Generation of threat: crediting football players for creating dangerous actions in an unbiased way

A.1: Selected games

In the same spirit as Section 4, we choose a collection of games where the formation is the same and starting lineup is as stable as possible. Table 8 shows the selected matches for Stade Rennais. The team plays in a 433 formation in all of these games but the starting 11 is not always exactly the same. In fact, some players are sometimes rotated for a game or two, but we assume that the substitute behaves approximately the same as the starting player. Stade Rennais line up as follows in the selected games, where the main player in each position is in bold:

1. Gomis/Alemdar

2. Traore – Omari/Bade – Aguerd/Bade/Santamaria – Truffert/Meling

3. Majer – Santamaria/Martin – Tait

4. Bourigeaud – Laborde/Guirassy – Terrier

We construct a 12-dimensional counting process from the selected Stade Rennais games regardless of the players starting. We use the data from each game as long as the 11 players on the pitch correspond to the scheme provided above. We then fit a 12-dimensional Hawkes process and associate the estimated metrics of each position with the main player occupying it.

Figure 7:

Graph summarizing the interactions between Stade Rennais players. The width of an arrow from player p₁ to player p₂ is proportional to the expected number of touches of player p₂ generated by one touch from player p₁. The size of the circle of player p is proportional to the sum of the arrow sizes received, indicating the involvement of the player in the considered games. The color of the circle represents the GoT ⁱ index for each player.

A.2: Results and discussion

In Table 9, we rank the Stade Rennais players with respect to generated threat metrics. Figure 7 graphically represents the direct interactions between them and Figure 8 displays the estimated branching matrix. We can see that the team adopts a 433 shape that progresses mainly through the wings. The danger creation is asymmetric with more combinations occurring on the right side, where Majer is the most creative midfielder. Interestingly, despite being a central midfielder, Flavien Tait delivers a large value of GoT 90 ( i n d ) , indicating that he is a significant contributor to the team’s offensive efforts. In contrast, although Santamaria has more possession, he has limited involvement in creating threats. This difference in their threat generation can be attributed to their distinct roles on the field. On one hand, Tait is a more box-to-box midfielder who frequently projects forward and has a considerable direct threat metric. On the other hand, Santamaria belongs to a class of defensive midfielders who act as anchor points. They participate in the buildup close to the center backs and have limited interactions with the forward positions.

The main threat sources are Bourigeaud, Majer, and Terrier. These three players are outstanding going forward. Terrier is the leader of the team in goalscoring and ranks third in Ligue 1 but seems to be involved in danger creation as well. Bourigeaud generating the most threat is not surprising since he is the creative force of the team. In fact, he ranks first in the league in terms of key passes with 3.2 per game, and first in accurate crosses with 104 in the season.

Figure 8:

Estimated branching matrix for Stade Rennais.

As expected, the center backs have zero direct threat contribution. However, in terms of indirect threat per 90 min  GoT 90 ( i n d ) , Aguerd and Omari rank fourth and sixth in the team respectively. The pair generates danger through their involvement in team build-up and possession. In particular, Aguerd and Omari are comfortable with the ball at their feet and rank eighth and twentieth in the league, respectively, in the number of passes per game with high success rates.

Finally, we can observe from Figure 7 some remarkable circuits that lead to dangerous situations. These patterns of play should be taken into account by an opposing team when facing Stade Rennais:

1. Aguerd → Truffert → Terrier → Threat.

2. Terrier → Tait → Threat. Terrier is highly effective in generating direct threats, but he also frequently combines with Flavien Tait to create danger. Similarly, Bourigeaud often gives the ball to Lovro Majer to generate indirect threat.

3. Omari → Traoré → Bourigeaud → Threat.

4. Omari → Bourigeaud → Threat. This is a straightforward pattern from defense to attack that should be controlled. Omari is highly successful in progressing the ball, both through slow build-up play by passing the ball to the right-back Traoré, as well as through fast transitions with direct passes to Bourigeaud.