Ajax vs PSV

How Height Is Linked to Set Pieces Efficiency in Football Matches

Set pieces were traditionally employed from managers to help their under-technical teams avoid relegation. Nowadays, set pieces are a characteristic of almost every club, constitute a large proportion of goals scored throughout a season and, as a result, hold a significant role to a team’s performance.


The aim of this research is to define whether height of a team actually aids its performance in dead ball situations. Set pieces are an important aspect of modern football and two Dutch teams that rely on them, PSV Eindhoven and Ajax, were examined for the needs of the report. Apart from a first statistical approach and a comparison between them, a forecasting model was also implied to observe in depth the relationship between height and set pieces.

Methodology and Data Collection

Data was obtained from season 2013/2014 up to 2016/2017, abbreviated with the first year in the graphs. For instance, season 2016/2017 is displayed as 2016. Results from current season were not taken into account. For the analysis of Dutch teams, only Eredivisie matches were examined, while European matches as well as Cup matches were excluded from the purpose of the research. At this point, it needs to be mentioned that set pieces consist only of corners and direct free kicks; no penalty kicks and indirect free kicks were accounted for.

For the calculation of the height two different approaches were made. Regarding the conceded goals, the height of the team was derived as the average height of the 14 players with the biggest number of appearances in the league (“defensive height”). On the other hand, the average height of the team in terms of scored goals (“offensive height”) was again derived from the 14 players with the most appearances, but this time goalkeepers were removed.

Comparison Between Ajax and PSV Eindhoven Strength in Set Pieces

Ajax as well as PSV Eindhoven are one of the biggest football clubs in the Netherlands in terms of history and titles. Even though they do not perform as well as they used to in European Competitions, they are always considered as league title challengers and try to thrive against their opponents. In order to achieve that, both of these teams heavily rely on set pieces, as there are no few occasions that they actually had taken the three points with a header from a corner or from a direct free kick.


The graphs illustrate that PSV scores more goals than Ajax from dead ball situations and exploit their advantage to achieve victories. It is interesting that in season 2014/2015 and 2015/2016, where PSV ability to score from set pieces was at its maximum level in this 4 year era, have actually managed to win the championship. On the other hand, during 2013/2014, where they only managed to score 9 goals, PSV had finished in the 4th position.

In contrast, Ajax was more stable during this period, with small deviations between scoring and conceding goals from set pieces. This is reflected also in their league performance, having finished only as champions or as runners up in the worst case scenario.

Correlation between Height and Goals

In order to determine the relationship between height and efficiency in attacking and defending set pieces, Spearman´s correlation was employed. Spearman’s rank correlation coefficient (rs) is a non-parametric measure of rank correlation. In other words, it assesses how well the dependence between two variables can be described using a monotonic function. A perfect Spearman correlation of +1 or −1 occurs when each of the variables is a perfect monotone function of the other.

Intuitively, Spearman’s correlation between two variables will be high (close to 1 or -1) when observations have a similar rank, and low (close to 0) when no statistical linear relationship between the two variables is presented.

The Null Hypothesis H0 implies that there is no significant linear correlation between the two variables (goals and average height). The confidence interval is taken to be 90%. Results are shown in Table 1 below.

 Scored: rs/p-valueConceded: rs/p-value
PSV 0.737/0.263-0.9486/0.0514

Scored goals do not seem to have a strong dependence on the average height of a team. Surprisingly, in the case of PSV height acts as a limiting factor to the scoring efficiency of the club. However, Eindhoven’s increase of squad height when it comes to defend in set pieces has an rs value of -0.9486 with a corresponding p-value of 0.0514. Therefore, in the above mentioned confidence interval, the null hypothesis is rejected and the two parameters have a strong linear dependence. The minus sign shows that this monotonic correlation is inversely proportional.

Modelling and Predictive Analysis

Furthermore, a simulation of PSV defence in set pieces was examined in the report. The analytic tool that was used was regression analysis.

Regression analysis is used in stats to find trends in data and quantify them. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed.In this way predictions about a specific event could be made.
The fitted result of the regression analysis, with b0=8.06 and b1=-4.34, is shown in the following graph. The linear model extracted has an R squared value around 0.989, meaning that the model can be fairly confident in forecasting.

Taking into account that PSV had already conceded 5 goals from set pieces this season, the model implies that the next 20 goals that will be scored against them will not come from corners or direct free kicks. PSV has conceded 26 goals so far this season, so unless something dramatically changes in their performance, one can predict that the overall number of goals from set pieces will be close to 5.


Overall, a statistical analysis of two Dutch teams was performed in order to observe their strength in defending as well as in attacking set pieces. Results had shown that there is a strong linear dependence of PSV Eindhoven’s average height when it comes to conceding goals from set pieces. A model was implied so that predictions for the current season could be made, having as a result that it is highly possible that PSV will not concede a goal from corners or free kicks for the remaining 9 matches in Eredivisie.


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As an engineer I have learned that it is not only about deriving the result but also explaining it. In Statathlon I found the unique opportunity to combine mathematics with my other passion, football, and strive to describe the phenomena that rule it.

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