{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,13]],"date-time":"2025-12-13T06:55:11Z","timestamp":1765608911019,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,7,22]],"date-time":"2022-07-22T00:00:00Z","timestamp":1658448000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Spiker\u2013blocker encounters are a key moment for determining the result of a volleyball rally. The characterization of such a moment using physical\u2013statistical parameters allows us to reproduce the possible ball\u2019s trajectory and then make calculations to set up the defense in an optimal way. In this work, we present a computational algorithm that shows the possible worst scenarios of ball trajectories for a volleyball defense, in terms of the covered area by the block and the impact time of the backcourt defense to contact the ball before it reaches the floor. The algorithm is based on the kinematic equations of motion, trigonometry, and statistical parameters of the players. We have called it the Attack-Block-Court Defense algorithm (the ABCD algorithm), since it only requires the 3D-coordinates of the attacker and the blocker, and a discretized court in a number of cells. With those data, the algorithm calculates the percentage of the covered area by the blocker and the time at which the ball impacts the court (impact time). More specifically, the structure of the algorithm consists of setting up the spiker\u2019s and blocker\u2019s locations at the time the spiker hits the ball, and then applying the kinematic equations to calculate the worst scenario for the team in defense. The case of a middle-hitter attack with a single block over the net is simulated, and an analysis of the space of input variables for such a case is performed. We found a strong dependence on the average impact time and the covered area on both the attack\u2013block height\u2019s ratio and the attack height. The standard deviation of the impact time was the variable that showed more asymmetry, respecting the input variables. An asymmetric case considering more variables with a wing spiker and three blockers is also shown, in order to illustrate the potential of the model in a more complex scenario. The results have potential applications, as a supporting tool for coaches in the design of customized defense or attack systems, in the positioning of players according to the prior knowledge of the opponent team, and in the development of replay and video-game technologies in multimedia systems.<\/jats:p>","DOI":"10.3390\/sym14081499","type":"journal-article","created":{"date-parts":[[2022,7,22]],"date-time":"2022-07-22T03:58:44Z","timestamp":1658462324000},"page":"1499","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["The Attack-Block-Court Defense Algorithm: A New Volleyball Index Supported by Data Science"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5616-2947","authenticated-orcid":false,"given":"Jos\u00e9 Roberto","family":"Cant\u00fa-Gonz\u00e1lez","sequence":"first","affiliation":[{"name":"Escuela de Sistemas, Universidad Autonoma de Coahuila, Unidad Norte, Ciudad Acu\u00f1a 26235, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5527-7141","authenticated-orcid":false,"given":"Filiberto","family":"Hueyotl-Zahuantitla","sequence":"additional","affiliation":[{"name":"C\u00e1tedra CONACyT, Mexico City 03940, Mexico"},{"name":"Facultad de Ciencias en F\u00edsica y Matem\u00e1ticas, Universidad Aut\u00f3noma de Chiapas, Tuxtla Guti\u00e9rrez 29050, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8833-1159","authenticated-orcid":false,"given":"Jes\u00fas Abraham","family":"Castorena-Pe\u00f1a","sequence":"additional","affiliation":[{"name":"Facultad de Ingenier\u00eda Mec\u00e1nica y El\u00e9ctrica, Universidad Autonoma de Coahuila, Unidad Norte, Monclova 25750, Mexico"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5191-3462","authenticated-orcid":false,"given":"Mario A.","family":"Aguirre-L\u00f3pez","sequence":"additional","affiliation":[{"name":"Facultad de Ciencias en F\u00edsica y Matem\u00e1ticas, Universidad Aut\u00f3noma de Chiapas, Tuxtla Guti\u00e9rrez 29050, Mexico"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,22]]},"reference":[{"key":"ref_1","first-page":"178","article-title":"Computational intelligence in sports: Challenges and opportunities within a new research domain","volume":"262","author":"Fister","year":"2015","journal-title":"Appl. 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