Evaluating the performance of elite level volleyball players

Gilbert W. Fellingham

doi:10.1515/jqas-2021-0056

Article

Evaluating the performance of elite level volleyball players

Gilbert W. Fellingham

Published/Copyright: February 23, 2022

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From the journal Journal of Quantitative Analysis in Sports Volume 18 Issue 1

Abstract

Evaluation of individuals in a team sport setting is inherently difficult. The level of play of one individual is fundamentally tied to the level of play of the teammates. One way to think about evaluation of individuals is to ‘insert’ the posterior distribution of the parameter that measures individual play into an ‘average’ team, and see how the probability of success (or failure) changes. Using a Bayesian hierarchical logistic model, we can estimate both the average contribution to success of various positions, and the individual contribution of all the players in that position. In this paper, we use data from the 2018 World Championships in Volleyball to model both the position played and the players within each position. Using both the posterior distributions for the mean performance of the different positions, and the posterior distributions for the individual players, we can then estimate the change in the number of points scored for a team with a change from an average player to the individual under consideration. We compute both the points scored above average per set (PAAPS) and the points scored above average per 100 touches (PP100) for 168 men and 168 women playing five different positions. Contributions of the various position groups and of individual players within each position are evaluated and compared.

Keywords: Bayesian models; hierarchical models; logistic regression; random effects

Corresponding author: Gilbert W. Fellingham, Brigham Young University, Provo, USA, E-mail: gwf@byu.edu

Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

Appendix A

Figure 3:

Trace plot for the parameter of male libero number 39 computed in the model of errors. The Geweke statistic for this parameter was −2.65.

Figure 4:

Trace plot for the parameter of female opposite number 61 computed in the model of kills. The Geweke statistic for this parameter was −2.54.

Appendix B

The following tables show the setter, libero, and opposite with the most touches, and the two middle blockers and outside hitters with the most touches for each team in the 2018 World Championship Volleyball tournaments for both men and women.

Table 4:

Performance of PAAPS and PP100 for the primary setter of each team entered in the 2018 Men’s World Championship Volleyball tournament.

Name	Position	Team	Mean	SD	TPS	Mean	SD
			PAAPS	PAAPS		PP100	PP100
Christenson	Setter	USA M	0.46	0.37	26.6	1.73	1.40
Fujii	Setter	Japan M	0.28	0.49	28.06	0.99	1.74
Arredondo	Setter	Cuba M	−0.37	0.48	27.58	−1.34	1.74
Cavanna	Setter	Argentina M	0.28	0.49	32.77	0.85	1.49
Blankenau	Setter	Canada M	−0.06	0.46	29.81	−0.19	1.54
Rezende	Setter	Brazil M	0.70	0.40	28.74	2.43	1.39
Peacock	Setter	Australia M	0.41	0.40	26.92	1.54	1.50
Mao	Setter	China M	−0.23	0.49	27.94	−0.83	1.76
Marouflakrani	Setter	Iran M	0.55	0.43	28.8	1.91	1.50
D’Hulst	Setter	Belgium M	0.32	0.45	28.15	1.14	1.59
Seganov	Setter	Bulgaria M	0.03	0.44	27.28	0.11	1.60
Tervaportti	Setter	Finland M	0.20	0.47	30.36	0.67	1.54
Slimene	Setter	Tunisia M	0.58	0.45	26.59	2.18	1.71
Toniutti	Setter	France M	0.52	0.41	28.62	1.83	1.45
Abdalla	Setter	Egypt M	0.19	0.43	23.47	0.80	1.82
Perez	Setter	Puerto_Rico M	0.45	0.48	27.56	1.63	1.74
Giannelli	Setter	Italy M	0.47	0.37	25.44	1.86	1.46
Vincic	Setter	Slovenia M	0.22	0.40	25.06	0.88	1.61
Haarlem	Setter	Netherlands M	−0.14	0.42	26.25	−0.54	1.59
Jovovic	Setter	Serbia M	0.02	0.38	26.87	0.08	1.41
Drzyzga	Setter	Poland M	−0.6	0.43	27.48	−2.17	1.58
Butko	Setter	Russia M	−0.29	0.41	25.31	−1.16	1.63
Burgos	Setter	Dominican_R M	0.06	0.53	28.06	0.21	1.88
Awal	Setter	Cameroon M	0.13	0.46	26.31	0.49	1.75

Table 5:

Performance of PAAPS and PP100 for the primary setter of each team entered in the 2018 Women’s World Championship Volleyball tournament.

Name	Position	Team	Mean	SD	TPS	Mean	SD
			PAAPS	PAAPS		PP100	PP100
Lloyd	Setter	USA W	0.10	1.24	73.00	0.14	1.70
Kitipova	Setter	Bulgaria W	1.89	1.19	65.82	2.87	1.81
Hanke	Setter	Germany W	2.46	1.16	62.81	3.91	1.85
Malinov	Setter	Italy W	1.26	0.97	61.95	2.04	1.57
Dijkema	Setter	Netherlands W	−0.50	1.08	63.57	−0.79	1.70
Startseva	Setter	Russia W	3.45	1.14	64.82	5.32	1.75
Ognienovic	Setter	Serbia W	3.35	1.03	65.30	5.13	1.58
Ozbay	Setter	Turkey W	−1.55	1.19	60.30	−2.58	1.98
Galiano	Setter	Argentina W	−0.89	1.32	54.00	−1.65	2.45
Ratzke	Setter	Brazil W	−0.61	1.05	52.13	−1.17	2.01
Ding	Setter	China W	0.93	0.98	62.16	1.50	1.57
Tashiro	Setter	Japan W	0.08	1.17	70.36	0.11	1.66
Akilova	Setter	Kazakhstan W	−0.14	1.33	51.27	−0.27	2.58
Guedpard	Setter	Thailand W	2.70	1.16	62.06	4.35	1.87
Cyr	Setter	Canada W	0.26	1.30	55.18	0.47	2.36
Sabin	Setter	Cuba W	−0.67	1.33	50.47	−1.33	2.64
Frica	Setter	Dominican_Rep W	2.34	0.97	51.78	4.52	1.88
Sashiko	Setter	Mexico W	−0.52	1.12	53.07	−0.99	2.12
Valentin	Setter	Puerto_Rico W	3.15	1.34	69.48	4.53	1.93
Wairimu	Setter	Kenya W	0.19	1.15	43.67	0.44	2.63
Lee	Setter	S. Korea W	0.08	1.36	59.41	0.14	2.29
Koulla	Setter	Cameroon W	−2.40	1.24	48.12	−5.00	2.58
Forde	Setter	Trinidad&Tobago W	1.75	1.24	51.31	3.41	2.41
Yagubova	Setter	Azerbaijan W	−0.79	1.10	53.67	−1.48	2.05

Table 6:

Performance of PAAPS and PP100 for the two primary middle blockers of each team entered in the 2018 Men’s World Championship Volleyball tournament.

Name	Position	Team	Mean	SD	TPS	Mean	SD
			PAAPS	PAAPS		PP100	PP100
Holt	Middle	USA M	0.12	0.17	9.73	1.27	1.70
Smith	Middle	USA M	0.10	0.13	7.12	1.39	1.77
Yamauchi	Middle	Japan M	0.01	0.17	8.76	0.12	1.95
Fushimi	Middle	Japan M	−0.07	0.09	4.27	−1.64	2.19
Arce	Middle	Cuba M	−0.05	0.21	10.71	−0.51	1.95
Rodriguez	Middle	Cuba M	−0.07	0.14	6.89	−1.07	2.07
Sole	Middle	Argentina M	0.13	0.20	11.51	1.09	1.71
Loser	Middle	Argentina M	−0.28	0.17	8.33	−3.38	2.05
Vigrass	Middle	Canada M	−0.01	0.17	9.46	−0.06	1.79
Vandoorn	Middle	Canada M	−0.10	0.12	5.95	−1.72	2.01
Saatkamp	Middle	Brazil M	−0.06	0.18	10.43	−0.53	1.71
Souza	Middle	Brazil M	−0.03	0.12	6.22	−0.43	1.87
Mote	Middle	Australia M	0.03	0.18	10.17	0.34	1.76
Graham	Middle	Australia M	0.11	0.13	7.32	1.51	1.79
Chen	Middle	China M	0.03	0.21	10.81	0.32	1.91
Rao	Middle	China M	−0.02	0.18	8.75	−0.23	2.02
Shafiei	Middle	Iran M	−0.09	0.19	10.46	−0.85	1.81
Eraghi	Middle	Iran M	0.01	0.12	6.68	0.13	1.87
Voorde	Middle	Belgium M	0.07	0.18	10.12	0.69	1.82
Verhees	Middle	Belgium M	−0.14	0.18	9.57	−1.46	1.93
Yosifov	Middle	Bulgaria M	−0.21	0.20	10.16	−2.02	1.94
Gotsev	Middle	Bulgaria M	0.02	0.13	6.89	0.27	1.95
Sinkkonen	Middle	Finland M	0.10	0.17	9.82	1.04	1.75
Siirila	Middle	Finland M	−0.02	0.11	5.63	−0.43	1.95
Miladi	Middle	Tunisia M	0.01	0.18	8.68	0.14	2.04
Agrebi	Middle	Tunisia M	−0.09	0.13	5.96	−1.57	2.21
Le Goff	Middle	France M	0.01	0.17	9.58	0.12	1.79
Chinenyeze	Middle	France M	−0.03	0.11	5.7	−0.51	1.98
Abou	Middle	Egypt M	0.11	0.15	7.74	1.36	1.97
Masoud	Middle	Egypt M	0.05	0.11	5.4	0.92	2.04
Colon	Middle	Puerto_Rico M	−0.13	0.20	9.49	−1.40	2.11
Rodriguez	Middle	Puerto_Rico M	0.00	0.15	7.36	0.00	2.06
Anzani	Middle	Italy M	0.01	0.16	9.41	0.11	1.74
Mazzone	Middle	Italy M	0.26	0.13	7.93	3.29	1.7
Pajenk	Middle	Slovenia M	−0.15	0.17	8.76	−1.74	1.9
Kozamernik	Middle	Slovenia M	0.10	0.15	8.30	1.15	1.78
Parkinson	Middle	Netherlands M	−0.19	0.21	10.61	−1.83	1.99
Diefenbach	Middle	Netherlands M	0.16	0.14	7.53	2.19	1.84
Lisinac	Middle	Serbia M	0.07	0.16	10.18	0.72	1.61
Podrascanin	Middle	Serbia M	0.07	0.12	6.82	1.02	1.74
Kochanowski	Middle	Poland M	0.04	0.17	9.98	0.36	1.73
Nowakowski	Middle	Poland M	0.06	0.17	9.73	0.66	1.76
Muserskiy	Middle	Russia M	0.23	0.17	10.03	2.29	1.67
Kurkaev	Middle	Russia M	−0.02	0.17	9.41	−0.19	1.83
Romero	Middle	Dominican_R M	−0.09	0.17	7.97	−1.15	2.16
Paulino	Middle	Dominican_R M	0.00	0.16	7.76	0.04	2.06
Dolegombai	Middle	Cameroon M	−0.05	0.20	10.34	−0.52	1.98
Engala	Middle	Cameroon M	−0.07	0.13	6.17	−1.07	2.13

Table 7:

Performance of PAAPS and PP100 for the two primary middle blockers of each team entered in the 2018 Women’s World Championship Volleyball tournament.

Name	Position	Team	Mean	SD	TPS	Mean	SD
			PAAPS	PAAPS		PP100	PP100
Akinradewo	Middle	USA W	0.53	0.46	23.6	2.26	1.96
Adams	Middle	USA W	0.63	0.35	15.97	3.92	2.18
Dimitrova	Middle	Bulgaria W	1.77	0.50	25.68	6.90	1.93
Ruseva	Middle	Bulgaria W	0.36	0.46	21.12	1.71	2.15
Grunding	Middle	Germany W	0.10	0.48	20.07	0.52	2.41
Vanjak	Middle	Germany W	−0.08	0.43	17.31	−0.44	2.49
Danesi	Middle	Italy W	0.03	0.40	21.33	0.15	1.88
Chirichella	Middle	Italy W	0.16	0.34	17.28	0.90	1.95
Belien	Middle	Netherlands W	−0.40	0.41	20.5	−1.96	2.00
Lohuis	Middle	Netherlands W	0.00	0.30	12.97	0.04	2.30
Koroleva	Middle	Russia W	0.30	0.48	21.9	1.36	2.17
Fetisova	Middle	Russia W	0.85	0.45	20.59	4.13	2.20
Rasic	Middle	Serbia W	1.05	0.42	22.31	4.71	1.89
Veljkovic	Middle	Serbia W	0.72	0.33	15.56	4.64	2.10
Dundar	Middle	Turkey W	1.00	0.50	24.12	4.14	2.07
Gunes	Middle	Turkey W	0.90	0.46	21.38	4.22	2.16
Sosa	Middle	Argentina W	0.75	0.56	20.43	3.67	2.74
Lazcano	Middle	Argentina W	−0.23	0.54	18.81	−1.24	2.87
Correa	Middle	Brazil W	0.22	0.45	19.62	1.12	2.28
Da Silva	Middle	Brazil W	0.19	0.30	11.04	1.74	2.71
Yuan	Middle	China W	1.52	0.42	24.00	6.33	1.76
Yan	Middle	China W	1.77	0.38	21.35	8.27	1.80
Shinomiya	Middle	Japan W	0.00	0.45	22.23	0.02	2.04
Okumura	Middle	Japan W	−0.70	0.47	22.04	−3.16	2.15
Petrenko	Middle	Kazakhstan W	0.30	0.54	18.97	1.58	2.86
Safronova	Middle	Kazakhstan W	0.06	0.33	10.07	0.58	3.26
Thinkaow	Middle	Thailand W	0.99	0.43	20.51	4.81	2.08
Nuekjang	Middle	Thailand W	0.92	0.38	17.56	5.22	2.14
Maglio	Middle	Canada W	0.73	0.49	18.21	3.99	2.70
Cross	Middle	Canada W	−0.10	0.51	17.42	−0.57	2.95
Aguiliera Carbajal	Middle	Cuba W	0.19	0.48	17.03	1.14	2.81
Suarez	Middle	Cuba W	−0.23	0.41	13.72	−1.71	2.97
Mejia	Middle	Dominican_Rep W	1.04	0.45	19.41	5.36	2.33
Martinez	Middle	Dominican_Rep W	0.36	0.36	14.35	2.48	2.52
Valle	Middle	Mexico W	−0.44	0.40	14.25	−3.06	2.83
Moreno Hernandez	Middle	Mexico W	−0.76	0.37	12.55	−6.02	2.96
Sofia Jusino	Middle	Puerto_Rico W	−0.91	0.51	18.66	−4.85	2.71
Ortiz	Middle	Puerto_Rico W	0.03	0.45	16.82	0.19	2.68
Mukuvilani	Middle	Kenya W	−0.58	0.47	14.7	−3.93	3.22
Atuka	Middle	Kenya W	−0.02	0.25	7.22	−0.23	3.48
Kim	Middle	S. Korea W	−0.14	0.50	17.50	−0.83	2.85
Lee	Middle	S. Korea W	0.55	0.30	9.70	5.72	3.07
Mogoung	Middle	Cameroon W	0.51	0.48	16.53	3.09	2.93
Aboa Mbeza	Middle	Cameroon W	−0.24	0.45	13.95	−1.75	3.22
Jack	Middle	Trinidad&Tobago W	0.98	0.37	14.44	6.81	2.59
Ross	Middle	Trinidad&Tobago W	−0.40	0.24	6.82	−5.79	3.47
Hasanova	Middle	Azerbaijan W	0.49	0.40	17.02	2.89	2.33
Imanova	Middle	Azerbaijan W	−0.52	0.36	13.47	−3.84	2.68

Table 8:

Performance of PAAPS and PP100 for the two primary outside hitters of each team entered in the 2018 Men’s World Championship Volleyball tournament.

Name	Position	Team	Mean	SD	TPS	Mean	SD
			PAAPS	PAAPS		PP100	PP100
Sander	Outside	USA M	0.09	0.27	18.38	0.49	1.47
Russell	Outside	USA M	−0.15	0.28	18.35	−0.84	1.52
Fukuzawa	Outside	Japan M	0.24	0.33	18.92	1.26	1.76
Ishikawa	Outside	Japan M	0.08	0.31	17.47	0.47	1.78
Castro	Outside	Cuba M	−0.20	0.35	19.18	−1.03	1.80
Hernandez	Outside	Cuba M	0.14	0.23	13.15	1.05	1.76
Poglajen	Outside	Argentina M	0.03	0.33	21.27	0.15	1.57
Conte	Outside	Argentina M	0.17	0.25	16.08	1.03	1.55
Hoag	Outside	Canada M	−0.06	0.29	18.97	−0.29	1.55
Perrin	Outside	Canada M	0.53	0.25	17.76	2.97	1.43
Souza	Outside	Brazil M	0.52	0.26	18.62	2.81	1.37
Fonteles	Outside	Brazil M	0.12	0.22	14.33	0.85	1.54
Sanderson	Outside	Australia M	−0.14	0.34	19.01	−0.76	1.77
Staples	Outside	Australia M	−0.18	0.22	12.2	−1.45	1.83
Liu	Outside	China M	0.16	0.32	18.86	0.86	1.70
Ji	Outside	China M	−0.19	0.23	11.49	−1.68	1.99
Ghara H.	Outside	Iran M	0.15	0.30	19.01	0.81	1.56
Manavinezhad	Outside	Iran M	0.08	0.18	11.05	0.71	1.67
Deroo	Outside	Belgium M	−0.05	0.30	18.63	−0.26	1.61
Rousseaux	Outside	Belgium M	0.03	0.19	10.63	0.25	1.74
Skrimov	Outside	Bulgaria M	0.10	0.32	19.69	0.53	1.63
Penchev	Outside	Bulgaria M	0.24	0.31	18.41	1.33	1.71
Krastins	Outside	Finland M	−0.50	0.34	19.75	−2.54	1.74
Suihkonen	Outside	Finland M	−0.12	0.28	15.92	−0.72	1.73
Hmissi	Outside	Tunisia M	−0.34	0.34	16.82	−1.99	2.00
Miladi	Outside	Tunisia M	−0.29	0.31	16.04	−1.81	1.94
Ngapeth	Outside	France M	0.10	0.29	19.69	0.52	1.50
Tillie	Outside	France M	0.04	0.22	12.91	0.34	1.67
Shafik	Outside	Egypt M	0.06	0.27	15.09	0.40	1.81
Hassan	Outside	Egypt M	−0.03	0.17	8.08	−0.34	2.06
Eddie	Outside	Puerto_Rico M	0.07	0.36	19.55	0.36	1.83
Guzman	Outside	Puerto_Rico M	−0.08	0.28	14.51	−0.53	1.96
Juantorena	Outside	Italy M	0.12	0.27	17.71	0.66	1.55
Lanza	Outside	Italy M	−0.38	0.21	11.63	−3.28	1.83
Urnaut	Outside	Slovenia M	−0.43	0.30	18.13	−2.37	1.67
Cebulj	Outside	Slovenia M	0.12	0.21	13.22	0.87	1.59
Horst	Outside	Netherlands M	0.13	0.32	19.48	0.69	1.62
Jorna	Outside	Netherlands M	−0.33	0.32	16.59	−1.96	1.90
Ivovic	Outside	Serbia M	0.51	0.27	19.37	2.66	1.40
Kovacevic	Outside	Serbia M	0.32	0.25	17.34	1.85	1.44
Szalpuk	Outside	Poland M	−0.14	0.31	19.70	−0.69	1.56
Kubiak	Outside	Poland M	0.31	0.25	17.48	1.77	1.41
Kliuka	Outside	Russia M	0.21	0.29	19.46	1.10	1.51
Volkov	Outside	Russia M	0.08	0.30	19.42	0.43	1.55
Lopez	Outside	Dominican_R M	0.32	0.32	18.19	1.77	1.76
Cruz	Outside	Dominican_R M	−0.07	0.13	6.54	−1.03	2.06
Hile	Outside	Cameroon M	0.08	0.35	18.94	0.41	1.85
Engohe	Outside	Cameroon M	−0.04	0.27	13.73	−0.27	1.97

Table 9:

Performance of PAAPS and PP100 for the two primary outside hitters of each team entered in the 2018 Women’s World Championship Volleyball tournament.

Name	Position	Team	Mean	SD	TPS	Mean	SD
			PAAPS	PAAPS		PP100	PP100
Larson	Outside	USA W	−1.73	0.82	50.30	−3.43	1.63
Hill	Outside	USA W	−0.31	0.69	40.89	−0.75	1.68
Dimitrova	Outside	Bulgaria W	0.06	0.84	46.14	0.14	1.82
Karakasheva	Outside	Bulgaria W	−2.17	0.81	40.47	−5.36	2.01
Geerties	Outside	Germany W	0.19	0.84	44.69	0.42	1.88
Brinker-Fromm	Outside	Germany W	0.92	0.59	31.16	2.96	1.88
Bosetti	Outside	Italy W	−0.12	0.70	45.44	−0.26	1.55
Sylla	Outside	Italy W	0.61	0.58	36.97	1.66	1.56
Balkestein-Grothues	Outside	Netherlands W	−1.57	0.79	45.07	−3.48	1.75
Buijs	Outside	Netherlands W	−0.55	0.70	42.86	−1.29	1.64
Voronkova	Outside	Russia W	−0.22	0.80	45.56	−0.49	1.75
Parubets	Outside	Russia W	0.83	0.80	44.64	1.87	1.78
Mihajlovic	Outside	Serbia W	−0.20	0.78	45.97	−0.45	1.71
Busa	Outside	Serbia W	−0.57	0.65	37.94	−1.49	1.72
Ismailoglu	Outside	Turkey W	1.31	0.81	42.93	3.05	1.89
Baladin	Outside	Turkey W	−1.50	0.63	26.99	−5.55	2.33
Fernandez	Outside	Argentina W	−0.87	0.99	39.93	−2.18	2.49
Rodriguez	Outside	Argentina W	0.62	0.94	39.52	1.58	2.39
Guimaraes	Outside	Brazil W	0.03	0.79	40.52	0.07	1.94
Rodrigues	Outside	Brazil W	0.73	0.68	34.67	2.12	1.96
Zhu	Outside	China W	−0.38	0.73	46.54	−0.81	1.56
Zhang	Outside	China W	0.17	0.47	26.11	0.64	1.78
Koga	Outside	Japan W	−1.50	0.82	47.91	−3.12	1.71
Ishii	Outside	Japan W	0.20	0.66	37.86	0.54	1.75
Anarkulova	Outside	Kazakhstan W	0.28	1.07	38.07	0.73	2.81
Beresneva	Outside	Kazakhstan W	0.44	0.74	26.18	1.66	2.83
Apinyapong	Outside	Thailand W	0.84	0.77	43.13	1.94	1.78
Sittirak	Outside	Thailand W	−1.04	0.75	39.38	−2.64	1.91
Bailey	Outside	Canada W	−1.28	1.00	40.47	−3.16	2.47
Gray	Outside	Canada W	0.04	0.73	29.15	0.13	2.5
Case Montalvo	Outside	Cuba W	0.51	0.89	36.53	1.41	2.43
Perez	Outside	Cuba W	0.17	0.76	30.76	0.57	2.46
Pena	Outside	Dominican_Rep W	−1.44	0.87	41.12	−3.51	2.12
Martinez	Outside	Dominican_Rep W	0.55	0.63	27.82	1.99	2.25
Bricio	Outside	Mexico W	1.12	0.70	36.18	3.09	1.93
Parra Quintero	Outside	Mexico W	0.59	0.65	31.31	1.87	2.06
Enright	Outside	Puerto_Rico W	−2.44	0.86	43.43	−5.61	1.97
Santana	Outside	Puerto_Rico W	0.33	0.81	43.19	0.76	1.87
Murambi	Outside	Kenya W	1.15	0.87	33.2	3.47	2.62
Moim	Outside	Kenya W	0.75	0.89	32.84	2.30	2.71
Kim	Outside	S. Korea W	−0.36	0.88	38.74	−0.92	2.28
Lee	Outside	S. Korea W	−1.59	0.63	22.84	−6.98	2.78
Nana	Outside	Cameroon W	0.90	0.88	34.41	2.60	2.55
Fawziya	Outside	Cameroon W	−0.69	0.75	26.93	−2.55	2.78
Ramdin	Outside	Trinidad&Tobago W	−0.74	0.91	35.62	−2.09	2.55
Channon	Outside	Trinidad&Tobago W	−0.30	0.87	35.30	−0.85	2.46
Bayramova	Outside	Azerbaijan W	−0.29	0.79	37.97	−0.76	2.09
Samadova	Outside	Azerbaijan W	−1.47	0.58	24.66	−5.97	2.36

Table 10:

Performance of PAAPS and PP100 for the primary opposite of each team entered in the 2018 Men’s World Championship Volleyball tournament.

Name	Position	Team	Mean	SD	TPS	Mean	SD
			PAAPS	PAAPS		PP100	PP100
Anderson	Opposite	USA M	0.08	0.23	15.09	0.52	1.52
Nishida	Opposite	Japan M	0.08	0.29	15.00	0.52	1.9
Gutierrez Miguel	Opposite	Cuba M	−0.40	0.30	15.63	−2.55	1.91
Gonzalez	Opposite	Argentina M	−0.10	0.29	15.60	−0.64	1.86
Vernon-Evans	Opposite	Canada M	0.04	0.22	12.66	0.35	1.75
Souza	Opposite	Brazil M	−0.09	0.25	15.14	−0.57	1.63
Williams	Opposite	Australia M	0.48	0.26	16.16	3.00	1.62
Jiang	Opposite	China M	0.17	0.31	17.72	0.96	1.75
Ghafour	Opposite	Iran M	−0.18	0.28	15.58	−1.16	1.77
Dries	Opposite	Belgium M	0.06	0.23	13.6	0.44	1.73
Uchikov	Opposite	Bulgaria M	−0.05	0.25	13.84	−0.39	1.8
Sivula	Opposite	Finland M	−0.35	0.30	16.16	−2.18	1.85
Boungui	Opposite	Tunisia M	0.19	0.30	16.06	1.21	1.89
Boyer	Opposite	France M	−0.06	0.25	14.69	−0.41	1.69
Abdelhay	Opposite	Egypt M	0.02	0.26	13.18	0.11	1.94
Torres	Opposite	Puerto_Rico M	0.18	0.29	16.25	1.09	1.79
Zaytsev	Opposite	Italy M	0.33	0.21	13.70	2.41	1.52
Gasparini	Opposite	Slovenia M	0.02	0.22	12.92	0.19	1.72
Abdel-Aziz	Opposite	Netherlands M	−0.26	0.30	16.66	−1.55	1.78
Atanasijevic	Opposite	Serbia M	0.11	0.25	15.78	0.69	1.59
Kurek	Opposite	Poland M	0.22	0.23	15.25	1.44	1.54
Mikhaylov	Opposite	Russia M	−0.02	0.24	14.78	−0.13	1.66
Santana	Opposite	Dominican_R M	0.02	0.27	13.50	0.18	2.00
Feughouo	Opposite	Cameroon M	0.08	0.31	16.25	0.50	1.93

Table 11:

Performance of PAAPS and PP100 for the primary opposite of each team entered in the 2018 Women’s World Championship Volleyball tournament.

Name	Position	Team	Mean	SD	TPS	Mean	SD
			PAAPS	PAAPS		PP100	PP100
Murphy	Opposite	USA W	−1.03	0.73	34.91	−2.94	2.09
Paskova	Opposite	Bulgaria W	−0.27	0.64	30.19	−0.90	2.12
Lippmann	Opposite	Germany W	0.76	0.74	38.07	2.00	1.95
Egonu	Opposite	Italy W	1.12	0.63	38.77	2.90	1.62
Sloetjes	Opposite	Netherlands W	2.28	0.66	40.06	5.70	1.64
Goncharova	Opposite	Russia W	2.17	0.72	34.22	6.33	2.10
Boskovic	Opposite	Serbia W	1.29	0.66	37.32	3.46	1.76
Boz	Opposite	Turkey W	0.16	0.68	31.13	0.52	2.17
Fresco	Opposite	Argentina W	−0.52	0.73	25.53	−2.04	2.86
Caixeta	Opposite	Brazil W	0.41	0.65	32.84	1.26	1.97
Gong	Opposite	China W	0.70	0.64	38.05	1.84	1.69
Shinnabe	Opposite	Japan W	−0.14	0.77	39.62	−0.35	1.93
Zhdanova	Opposite	Kazakhstan W	−0.98	0.82	25.8	−3.79	3.19
Kanthong	Opposite	Thailand W	−0.75	0.81	40.16	−1.87	2.02
Van Ryk	Opposite	Canada W	−0.56	0.76	29.29	−1.90	2.58
Sabin	Opposite	Cuba W	0.43	0.87	29.18	1.49	2.97
Isabel	Opposite	Dominican_Rep W	−0.37	0.73	32.13	−1.15	2.26
Rangel	Opposite	Mexico W	1.45	0.63	31.53	4.60	2.01
Ocasio	Opposite	Puerto_Rico W	0.97	0.6	29.59	3.27	2.04
Makuto	Opposite	Kenya W	−0.23	0.67	20.67	−1.13	3.26
Park	Opposite	S. Korea W	0.57	0.89	32.9	1.74	2.71
Bassoko	Opposite	Cameroon W	0.59	0.79	29.19	2.01	2.72
Esdelle	Opposite	Trinidad&Tobago W	−1.02	0.73	27.06	−3.77	2.69
Rahimova	Opposite	Azerbaijan W	1.98	0.60	28.8	6.89	2.10

Table 12:

Performance of PAAPS and PP100 for the primary libero of each team entered in the 2018 Men’s World Championship Volleyball tournament.

Name	Position	Team	Mean	SD	TPS	Mean	SD
			PAAPS	PAAPS		PP100	PP100
Shoji	Libero	USA M	−0.06	0.15	8.86	−0.72	1.69
Tsuiki	Libero	Japan M	0.11	0.22	11.18	1.01	1.97
Alvarez	Libero	Cuba M	0.02	0.16	8.63	0.24	1.90
Gonzalez	Libero	Argentina M	0.25	0.16	9.69	2.62	1.65
Marshall	Libero	Canada M	−0.45	0.22	10.61	−4.26	2.11
Hoss	Libero	Brazil M	0.21	0.14	8.97	2.37	1.58
Perry	Libero	Australia M	0.04	0.15	8.91	0.49	1.72
Tong	Libero	China M	0.08	0.16	8.50	0.89	1.89
Marandi	Libero	Iran M	−0.16	0.22	11.20	−1.43	1.98
Stuer	Libero	Belgium M	0.09	0.18	9.83	0.92	1.83
Salparov	Libero	Bulgaria M	−0.02	0.18	9.89	−0.21	1.78
Kerminen	Libero	Finland M	0.13	0.17	9.70	1.33	1.73
Taouerghi	Libero	Tunisia M	−0.08	0.20	10.18	−0.75	1.97
Grebennikov	Libero	France M	0.10	0.16	9.47	1.03	1.71
Abdelaal	Libero	Egypt M	−0.09	0.21	9.65	−0.94	2.19
Del Valle	Libero	Puerto_Rico M	0.07	0.23	11.65	0.57	1.94
Colaci	Libero	Italy M	0.11	0.13	7.60	1.42	1.75
Kovacic	Libero	Slovenia M	0.01	0.15	8.33	0.09	1.77
Sparidans	Libero	Netherlands M	0.21	0.19	11.18	1.90	1.66
Rosic	Libero	Serbia M	0.03	0.15	8.4	0.36	1.74
Zatorski	Libero	Poland M	0.22	0.15	9.69	2.29	1.54
Verbov	Libero	Russia M	−0.34	0.18	9.36	−3.62	1.92
Mieses	Libero	Dominican_R M	−0.29	0.21	9.69	−3.00	2.16
Fossi	Libero	Cameroon M	0.05	0.16	8.31	0.56	1.93

Table 13:

Performance of PAAPS and PP100 for the primary libero of each team entered in the 2018 Women’s World Championship Volleyball tournament.

Name	Position	Team	Mean	SD	TPS	Mean	SD
			PAAPS	PAAPS		PP100	PP100
Robinson	Libero	USA W	0.03	0.47	25.90	0.13	1.83
Todorova	Libero	Bulgaria W	−0.64	0.59	28.04	−2.27	2.10
Durr	Libero	Germany W	0.13	0.52	25.20	0.52	2.08
De Gennaro	Libero	Italy W	−0.37	0.45	25.27	−1.45	1.79
Knip	Libero	Netherlands W	0.19	0.45	22.31	0.83	2.01
Galkina	Libero	Russia W	−1.08	0.58	25.96	−4.15	2.23
Popovic	Libero	Serbia W	0.17	0.39	19.93	0.87	1.95
Sebnem Akoz	Libero	Turkey W	1.21	0.45	21.30	5.68	2.13
Martinez Franchi	Libero	Argentina W	0.43	0.63	23.13	1.85	2.72
Pinto	Libero	Brazil W	0.00	0.43	19.7	0.02	2.17
Wang	Libero	China W	0.82	0.40	21.53	3.8	1.88
Kobata	Libero	Japan W	1.27	0.51	26.55	4.79	1.93
Fendrikova	Libero	Kazakhstan W	−1.17	0.65	21.53	−5.44	3.03
Pannoy	Libero	Thailand W	−0.25	0.54	25.11	−1.01	2.17
Niles	Libero	Canada W	0.25	0.53	19.88	1.24	2.64
Tamayo	Libero	Cuba W	−0.40	0.51	17.59	−2.28	2.89
Castillo	Libero	Dominican_Rep W	−0.13	0.56	25.07	−0.51	2.22
Lopez Robles	Libero	Mexico W	0.53	0.46	20.23	2.63	2.26
Venegas	Libero	Puerto_Rico W	0.68	0.49	23.55	2.90	2.10
Wanyama	Libero	Kenya W	−0.48	0.62	19.47	−2.47	3.20
Kim	Libero	S. Korea W	0.18	0.62	24.41	0.74	2.52
Ntame	Libero	Cameroon W	0.49	0.60	23.06	2.14	2.60
Olton	Libero	Trinidad&Tobago W	0.27	0.59	22.12	1.21	2.68
Karimova	Libero	Azerbaijan W	−0.3	0.50	22.40	−1.32	2.24

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Received: 2021-06-29

Accepted: 2022-01-27

Published Online: 2022-02-23

Published in Print: 2022-03-26

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Articles in the same Issue

https://doi.org/10.1515/jqas-2021-0056

Keywords for this article

Bayesian models; hierarchical models; logistic regression; random effects