Understanding passing network characteristics and their link to match outcome in elite Netball

Figures & data

Table 1. Sport specific network metric definitions.

Network Metric	Common name	Definition
Edge count	Effective passes	The total number of interactions between players on a team, achieved via effective passes of the ball.
Edge density	Pass density	The number of connections between players in a team achieved through made passes, in proportion to the total number of possible connections. Range is associated with team size (n=7 in Netball).
Betweenness centrality	Link centrality	The number of players that act as a link along the shortest path between any two other players in the same team, in proportion to the total possible number. When a team’s betweenness centrality value is high, a large proportion of passing sequences, are dependent on a relatively small number of players. Range = 0–1
Degree centrality	Pass centrality	The sum of the differences between the player with the maximum total of passes made and received, and the total number of passes made and received by all other players in the team. This is then divided by the maximum possible sum of differences. A team has high degree centrality when one player is more prominent than all other players in the team. A team has low degree centrality with a more even contribution between players.
Eigenvector centrality	Key player centrality	The dependence of a team on a relatively small group of players that have a large number of interactions with a large number of other players. Teams with a more even contribution from players will have a lower eigenvector centrality. Range = 0–1
Reciprocity	Mutual connectedness	The proportion of players in a team who both give and receive possession to one another. Range = 0–1

Figure 1. Boxplot of pass density for each team in the SSN competition grouped by match outcome. The horizontal line represents the median, the box represents the interquartile range and the whiskers, the range.

Figure 2. Boxplot of link centrality for each team in the SSN competition grouped by match outcome. The horizontal line represents the median, the box represents the interquartile range and the whiskers, the range.

Figure 3. Boxplot of pass centrality for each team in the SSN competition grouped by match outcome. The horizontal line represents the median, the box represents the interquartile range and the whiskers, the range.

Figure 4. Boxplot of key player centrality for each team in the SSN competition grouped by match outcome. The horizontal line represents the median, the box represents the interquartile range and the whiskers, the range.

Figure 5. Boxplot of mutual connectedness for each team in the SSN competition grouped by match outcome. The horizontal line represents the median, the box represents the interquartile range and the whiskers, the range.

Table 2. Summary table of main effects and interactions for each teamwork characteristic. *Two-way ANOVA results. The effect size is based on the generalised eta squared; 0.02 (small), 0.13 (moderate), 0.26 (large).

Teamwork Characteristic	Factor	F	p-value	Effect size
Link centrality	Team	1.08	.38	0.07 (small-moderate)
	Outcome	2.01	.16	0.02 (small)
	Team:outcome	1.06	.39	0.06 (small)
Pass centrality	Team	12.06	<.001	0.48 (large)
	Outcome	7.61	<.01	0.07 (small-moderate)
	Team:outcome	0.41	.87	0.03 (small)
Key player centrality	Team	3.04	<.01	0.19 (moderate)
	Outcome	0.93	.38	0.01 (small)
	Team:outcome	1.42	.21	0.08 (small-moderate)
Pass density	Team	12.04	<.001	0.47 (large)
	Outcome	65.09	<.001	0.41 (large)
	Team:outcome	.09	.99	0.01 (small)
Mutual connectedness	Team	13.38	<.001	0.50 (large)
	Outcome	2.46	.12	0.03 (small)
	Team:outcome	0.31	.93	0.02 (small)

Table 3. Multiple linear model for all teamwork characteristics. The estimates include 95% confidence interval within parentheses. *=p < .05, **=p < .01, ***=p < .001. Std = standardised.

Predictors	Estimated Regression Coefficient	Std. Beta	t- statistic	p-value
Intercept	0.00 (−0.00)	−0.00 (−0.10–0.10)	0.00	1.000
Link Centrality relative	−19.13 (−0.08)	−0.08 (−0.18–0.02)	−1.58	0.116
Pass centrality relative	−1.07 (−0.21)	−0.21 (−0.34 – −0.07)	−3.03	0.003
Pass density relative	6.06 (1.03)	1.03 (0.90–1.15)	16.11	<0.001
Key player centrality relative	33.32 (0.18)	0.18 (0.06–0.30)	3.08	0.003
Mutual connectedness relative	−48.23 (−0.31)	−0.31 (−0.45 – −0.17)	−4.36	<0.001
Observations	54
R^2 /R^2 Adjusted	0.757/0.731

Table 4. Playing positions in netball and their court restrictions.

Playing position	Abbreviation	Court restrictions
Goal Keeper	GK	Allowed in the defensive goal third and shooting circle
Goal Defence	GD	Allowed in the defensive and centre thirds, and the shooting circle
Wing Defence	WD	Allowed in the defensive and centre thirds, but not the shooting circle
Centre	C	Allowed in all thirds, but not in either shooting circle
Wing Attack	WA	Allowed in the attacking and centre thirds, but not the shooting circle
Goal Attack	GA	Allowed in the attacking and centre thirds, and the shooting circle
Goal Shooter	GS	Allowed in the attacking goal third and shooting circle

Figure 6. A case study example of the passing networks of two teams in a match. the nodes represent players, labelled by playing position and their size provide an indication of the number of passes a player has been involved in. The location in which the players are placed in the graph represents how central a player is to a team’s passing network. The thickness of the lines between the nodes represents the relative number of passes between the players. GK = goal keeper, GD = goal Defence, WD = Wing Defence, C = centre, WA = Wing attack, GA = goal attack, GS = goal Shooter.

Table 5. Network metrics for the teams that appear in Figure 6. See Table 1 for the definitions of the network metrics.

Network Metric	Winner	Loser
Pass density	10.57	9.74
Pass centrality	7.89	7.01
Link centrality	0.05	0.07
Mutual connectedness	0.46	0.50
Key player centrality	0.34	0.23