmino winner to walk away with a 2-1 victory.
What is even more surprising about Liverpool’s record is they aren’t even the team that is most likely to hold it given xGoals generation. Manchester City, despite sitting 22 points back of Liverpool, had a 0.0002881% or approximately 1 in 347,000 of having 73 points at this point in the season. This is 27 times more likely than Liverpool given their expected goal generation due to deserving to win (win over 50%) in 17 of 25 games this season and only being out xGoals twice this season.
Expanding the results
After pulling all the data for Liverpool and Manchester City, I realised scaling this project to evaluate xGoals performance for all teams across the league would not be difficult. Through multiplying the chance of a team winning by 3, and chance of a team drawing by 1, I calculated the ‘points deserved’ from each game and built standings. The results revealed were quite surprising.
At the top of the table, Man City is currently sitting at 51 points which is quite close to where they should be given their expected goal generation relative to opponents. It is Liverpool though that sits atop the table in reality with 24.32 more points than they should have given their performance. Additionally, Leicester now sits in a Europa League spot, 2.25 points back of Man United despite holding a 14 point cushion over United in reality.
Down the table, both Watford and Norwich have jumped out of the relegation zone with 9.14 and 9.11 points less than deserved respectively. Meanwhile, Newcastle drops to the bottom of the table with only 20.93 deserved points, 10.07 less than the 31 they actually have.
Notable games
Most Deserving Win - Man City vs Watford
In a rematch of the FA Cup final from last year which saw City win in dominating fashion 6-0, Watford put up a similar performance losing 8-0 to Manchester City. Conceding 5 goals and 2.8 xGoals within the first 18 minutes, City continued to dominate taking 20 shots from within the box and 28 total to Watford’s 5 total while holding 70% possession despite the early lead. The result was the most deserving victory of the season as City deserved to win 99.84% of the time.
Least Deserving Draw - Man City vs Tottenham
Of the top three least deserving draws of the season, City lead in xGoals in all 3. A week 2 clash with Tottenham saw City pepper the goal with 30 shots throughout the night, 22 of which were within the box good for 3.2 xGoals. However, City only scored twice. Meanwhile, Tottenham registered 3 shots all night; a shot from well outside the box against an out of position Ederson – goal, a header from the corner of the 6 yard box off a corner – goal, and a Harry Kane shot from well beneath half – well wide. Good for 2 goals off of 0.07 xGoals and a draw in a game that City deserved to win 89.39% of the time.
Least Deserving Win - Man City vs Tottenham
Notice a trend yet? This past Saturday, Tottenham again stole points off Man City. Early on, Man City dominated earning 3.03 xGoals, including a missed penalty, before Tottenham registered a shot. However, after a red card from Zinchenko in the 60’, Tottenham quickly tallied 2 off of 3 shots and only 0.43 xGoals before holding on to win 2-0 in a game City deserved to win 85.35% of the time and Tottenham deserved to win only 2.95% of the time.