Fig 1.
Transitions between the phases of play within games 1 and 2.
The nodes represent the phase of play for the home team (blue for attack, green for defence and grey for out-of-play), the edges (in red) indicate the transition and the arrows indicate the direction of the transition. The weights on the edges represent the proportion of each transition out of all transitions that take place across the two matches analysed. The total cumulative time spent within each phase of play (in minutes) is listed with each phase.
Fig 2.
The distribution of the duration individual segments of play (i.e. ‘plays’) in each phase (Attacking, defending and out-of-play) across both games.
Fig 3.
Demonstration of the steps for binning the player movement vectors for the calculation of the collective entropy Hgroup.
Starting with the series of movement vectors for each player for each time step within the window (in this example 3), depicted in (A), the movement vectors are transformed so that each vector starts at the origin (0,0), depicted in (B). These transformed vectors are designated to a 2-dimensional bin, depicted in (C), allowing for the calculation of P(xij) for all bins.
Fig 4.
Density plots for polarisation, angular momentum and mean group speed.
(A) Density plot for paired angular momentum (mgroup) and polarisation (pgroup) values, with the divisions of the order parameter space overlayed in red, indicating the polar (p), swarm (s), milling (m) and transitional states. (B) Density plot for paired mean group speed () and polarisation (pgroup) values.
Fig 5.
(A) Density plot for paired group entropy (Hgroup) and mean group speed () values and (B) paired surface area (Agroup) and mean group speed (
) values.
Fig 6.
(A) Density plot for paired values of group entropy (Hgroup) and polarisation (pgroup), and (B) surface area (Agroup) and mean group speed () as.
Fig 7.
Density plots for paired angular momentum and polarisation across the attacking (A), defending (B) and out-of-play (C) game phases from both games.
The divisions of the order parameter space overlayed in red, indicate the polar (p), swarm (s), milling (m) and transitional states.
Fig 8.
Survival curves for the durations spent in the polar, swarm and transitional collective states in the (A) attacking, (B) defending and (C) out-of-play game phases.
These plots provide insight into the collective state structure within each game phase.
Fig 9.
Density plots for paired group area (Agroup) and polarisation (pgroup) values across the attacking (A), defending (B) and out-of-play (C) game phases.
Fig 10.
Density plots for paired mean group speed () and polarisation (pgroup) values across the attacking (A), defending (B) and out-of-play (C) game phases.
Fig 11.
Density plot for paired angular momentum (mgroup) and polarisation (pgroup) values across the collective state transitions.
(A) Transition from the swarm to polar state, (B) transition from the polar to swarm state, (C) transition from the polar to polar state and (D) transition from the swarm to swarm state. The quivers overlayed on each plot indicate the mean direction of movement in the state-space for time series points that lie within each bin. The divisions of the order parameter space overlayed in red indicate the polar (p), swarm (s), milling (m) and transitional states.
Fig 12.
Player position traces and order parameter time series plots for an exemplar polar to swarm transition.
The blue, green and red sections of the traces denote the segments of the transition spent in the polar, transitional and swarm states respectively in all plots. (A) The position traces for all players (excluding the goal keeper) across the transition period. (B) The position trace for the centroid (mean position) of the team. (C) The plot of polarisation (pgroup) time series for the team across the transition period. (D) The plot of the mean group speed () time series for the team. (E) The plot of the of group entropy (Hgroup) time series.