The Value of Goals
It is a commonplace in football to evaluate players’ psychological strength by their performances against stronger teams or how they perform in finals. Some superstars are sometimes criticized for not being able to show leadership during challenging times and not scoring enough in big games.
Another essential debate in football is evaluating players’ adaptability to a stronger team with a different playing style. How a player who showed outstanding performance in a relatively weaker team that plays counterattack would perform in a stronger team that plays mostly against defensive teams that await the opponent with ten men behind.
To better grasp these issues, I tried to establish a metric that can show the values of goals. For this, I used the sample of La Liga 2021/2022 and how Real Madrid’s players performed this season.
Real Madrid scored a total of 80 goals this season in La Liga. Benzema scored 27 goals, 17 from Vinicius Jr., 10 from Asensio, and the rest of the team scored 26 goals. What I wanted to evaluate was the values of these goals. Some metrics measure the importance of a goal by assessing the minute it was scored. Some measure goals by if it was a leading goal or just the fifth goal in a 4-0 game. Some metrics compare xG with goals scored to understand players’ ability to finish.
I wanted to differentiate goals that have been scored against Barcelona (finished at the second position) and Alaves (finished at the bottom). Every team has a different strength, and we need to be able to differentiate goals that have been scored against stronger teams and weaker teams.
First, I wanted to decide the strength of every team at the table. Bear in mind that every statistical decision is a trade of some information with others. Therefore, whichever metric we use can only measure some aspects of reality.
I decided to evaluate the strength by sheer performance, or more accurately, points that a team has collected. I took the possible points to be collected as my denominator and points actually collected as my numerator. Therefore 38 games with a maximum of 3 points in each game would make 114 maximum points. For instance, Barcelona collected 73 points this season, and their strength equals 73/114 = 0.6403509. Alaves at the bottom of the table collected 31 points, and their strength is 31/114 = 0.2719298. I excluded Real Madrid from this table since I wanted to measure Real Madrid’s goal scorers, and here is the table of strength for La Liga this season:
This table is the same as the league table, with teams’ strengths assigned to a value between 0 and 1. Now for measuring the value of goals, I wanted to transform the teams’ strengths into the value of goal that has been scored against these teams. For doing that, I used the median. The median of the teams’ strength is 0.4035088. That’s the strength of Celta Vigo, the team in the middle of the table. I wanted to assign 1 goal value to an actual goal that has been scored against Celta Vigo since they represent the median value of La Liga (when we exclude Real Madrid).
We need to do the following: 1/0.4035088 to find our multiplier, which is 2.478261. This also means if we had an ideal team that collected all the possible points, scoring against them would have the value of 2.478261 goals. If we had a terrible team that collected zero points, scoring against them would not give you any goal value. Therefore, if we multiply this number by the team’s strength, we can see the value of goals against each team.
According to the new table, scoring 1 goal against Barcelona would have the value of 1.5869567, and scoring against Alaves would be counted as 0.6739130 goals. Now we have values of scoring against each team. Let’s take a look at Carvajal and Bale. Each player scored only one goal this season. Carvajal scored his goal against Real Betis, whose goal value is 1.4130435, whereas Bale’s only goal was against Levante, which is 0.7608695. While it looks like they scored an equal amount of goals, Carvajal’s goal was much more valuable when considering the opponent’s strength.
To be fair, these small numbers tend to misinform us. There are many more variables to evaluate players, and this variable only evaluates the values of two specific goals in this example. Additionally, in this particular measurement, we do not consider how many minutes the player played, how many chances he got, and so on. We measure the value of the goals, not the players.
More significant numbers can give us a better understanding of the value of goals and goal scorers. For this purpose, I grouped Real Madrid players into four categories. Benzema with 27 goals, Vini with 17 goals, Asensio with 10 goals, and the rest of the team with 26 goals. I did not take other players as individuals because their numbers of individual goals were fairly low. Each goal is multiplied by the value of the opponent team’s conceded goals. For instance, Benzema’s 3 goals against Alaves give him only the 2.0217391 goal value. Almost as if he did not score one of his goals. At the same time, his 2 goals against Sevilla give him the value of 3.0434785, which means we assign an extra value of one goal to his total. Here is the table:
For a larger table click here.
The first thing that strikes the eye is Benzema’s goal values are almost equal to his goals. Therefore, we can think that Benzema’s actual goals are almost equally distributed (it can be seen in the table).
Asensio scored only 3 goals against the first half of the table and 7 goals against the second half. Since his goals were not distributed equally, the values of his goals are equal to 9.6956527.
In other words, Asensio’s goals are %3.04 less valuable than their actual number. This value is %0.32 for Benzema. For Vinicius Jr., we have a more dramatic decline. His goals are %7.92 less valuable than their actual value. Finally, all the other players scored a total of 26 goals for Madrid this season, and their goals’ value equals 27.2826103. This means all the other players scored %4.93 more valuable goals for Madrid. Therefore, they mainly scored against stronger teams. You can see how the distribution of the goals differs from the values of goals in the tables.
We can assume that Madrid immensely benefited from their other players against stronger teams. This might suggest relying more upon set pieces against stronger teams or using the element of surprise for big games or any other meaning that requires additional data to decide. Or, you know, watching the games again.
What about Vinicius Jr., though? For me, his numbers are the most different from what I see on the pitch. Does Vini score more manageable goals, or does he disappear in the big games? That does not make sense to me for one simple reason. Vini is great at exploiting open spaces. Additionally, his first touch is not the best to perform effectively in narrow spaces. Therefore, I would have expected him to score more against stronger and less against parking-the-bus teams.
I rewatched his 5 goals against stronger teams. He scored those goals against Sevilla, Real Sociedad, and Valencia outside his usual style. However, his goals outside of La Liga against Barcelona and Manchester City were exactly how I remembered, exploiting the open spaces. His goals against weaker teams are very sensational. He is always on the run, even in small spaces. Therefore, he expects to receive the ball rather than starting the possession, unlike Salah or Son. It can sound like a disadvantage, and it is, in a way. However, he is still young, and he has time to improve. We cannot conclude that a lower value of goals is terrible for a player. Nonetheless, Vini has to improve his performance against stronger teams, without a doubt.
The value of goals can be an interesting metric to investigate more. Additionally, distribution tables could have been a critical concomitant to it. When a strong team buys a player, it can be an excellent measurement to see how the player performs against weaker and more defensive teams. When Real Madrid is interested in a weaker team player, it might be beneficial to know how the player performs against the weaker teams by looking at the goal distribution. When an attacker moves to a bigger team, the most considerable doubt about them is how well they utilize the narrow spaces. The distribution to the left in the table can give us some helpful information. However, a player from a weaker team with a positive value in their goals and goal value comparison could introduce problems for a big team. Benzema has almost perfect distribution and is a complete player on the pitch. However, it is fair to expect the values of goals to be lesser than actual numbers since it is expected to score more against weaker teams. How much difference is acceptable, then? This question requires much more data to decide what the norm is.
The value of goals can be a useful measurement in football stats. However, it is just an idea. It is open to revisions, suggestions, or complete refutations. If you have anything to add, please let me know to improve.