Identifying positional advantage in tennis by examining interpersonal coordination

When Federer hits the ball cross-court to Nadal’s backhand, he will then begin to move to a position where he thinks Nadal will hit his next shot. As Federer moves laterally in one direction, there is a good chance Nadal will also move laterally, either in the opposite direction or the same direction. Likewise, if Federer decides to approach the net, in an attempt to gain an advantage in the rally, Nadal will react by moving to a position that will allow him to return the subsequent shot.

The coordination between each player’s movements is referred to as interpersonal coordination.

Joao Carvalho and colleagues developed a model that predicted positional advantage during a rally and identified when there was a rally break (i.e., when the coordination between players becomes unstable).

The study

27 rallies from 3 professional tennis rallies were examined. All rallies started with the players positioned behind the baseline, with no positional advantage for either player. Additionally, all rallies featured a rally break, whereby the stability of the coordination between the players was altered due a specific shot, which ultimately led to a point being won.

The model

Here is a basic description of the model.

The player’s lateral and longitudinal displacements were tracked. Lateral displacement referred to the distance from the centre of the court. Longitudinal displacement refereed to the distance from the net.

These displacements were then used to create a single value that described a position on the court. A weighting system of 2:1 (lateral:longitudinal displacement) was used to calculate this value. This value was referred to as the PA index (i.e., the positional advantage index).

Testing the model’s accuracy

Expert tennis coaches identified when the rally break occurred in each rally. The model was then tested to determine whether it also predicted the same rally break.

It was evident that the model accurately identified rally breaks, as the PA index increased considerably after this moment in the rally.

What can the model tell us?

The PA index provides an objective measurement of which player has the positional advantage in the rally.

Results suggested that a PA index of close to 0 represents no positional advantage for either player (i.e., the player’s are moving in sync with one another). As the PA index moves above or below 0, one of the player’s is considered to have the upper hand in the rally. And when the PA index reached a critical value, one player was in a position to make the attacking shot in an attempt to win the point.

Practical implications

The PA index can highlight a player’s ability to attack or defend in specific situations. For example, a high PA index might represent an opportunity to attack. But this will only occur if the player is capable of attacking. Alternatively, the PA index can be used to identify player’s who have an incredible ability in reversing a situation when they are in a defensive position. Coaches can use this information to guide training.


Carvalho, J., Araújo, D., Travassos, B., Esteves, P., Pessanha, L., Pereira, F., & Davids, K. (2013). Dynamics of players’ relative positioning during baseline rallies in tennis. Journal of sports sciences31(14), 1596-1605.

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