Multiple models are designed to quantify the efficiency of passes within a football match, to name a few:
Dangerousity (based on change in goal-scoring probability) (Link et al. 2016),
Risk-Reward Model (based on difficulty of a pass vs likelihood of a goal) (Power et al., 2017).
All passes that 'create space' but are not forward (direction of play) will contribute negative to these measures, which is debatable. Robert Rein, Dominik Raabe, Daniel Memmert (2017), therefore, introduced a Space Control Model as a quantitative measure for pass effectiveness.  They compared two approaches on calculating the efficiency of a pass. Their expectations regarding increased chances of winning a game when average increases in space dominance or number of outplayed defenders is greater were confirmed.
The first method is regarding to changes in space dominance due to passing behaviour. Combining passing event information with space dominance using a Voronoi-diagram (figure 1).  Rein et al. computed pass effectiveness based on the change in space control in the final third of the field between the moment of the pass and the moment of the subsequent reception using Voronoi diagrams.
The second method was counting the number of outplayed defenders as a measure of pass effectiveness (Duarte, Araujo, Freire, et al., 2012; Silva et al., 2014). 

Traditionally, investigations of passing behaviour in elite soccer are based on notational analysis approaches focussing on variables like passing frequencies or passing streak lengths and their correlation with overall game performance (Carling, Williams, & Reilly, 2005; Hughes, 2003; Hughes & Bartlett, 2002; James, 2006; Mackenzie & Cushion, 2013).

The results showed that the number of penetrative passes was positively correlated with scoring opportunities (compare also Tenga, Holme, Ronglan, & Bahr, 2010). The key idea behind penetrative passing is for the attacking team to achieve a positional advantage over the defending team. Thereby, a positional advantage can be interpreted from two different perspectives. 

Either -the attacking team tries to establish a majority situation in front of the goal by outplaying as many defenders as possible or  -the attacking team tries to position the ball to control critical space in front of the goal leading to goal scoring opportunities (Duarte et al., 2012; Silva et al., 2014).

The defenders thereby try to prevent exactly this situation from occurring (Olthof, Frencken, & Lemmink, 2015; Vilar, Araújo, Travassos, & Davids, 2014).

Main quantitative information is the number of outplayed opponents. Additional calculation is based on the respective distance between the involved players A1 and A2 and their closest opposing players B1 and B2.

Figure 2: pass efficiency

Assessing the effectiveness of a pass
The effectiveness of a pass can be assessed by investigating the changes in space control exerted by the attacking team. Pollard, Ensum, and Taylor (2004) found that the odds of scoring from within the penalty area more than double if the attacker is more than one meter away from the nearest defender (Vilar et al., 2014). Consequently, passes which increase the attacker’s space control in front of the goal can be ranked as effective passes. This leads to variations of the Voronoi diagram. 

Method one: Voronoi-diagram
Regarding changes in space dominance due to passing behaviour we combined passing event information with space dominance using a Voronoi-diagram approach.

The football pitch was divided into three regions of interest: defensive third, mid-field, attacking-third. Passes were classified according to their origin and target. For the present analysis only passes from the defensive third into the mid-field, passes within the mid-field, passes from the mid-field into the attacking third, and passes within the attacking-third were analysed. To obtain a measure of the passing efficiency, they linked passing behaviour and space control using Voronoi-Diagrams

Voronoi diagram The Voronoi diagram is based on a tessellation of the soccer pitch into individual cells according to the (x,y)- positions of the players. All locations contained within a given cell are closest to the respective player compared to all other players and are therefore assumed to be controlled by this player. By accumulating the cells associated with the teams, the total area dominated by the team can be estimated:

In summary, the results suggest that assessing passing efficiency with respect to changes in space control in the attacking third as well as regarding the number of outplayed players provides a valid measure to investigate successful game performance in elite soccer. (Rein, Raabe 2017).



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