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Edited by: Pietro Avanzini, University of Parma, Italy

Reviewed by: José Afonso, University of Porto, Portugal; Enrique Ortega, University of Murcia, Spain

This article was submitted to Movement Science and Sport Psychology, a section of the journal Frontiers in Psychology

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

In volleyball, each team must use no more than three hits to return the ball to the opponent’s court. This unique aspect of volleyball means that playing actions can be grouped into different complexes, mainly based on the initial defensive action. The purpose of this study was to find out which game complexes are most common in women’s volleyball and how those phases are sequenced. The study analyzed 4,252 complexes from 1,176 rallies or points (seven matches, with 27 sets in total) in the 2015 and 2016 Copa de la Reina. The variables analyzed were the game complex, complex efficacy, and number of complexes per point. Two Markov chains were defined to visualize how the complexes are sequenced. The first chain looked only at categories of the game complex variable, taking seven states and 24 transitions into consideration. The second chain combined the game complex and complex efficacy variables, taking 26 states and 125 transitions into consideration. These chains provide practical information regarding which sequences of complexes occur most frequently in the competition analyzed, and therefore which ones should be the main focus in training sessions. The most frequent sequence was Complex 0 (the serve), followed by Complex I with in-system attack, followed by Complex II without continuity.

Volleyball is a sport in which two teams compete against each other from opposite sides of a court divided by a net. The objective is to send the ball over the net and make it touch the floor in the opposite team’s court. Each team can use up to three hits (excluding the block and a consecutive contact at the first hit of a team) to send the ball over the net. The official rules published by the

Initially, when the old

Specialized theoretical literature on volleyball that diagrams the sequencing of game actions (e. g.,

Various researchers recently addressed this shortcoming by using social network diagrams and measuring eigenvector centrality to analyze the connections between game complexes in elite women’s and men’s volleyball (

We analyzed 4,252 game complexes from 1,176 points in two matches (six sets) in the 2015 Copa de la Reina (the Spanish national knockout cup competition in women’s volleyball) and five matches (21 sets) in the 2016 competition. The matches involved seven teams: CVB Barça, Feel Volley Alcobendas, Fígaro Peluqueros Haris, GH Leadernet Navarcable, Haro Rioja Voley, Naturhouse Ciudad de Logroño, and VP Madrid. All teams used a 5-1 offensive formation, a two- or three-player serve-receive pattern, and a player-back defensive system (

The

The

The variable for the

The two competitions were recorded using a digital video camera on a tripod located in the center of one of the stands situated at one end of the court. The recorded video files were played back using the sports video analysis software Kinovea v. 0.8.15 (Joan Chartman and contributors, Free Software Foundation, Inc., Boston, MA, United States) and the data were recorded in a Microsoft Excel 2013 (Microsoft Corp., Redmond, WA, United States) spreadsheet.

To analyze the reliability of the data, a set from one match in the sample was selected at random. The chosen set had 154 game complexes and 41 points. Two observers – both certified volleyball coaches – recorded data for the set. The first observer recorded the data, then did the same again 2 weeks later; the second observer recorded data only once. Before this reliability test, both observers trained for 2 h to familiarize themselves with the log sheet and the variables being studied. Agreement among the observations was estimated using Cohen’s kappa coefficient. The coefficient was greater than 0.97 for all three variables both in the comparison of the two observations by observer 1 and in the comparison between observers 1 and 2. In accordance with the scale proposed by

Firstly, a descriptive analysis was carried out for two variables: number of complexes per point and game complex. For the game complex variable, the confidence interval for a proportion (1-α confidence interval for π) was also calculated using the Wilson method.

Secondly, the relationship between the game complex and complex efficacy variables (and their respective categories) was studied using Pearson’s chi-squared test (χ^{2}), the corrected contingency coefficient (_{corr}), and adjusted residuals or Allison and Liker _{corr} < 0.30), moderate (_{corr} ≥ 0.30 and ≤ 0.70), or strong (_{corr} > 0.70) (

Finally, two Markov chains or state transition diagrams were constructed to show transition probabilities (_{ij}) between different game complexes. The first chain took complex efficacy into account; the second did not. According to

These transition probabilities (_{ij}) were calculated from two two-dimensional contingency tables, applying the following equation in each table cell:

where _{ij} is the frequency observed in the cell located in row _{xi} is the total frequency of row

All the statistical analysis was performed in Stata/IC v. 15.1 (StataCorp, College Station, TX, United States) and the Markov chains were performed in MATLAB v. 9.6 (The MathWorks, Inc., Natick, MA, United States). A significance level of 0.05 was used for all the statistical tests.

The mean number of complexes per point was 3.62, with a standard deviation of 1.78. Every point had from 1 to 13 complexes. The median number of complexes was 3 and the interquartile interval was 3–4.

The most frequent numbers of complexes per point were 3 (45.1%), 4 (16.5%), 5 (10.7%), 1 (9.5%), 2 (6.8%), and 6 (5.2%). Only 6.2% of the points had from 7 to 13 complexes.

As shown in

A descriptive analysis (absolute and relative frequencies) and inferential analysis (confidence interval for a proportion calculated using the Wilson method) of the game complex variable.

95% CI |
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Game complex | % | |||

Complex 0 | 1,176 | 27.66 | 26.33 | 29.02 |

Complex I | 1,064 | 25.02 | 23.74 | 26.35 |

Complex II | 711 | 16.72 | 15.63 | 17.87 |

Complex III | 680 | 15.99 | 14.92 | 17.12 |

Complex IV | 280 | 6.59 | 5.88 | 7.37 |

Complex V | 249 | 5.86 | 5.19 | 6.60 |

Undefined | 92 | 2.16 | 1.77 | 2.65 |

A significant moderate relationship was found between the game complex and complex efficacy variables (χ^{2} = 1,093.49, _{corr} = 0.59). Furthermore, eight significant positive relationships were found between categories of these two variables (adjusted residuals or

Relationships between the game complex and complex efficacy variables (adjusted residuals).

Game complex |
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Complex performance | Complex I | Complex II | Complex III | Complex IV | Complex V | Undefined |

No continuity | −22.95*** | 15.38*** | 10.03*** | 6.34*** | −8.77*** | 4.94*** |

No spike | –0.52 | –0.14 | –0.36 | 2.96** | –1.83 | 0.60 |

Out-of-system offense | 1.07 | –1.34 | 2.52* | –1.55 | –1.05 | –1.52 |

In-system offense | 23.39*** | −14.74*** | −12.68*** | −7.22*** | 11.46*** | −4.13*** |

Game-complex transition probabilities (without taking complex efficacy into account) shown in a Markov chain consisting of seven states and 24 transitions. K0, complex 0; KI, complex I; KII, complex II; KIII, complex III; KIV, complex IV; KV, complex V; UK, undefined complex.

Game-complex transition probabilities (taking complex efficacy into account) shown in a Markov chain consisting of 26 states and 125 transitions. 0, no continuity; 1, no spike; 2, out-of-system offense; 3, in-system offense.

The main objective of this study was to understand how game complexes are sequenced in women’s volleyball by analyzing them using Markov chains – a different approach from social networks. Although the structure might look identical, the information that a Markov chain (state transition diagram) provides is not exactly the same as what a social network (sociogram) provides. Both processes involve a series of dots, points, events, states, nodes, or vertices connected to each other by lines, arrows, transitions, edges, tiles, bridges, links, or connections. In sociograms, however, the size of the nodes tends to be modified to indicate the node degree (number of edges connected to a node) and the thickness of the edges tends to be modified to indicate the weight or “cost” of the connections in the network (

Regarding the number of game complexes per point, almost half of the points in the present study had only three game complexes each. This fact and the transition probabilities shown in the first Markov chain (

The analysis of the relationship between game complexes and their efficacy found that KI and KV were most closely associated with an in-system offense, whereas KII, KIII, KIV, and UK were most closely associated with no continuity. This may be because the defensive actions that initiate KI (receiving a serve) and KV (defending a free-ball) start further away from the net, thus allowing a longer reaction time than the defensive actions that initiate KII (defending an attack), KIII (defending a counterattack), KIV (defending an offensive block), and UK (defending an overpass spike or a joust).

The Markov chain in

There are two other important matters to consider regarding the first Markov chain, which did not take complex efficacy into account: (a) there were seven main transitions between complexes (K0 to KI; KI to KII; and KII, KIII, KIV, KV, and UK to KIII), each with a transition probability of around 0.60 or higher; and (b) even without taking into account the transitions involving the UK, this Markov chain showed three transitions (KII to KV, KIV to KIV, and KV to KV) that were not present in the theoretical diagram by

Finally, despite the contributions of the present study, a number of methodological constraints have been identified that could be covered in future research. First, only senior women’s volleyball at the national level was analyzed. Future studies should therefore check whether game complexes follow similar sequences in men’s volleyball, in other age categories, and at other levels of competition (initial stages and top-levels). Second, the transitions between complexes were analyzed without taking into account contextual variables such as quality of opposition, match status, and match period, even though performance analysis in team sports such as soccer (

The research presented in this paper found that the most frequent number of game complexes per point in the national championship analyzed is three. The most common complex is K0, followed by KI, KII, KIII, KIV, KV, and UK, in that order. KI and KV are associated with an in-system offense, while KII, KIII, KIV, and UK are more closely associated with no continuity. The most common sequence of complexes is K0 (the serve), followed by KI with in-system attack, followed by KII without continuity.

The methodology of analyzing game-complex transitions using Markov chains is considered a valid alternative to the social networks methodology, providing practical information about which sequences are most likely to occur in competition, thus indicating which sequences training sessions should focus on the most. The two Markov chains presented in this paper show that the sequencing of game complexes in competition is not as straightforward as various theoretical diagrams have traditionally proposed. Moreover, the Markov chain that takes complex efficacy into account reflects the reality of the game of volleyball much better than the one that does not.

The main contributions of this paper that coaches can apply in training are as follows: (a) the game complexes that are most important for the analyzed women’s volleyball teams to work on are K0 and KI, followed by KII and KIII; (b) KIV should be worked on slightly more than KV; (c) teams looking to work on short rallies should focus in particular on the K0→KI-3→KII-0 sequence, with a controlled serve to make it easier for the team receiving serve to build an in-system offense; and (d) teams looking to work on long rallies should carry out ball control drills in which the ball crosses the net four to six times in total, with the sequence starting with a poor reception of serve or a poor defense, resulting in a free-ball or an out-of-system offense. The findings would allow designing an adequate training session following specific competition demands. Moreover, trainers or strength and condition coaches may find in this study a useful guide of the most frequent movements and the sequence of actions demanded in these game complexes. Thus, the development of youth players and/or the sign up of new players may develop according to the demands of this specific context.

The datasets generated for this study are available on request to the corresponding author.

Ethical review and approval was not required for the study on human participants in accordance with the local legislation and institutional requirements. Written informed consent from the participants was not required to participate in this study in accordance with the national legislation and the institutional requirements.

RH worked on the conceptualization and design of the study, analysis and interpretation of the data, and drafting of the manuscript. MA worked on the collection and interpretation of the data, and drafting of the manuscript. AG participated in the data interpretation and reviewed the content of the manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

We would like to thank the Spanish Royal Volleyball Federation and Madrid Volleyball Federation for allowing the filming of matches from outstanding locations. We are especially grateful to Mr. Adan Aliseda for his help in the reliability process.