The contribution of skills in the interpretation of a volleyball set result with minimum score difference across genders

Abstract

The aim of the present study was to identify volleyball skills that best discriminate between winning and losing in a set with the minimum score difference of men’s and women’s volleyball. The data have been collected for men from 140 and for women from 98 teams’ performances in all sets finished with 2 points difference between the top four teams in the final ranking during the men’s and women’s Greek Volleyball League for five seasons (2013–2014 until 2017–2018). The primary recorded and evaluated skills from 119 sets for men and women respectively are: 3422 and 2419 serves, 2916 and 2120 passes, 2566 and 1656 attacks after serve’s pass, 1518 and 1804 counter-attacks (after defense) and 1595 and 818 blocks. For the evaluation scale of each skill, a six-level ordinal scale was employed, with the value of “one” indicating a poorly executed skill and the value of “six” an excellent executed skill. The analysis revealed significant multivariate differences in gender and in the type of result and not in their interaction. A follow-up discriminant analysis showed that attack 1 is the most important performance indicator for male teams. Meanwhile, for female teams, the most important performance indicators are winning attack after serve’s pass but also counter-attack. The discriminant function classified correctly 67% and 58%, for men and women respectively, allowing space for further improving the critical performance indicators for both genders.

Keywords

Performance analysis sport analytics team sport

Introduction

In most team sports, men’s and women’s competitions are governed by the same rules and regulations. Volleyball is a highly popular sport around the world, and surprisingly the gender of the players is not a real deal-breaker when it comes to the quality and watchability of the sport. Technical skills are common to both genders, while the hierarchical structure of the game requires similar tactics. In volleyball, the only difference in the rules is the height of the net, which is at 2.24 in women’s competitions and 2.43 in men’s competitions.¹

There are a few studies focusing on the effectiveness of different volleyball skills between males and females. Kountouris et al.² compared the differences in the effectiveness of five volleyball skills between men and women at the last four consecutive Olympics (2000–2016) and results showed that volleyball at a high level is differentiated completely between genders in serve and attack. Bergeles et al.³ examined the attack performance in relation to performance in setting. Results showed that the higher the performance of setters, the higher the performance of the attackers in both genders. The findings in the study of Palao et al.⁴ with performance data of the Sydney 2000 Olympics showed that in males there was a significant difference between the teams’ levels for attacking and blocking and in females for attacking. Palao et al.⁵ in 2009 study analyzed games from the Mediterranean Games of Almeria and were found that serve was more effective for females compared to males, while serve reception was more effective for males and attack efficacy was similar for both genders. João et al.⁶ in 2010 study analyzed games from several World Championships in 2007 to identify the game-related statistics which better discriminate performance by sex. The analysis emphasized on serves errors, attack, and reception. Men’s teams were better associated with terminal actions (serve errors) and women teams were characterized by continuous actions (in defense and attack).

All the previous studies have a common characteristic. With the use of accumulated data authors have examined game-related statistics and their effect on team’s performance with all the sets being completed in one or more volleyball tournaments. However, when analyzing all the sets of a match, a tournament or a championship, there are sets included whose difference in the outcome, and consequently in the performance of the two teams, was large. Doubtless, the quality of opposition has a clear influence on team performance for both genders.^7,8 Thus, there is a risk that the importance of critical technical skills may be biased and, since the interactions between the teams are not taken into account, the amount of significance of several performance indicators may be increased.⁹ The need to address this problem has led Drikos and Vagenas¹⁰ to classify sets, using clusters analysis, according to final set difference with data from male volleyball. In their study¹⁰ a tendency was revealed for the number of important skills which are decreased along with the decrease in the score difference. Using the same classification method for sets with data from female volleyball teams Drikos et al.¹¹ indicated that the number of significant performance indices in women’s volleyball is reduced as the difference in points between the two challenging teams decreases.

The study of performance indicators as a function of the variations between genders in sets with minimum score difference is becoming an important variable to consider, given the instantaneous effect of the row score on the continuous interaction between the two opposing teams during each set. As a consequence, the aim of the study is to identify volleyball skills that best discriminate between winning and losing a set with the minimum score difference of two points, in male and female volleyball.

Methods

Data from 238 teams’ performances in all sets (N = 119) with the minimum score difference played between the top four teams in the final ranking during the men’s and women’s Greek Volleyball League for five seasons (2013–2014 to 2017–2018) were collected.

In this study, each team’s performance was classified according to gender (male–female) and set result (win–lose). The primary recorded and evaluated skills from 119 sets (70 for men and 49 for women) were: 5.841 serves (3422 for men and 2419 for women), 5.036 passes (2916 for men and 2120 for women), 4.222 attacks 1 (after the pass; 2566 for men and 1656 for women), 3.322 attacks 2 (counter-attack; 1518 for men and 1804 for women), and 2.413 blocks (1595 for men and 818 for women). For the evaluation scale of each skill, a six-level ordinal scale is employed, with the value of “one” indicating a poorly executed skill and the value of “six” an excellent executed skill. The entire evaluation scale is presented in Table 1. Further definitions for the evaluation scale per skill are included in Drikos et al.¹² about the serve, Costa et al.¹³ about the attack, Palao et al.⁵ about the block, and Drikos¹⁴ about the serve’s pass.

Table 1.

Evaluation ordinal scale for volleyball skills.

Skill/Level
Skill/Level	Serve	Attack 1,2	Block	Pass
6	Ace (point)	Win-kill (point)	Win-kill (point)	Excellent pass. All options for an attack without adjustments for the setter
5	OverThe ball to the serving team	The ball to the attacking team with good conditions or to the defending team with bad conditions	The ball to the blocking team with good conditions or to the attacking team with bad conditions	Good pass.All options for the attack
4	One option for the attack for the receiving team	The ball to the attacking or defending team with average conditions	The ball to the blocking or attacking team with average conditions	Two options for the attack from the sidelines
3	Two options for the attack for the receiving team	The ball to the attacking team with bad conditions or to the defending team with good conditions	The ball to the blocking team with bad conditions or to the attacking team with good conditions	One option for the attack or attack out of the system
2	All options for the attack on the receiving team	Stuffed by a Kill block (lost point)	Error on the net(Incorrect touch of the net, lost point)	OverpassThe ball was passed directly to the serving team court.
1	Error(lost point)	Error(lost point)	Error(lost point)	Error(lost point)

By convention in the Greek Volleyball Championship, every home team has a specialized person responsible for the recording and uploading of the video to the official league’s server. The recording and entry of the data were done as following: all the sets with minimum score difference are downloaded and the first author who is an expert in the evaluation and recording of volleyball performance data as well an excellent user of the software Data Volley,¹⁵ evaluated all the skills. In order to check the intra-observer reliability of data recording a test–retest procedure of 20% of total sample per gender (14 sets for men–10 sets for women) with two weeks interval was established and the Adjusted Κ Cohen¹⁶ was calculated. Kappa values between 0.81 and 0.99 represent an “almost perfect agreement” between repeated measures.^17–19 Acceptable values (κ = .81–.89) were found for the recorded skills.

Set statistics included variables of efficacy (the number of the categorized events divided by the total number of the skill) for serve, serve’s pass, attack 1 (after serve’s pass) and attack 2 (after defence). The relevant variable for the block is points earned due to block divided by total set points. A volleyball team can get points in four different ways: serve, block, attack and the points gained from the errors of the opposing team. In order to materialize a complete view of all the ways teams earned points, a variable of opponents’ errors was also added. As for the opponent errors all the unforced errors (serve errors, attack errors, an illegal touch of the net, mishandling of the ball) of the opponent are included divided by total set points. So, the data set consists of the following 12 indicators (abbreviations): (1) opponent errors per set points (OPPerr%), (2) Serve Error (Serr%), (3) Serve win (Swin%), (4) Pass Error (Perr%), (5) Pass precise % (Pass perfect% + Pass excellent%) (Pprc%), (6) Attack 1 Errors (A1err%), (7) Attacks 1 blocked (A1blk%), (8) Attack 1 win (A1win%), (9) Attack 2 errors (A2err%), (10) Attacks 2 blocked (A2blk%), (11) Attack 2 win (A2win%), (12) Block points per set points (Bset%).

By using a factorial multivariate analysis of variance (MANOVA) design the present study tested the effect of two independent factors (gender and type of result) as well as the various interactions of factors in a set of 12 dependent variables (selected performance indicators of volleyball) in a sample of sets with the minimum score difference of two points. A two-way MANOVA applied to compare all 12 performance indicators including gender and type of result as between-subjects effects. This allowed the influence of gender, the type of result, and the interaction of gender and type of result to be tested. One way analysis of variance (ANOVA) was carried out to identify the differences in the performance indicators between the genders for victory or defeat. A stepwise discriminant analysis was carried out as a follow-up procedure to MANOVA to identify each gender: (a) the canonical discriminant function that best separates the group means with the calculation of the eigenvalue, canonical correlation coefficient and Wilk’s lambda, (b) which of performance indicators are best predictors of set final result with the use of the correlation coefficients greater than |0.3| between the standardized canonical discriminate function and z-values of the discriminant function²⁰ and (c) the accuracy of the equation that best classifies cases between types of result. In order to decrease the bias entered in classification, jackknifed classification was used.¹⁶ The statistical analysis was performed using SPSS 19.0 software and significances were tested at p < .05.

Results

Table 2 summarizes the descriptive statistics from all the variables employed in this study per gender in total loss and win sets. Also, Figure 1 visualizes total values per gender and Figure 2 visualizes values per type of result for each gender.

Table 2.

Descriptive statistics of the performance indicators.

Gender	Male			Female
Type of result	Loss	Win	Total	Loss	Win	Total
OPPErr%	26.3 ± 8.3	27.4 ± 8.0	26.7 ± 8.0	30.2 ± 10.0	27.9 ± 8.8	28.8 ± 10.3
Serr%	15.0 ± 6.3	14.3 ± 6.5	14.6 ± 6.4	12.0 ± 6.7	12.4 ± 6.0	12.2 ± 6.3
Swin%	4.2 ± 4.2	5.0 ± 4.2	4.6 ± 4.2	8.6 ± 6.0	8.3 ± 6.3	8.4 ± 6.1
Perr%	5.9 ± 5.0	4.9 ± 5.0	5.4 ± 5.0	9.4 ± 7.3	9.9 ± 6.9	9.7 ± 7.1
Pprc%	55.7 ± 13.2	56.0 ± 13.3	55.8 ± 13.2	43.0 ± 11.4	45.6 ± 13.9	43.0 ± 14.2
A1err%	8.5 ± 5.1	5.4 ± 5.3	7.0 ± 5.4	7.6 ± 5.7	7.2 ± 4.9	7.4 ± 5.3
A1Blk%	7.7 ± 5.2	6.9 ± 6.6	7.3 ± 6.0	6.4 ± 5.4	7.5 ± 6.5	7.0 ± 6.0
A1win%	51.0 ± 10.4	56.0 ± 11.2	53.4 ± 11.1	36.1 ± 11.3	42.5 ± 12.7	39.3 ± 12.4
A2err%	9.5 ± 9.6	7.9 ± 7.9	8.7 ± 8.8	9.2 ± 6.6	9.7 ± 7.2	9.5 ± 6.8
A2Blk%	10.5 ± 9.8	8.7 ± 9.7	9.6 ± 9.8	8.6 ± 9.4	8.0 ± 6.1	8.3 ± 7.9
A2win%	44.8 ± 17.3	44.8 ± 14.6	44.8 ± 16.0	31.6 ± 14.1	38.0 ± 11.8	34.8 ± 13.3
Bset%	9.4 ± 5.9	10.2 ± 5.1	9.8 ± 5.6	1.9 ± 1.5	1.7 ± 1.4	1.8 ± 1.5
N	70	70	140	49	49	98

Figure 1.

Radar chart for the performance indicators per gender.

Figure 2.

Radar chart for the performance indicators per type of result for each gender.

No missed values, extreme scores, and outliers were noted in the present data. Basic statistical assumptions were tested and met. The Box’s test of equality of covariance matrices was statistically significant (Box’s M = 1399.023, p < .001), indicating heterogeneity of the variance–covariance matrices across groups, so the Pillai’s trace multivariate test was used.²⁰ The Bartlett Test of Sphericity (approx. chi-square = 13,557.428, p < .001) indicated that significant correlations were present among the dependent variables to proceed with the analysis. In particular, there was no multicollinearity between the dependent variables as the simple correlations, presented in Table 3, were all <|.6|). In addition, based on the statistics presented in Table 3, the 12 variables appear not to be affected even by moderate collinearity as tolerances were high (from .642 for A2win to .872 for A1Blk) and variance inflation factors’ values were small (from 1.146 for A1Blk to 1.558 for A2win). Therefore, all dependent variables were appropriate for multivariate analysis.

Table 3.

Collinearity diagnostics and correlations’ indices among the 12 performance indicators.

	1	2	3	4	5	6	7	8	9	10	11	12	Tol.	VIF
(1) .OPPErr%	1												.756	1.322
(2) Serr%	−.094	1											.850	1.176
(3) Swin%	−.068	−.036	1										.782	1.278
(4) Perr%	.153	−.047	.109	1									.797	1.255
(5) Pprc%	−.214	.022	−.018	−.391	1								.670	1.493
(6) A1err%	.100	.004	.100	.008	.007	1							.860	1.163
(7) A1Blk%	−.020	−.010	.109	−.068	.077	−.133	1						.872	1.146
(8) A1win%	−.247	.118	−.289	−.069	.335	−.265	−.050	1					.682	1.466
(9) A2err%	−.007	−.205	.056	−.032	−.136	−.010	−.062	.006	1				.854	1.171
(10) A2Blk%	.048	−.004	−.010	−.057	.196	.042	−.099	.134	−.162	1			.827	1.209
(11) A2win%	−.334	.322	−.115	−.030	.032	.038	.208	.099	−.187	−.264	1		.642	1.558
(12) Bset%	−.154	.075	−.320	−.254	.309	.000	−.014	.308	.029	.074	.135	1	.764	1.309

Tol.: tolerance = 1 − R_i², with R_i² = % variance in common with the other variables.

VIF = 1/(1 − R_i²) = variance inflation factor.

The main results of MANOVA having as dependent variables the 12 performance parameters and independent variable the fully crossed factors “gender” and “type or result”, which are given in Table 4, showed that the linear combination of the 12 performance indicators differ significantly across the two genders (Pillai’s trace = 0.759, F(12, 223) = 58.542), p < .001, partial η² = .759) and the two types of result (Pillai’s trace = 0.134, F(12, 223) =2.879), p = .001, partial η² = .134), but did not differentiate significantly their crossed combination (gender X type of result; Pillai’s trace = 0.085, F(12, 223) = 1.732, p = .061, partial η² = .085). A series of F tests were carried out on each significant main effect of MANOVA and according to the results (presented in Table 5) with respect to the factor “gender” variables connected with serve (Serr & Swin), with pass (Perr & Pprc), and with attack (A1err, A1win & A2win) were highly significant (p < .001). Similar results were found for the univariate F’s with respect to the factor “type of result”, with variables A1win to be highly significant (p < .001) and A1err to be significant (p > .05). An inspection of the mean values showed that in variables representing serve errors, pass, kill attack, and errors in attack 1 women teams perform poorly than men teams, while in serve aces women perform better than men.

Table 4.

Multivariate tests of statistical significance.

Effect	Pillai’s Trace	F (Hypothesis df, Error df)	Sig.	Partial eta squared
Gender	0.759	58.542 (12, 223)	.000	.759
Type of result	0.134	2.879 (12, 223)	.001	.134
Gender × Result	0.085	1.732 (12, 223)	.061	.085

Table 5.

Univariate tests of significance.

Performance indicators	Gender		Result
Performance indicators	F	Sig.	F	Sig.
OPPErr%	2.720	.100	0.523	.470
Serr%	8.583	.004	0.010	.920
Swin%	32.915	.000	0.121	.728
Perr%	29.293	.000	0.084	.773
Pprc%	44.930	.000	0.726	.395
A1err%	0.492	.000	6.588	.011
A1Blk%	0.176	.675	1.036	.894
A1win%	89.326	.000	14.282	.000
A2err%	0.507	.477	0.351	.554
A2Blk%	1.226	.269	1.036	.310
A2win%	26.173	.000	2.684	.103
Bset%	300.844	.611	0.482	.488

Bold p values signify <.05

The test of equality (EQ) of the male teams for “type of result” was highly significant for A1err (p < .001) and significant (p < .01) for A1win. All the other variables did not present significant differences in terms of winning or losing a set. By the same token for the female teams, the variables connected with winning attack (A1win & A2win) present significant differences (p < .05), while the other variables do not (Table 7).

Table 7.

Tests of significance (p values, in bold <.05) for the equality of group means (EQ), structure coefficients (SC, in italics >|.3|), and standardized canonical coefficients (SCC, underlined) for the type of result in both genders.

Performance indicators	Male			Female
Performance indicators	EQ	SC	SCC	EQ	SC	SCC
OPPErr%	.395	.116	.589	.166	− .336	.583
Serr%	.519	−.088	−.226	.681	−.099	−.034
Swin%	.275	.149	.469	.798	−.062	.236
Perr%	.256	−.155	−.615	.725	.085	−.126
Pprc%	.912	.015	−.004	.300	.251	−.004
A1err%	.000	− .486	−.651	.713	−.089	.138
A1Blk%	.399	−.115	−.289	.384	.211	.003
A1win%	.008	.363	.652	.010	.632	.970
A2err%	.260	−.153	−.407	.760	.074	.245
A2Blk%	.260	−.153	−.233	.728	−.084	−.045
A2win%	.996	−.001	.375	.016	.588	1.057
Bset%	.407	.113	.562	.615	.063	.155

The eigenvalues, the canonical correlations, the chi-square values, the respective significances as well the correct classifications of the discriminant functions are presented in Table 6. The discriminate function for male teams was statistically significant (p < .001) and the canonical correlation coefficient (=.532), namely the measure of association between the discriminate function and the outcome variable, is moderate. Consequently, the squared canonical correlation (=.283) is the amount of variance accounted for by the discriminant function. On the contrary, for female teams, the canonical correlation coefficient is .390 and the percentage of variance explained of it was just 15%. Therefore, the Wilk’s lambda tested the significance of the eigenvalue for the discriminant function for female teams and it was extremely high (=.848); thus, the discriminant function was not significant.

Table 6.

Eigenvalue, test of the significance, and classification table.

Type of result	Male	Female
Eigenvalue	0.395	0.180
Canonical correlation	.532	.390
Wilks’ Lambda	.717	.848
Chi-square	43.919	14.874
df	12	12
p	.000	.248
Correct classification	67.1%	58.2%

To infer the meaning of the discriminant function and to assess the relative contribution of each performance indicator in maximizing the multivariate difference for type of result (win or lose) for each gender, the discriminant structure coefficients (SC) and the standardized canonical discriminant function coefficients (SCC) were examined (Table 7, in italics and underlined). SCs with loadings >|.3| are meaningful and indicate the substantial contribution of the respective independent variables in the separation between the levels of the dependent variable.²¹ In more details, according to Comrey and Lee²² loadings in excess of .71 are considered excellent, .63 very good, .55 good, .45 fair, and .32 poor. So, the variables considered to be central in defining discriminant dimension for male teams are A1win (.363, poor) and A1err (−.486, good) and for female teams are A1 win (.632, very good), A2win (.588, good), and OppErr (−.336, poor). The negative sign in this variable indicates the negative effect on the team’s performance. For male teams, the squared SC values of A1win and A1err indicated that 13% and 24% respectively of the variance in these two variables are accounted for by the discriminant function. Their combination leads to the substantial explanation that the main difference between the two groups of sets (win–lose) reflects mainly the status of attack after serve’s pass. The squared SC values for female teams of A1win, A2win, and OppErr pointed out that 40%, 35%, and 11%, respectively, indicated the proportion of variance between each variable and the discriminant function. In female volleyball, the best interpreting variables are those connected with winning attack in both complexes of the game. Figure 3 presents the group centroids of male and female gender with respect to A1win% and A2win%, while Figure 4 presents the group centroids for real values of the two variables in X- and Y-axis per gender and type of result. Cross-validation results showed that the discriminant function was correctly classified for male teams 46 wins and 48 lost out of the 70 sets (predictive accuracy: 67.1%) and for female teams 29 wins and 28 lost out of the 49 sets (predictive accuracy: 58.2%).

Figure 3.

Group centroids per gender for A1win% and A2win%. Reference lines represent the mean values for each variable per gender.

Figure 4.

Discriminant function plot of the group centroids for A1win% and A2win% per gender per type of result (win/lost sets).

Discussion

This study aimed to identify volleyball skills that best discriminate between winning and losing a volleyball set with the minimum score difference. The data found that efficacy and importance of skills were different for males and females, therefore training methods, tactical directions, and decision making during a match should also be different.

More analytically, with regard to serve skill in total sets, women tend to present higher values in serve aces and lower values to serve error than men. Thus, analyzing the balance of serve errors and serve aces according to the serve efficiency ratio (SER) proposed by Drikos et al.²³ a female team should be capable of winning an ace for every 1.45 serves that it loses, while for male teams this ratio increases to 3.2. Concerning the result per gender in this study, the SER for defeated male teams is higher (worse) than for winning male teams (3.6 and 2.9, respectively) but, surprisingly, defeated female teams have slightly lower (better) SER than winning teams (1.4 and 1.5, respectively). The above findings may partly explain the different importance of the serve for each gender. Male teams more often risk at serve in order not to lose the action directly.¹² This happens because of the overall performance in the skills of the complex 1 (side-out). Men present higher values than women in the quality of serve’s pass⁴ and, consequently, in the effectiveness of attack 1 (after serve’s pass).²⁴ Female teams served more conservatively comparing to male teams, as they lost fewer serves. The better SER is caused by the interaction between serve and reception because women receive serve in lower standards than men and thereafter attack 1 is not so efficient compared to men.

Regarding serve’s pass, due to the fact that serves efficacy and reception efficacy are inversely related, the results are coextended. There has been a difference of 13% in the efficacy of pass precise across genders (56% for men and 43% for women) and also a difference in passing errors (5.4% for men and 9.7% for women). This is in agreement with earlier studies at all levels of volleyball.^25,26 According to Kountouris et al.² the vast difference in serve and serve’s pass between men and women is the primary repercussion of the 19 cm difference in the height of the net. The higher net (2.43 cm) in men makes serving more difficult and passing easier, even the power-jump serve advantage was neutralized by the use of the underhand-frontal pass in reception.²⁷ The lower net (2.24 cm) in women makes serving easier and passing more difficult even in sets with a final score of a minimum difference when teams of the same level compete. In addition to this aspect, the anthropometric and physical characteristics imbalance of genders²⁸ has probably impacted differently the use of techniques with the men being able to apply more efficiently the serve pass skill compared to women.⁵

Attack 1 is the necessary condition in male volleyball to claim the victory because in terms of probability winning a point when receiving is easier than when serving.^29,30 The combination of serving difficulty and the high value of the precise receptions for men leads to a higher percentage of fast tempo spikes³¹ and consequently to a higher attack 1 efficacy of the male teams comparing to female ones (53% vs. 39%, respectively). Similar results with a difference of approximately 7.5% between men and women were found by Ciemiński²⁴ with data from three consecutive tournaments of men’s and women’s European Volleyball Championship but without separating attack 1 and 2. The lower values in female volleyball of attack 1 win result in the longer duration of women rallies and matches.^5,32 The importance of attack 1 is certified of its appearance as discriminative variable with the higher loading in the discriminant functions for both genders. The results of the present study for the importance of attack 1 win are in accordance to the findings of Zetou et al.³³ and Stankovic et al.³⁴ but in a partial agreement with those of Stutzig et al.³⁵ who mentions about men’s volleyball that the differences in attack win are balanced between teams of different levels. A small but statistically significant difference exists in attack errors for both genders. Women make slightly more errors in attack than men (7.4% and 7.0%, respectively) but without this variable discriminating between winning and losing teams. On the contrary, for men attack 1 error is a discriminative variable for winning a set, pointing out the importance of attack 1 for male volleyball^4,29,36 even in sets with 2 points gap in the final score.

With regard to attack after defense (counter-attack), the results did not significantly differ in terms of attack 2 blocked and errors across genders and, thus, they are not decisive factors for the structure of the discriminant function. However, according to attack 2 win, there is difference in performance between genders. Men outperform women in successful attacks 2 by almost 10% (44.8% and 34.8% for men and women respectively) in sets with minimum score difference. Nevertheless, attack 2 for women is a discriminative and meaningful variable with very good loading (.59), while in men, despite the fact that the values of attack 2 win are higher, it does not contribute to the relevant discriminant equation that best separates group means of winning and losing teams.

Winning points of block per total points are greater in male’s teams (10%) than in female’s (2%). Nonetheless, the block did not emerge as a predicting factor for both genders, a finding that is in agreement with Stutzig et al.³⁵ for men and with Kountouris et al.² for women, but in disagreement with Marcelino et al.³⁷

As predicting factor for success for female teams the variable opponents’ errors are presented marginally in the equation, with a negative sign on its loading (−.34) since it indicates the effect of the opponent on team’s set points. This finding points out the importance of avoiding unforced errors in accordance to Valladares et al.³⁸

The purpose of this article was to identify the best variables among a set of candidates through the implementation of a variable selection procedure, such as the discriminant analysis. The analysis is valuable when the quantification of the importance of skills and the correct classification of cases is achievable. With the use of discriminant analysis in previous studies with typical volleyball sets, without taking into consideration the final score difference, the correct classification was 80%,⁸ 89%,³⁵ 90%,³⁸ and 74%.³⁹ In this study, using volleyball sets with the minimum score difference of 2 points between winning and losing teams, the correct classification results were 67% for men and 58% for women. Thus, a novel finding came to attention: along with the decrease in the score difference, there is also a decrease in the number of important skills^10,11 and a decrease in the percentage of cases’ correct classification³⁹ let alone the fact that the discriminatory power of the equation is not stable for both genders. In the case of men, the variables had discriminatory power, as shown by the Wilk’s Lambda values, whereas the discriminant function for women was not considered statistically significant at the significance level <0.05. For both genders, the amount of variance accounted for by the discriminate function was limited especially for women. The need for the correction of this inconsistency indicates the necessity of further research in order to define performance indicators, even those that are not captured by typical or boxscore statistics. A total of infrequent micro-actions in a volleyball set like mishandling of the ball, illegal touch of the net, illegal attack from the defensive zone, penalties or sanctions by the referee may be important variables which can increase the percentage of correct classification. However, a limitation appears in this study. The men’s and women’s Greek Volleyball League is not included in the top-level leagues of the continent. Nevertheless, the level of the best teams of the leagues is on comparison level with the top-level volleyball, since they participate in European club competition finals.

Overall, in women, the effectiveness of attack 1 and 2 are the best determinants of winning a volleyball set, while for men the attack after serve’s pass is sufficient. In conclusion, interpreting the result in a volleyball set with the minimum score difference is easier for men’s teams than for women’s as it has higher rates of correct classification even with fewer variables in the equation.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Sotirios Drikos

References

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