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Journal of Quantitative Analysis in Sports

An official journal of the American Statistical Association

Editor-in-Chief: Mark Glickman PhD

SCImago Journal Rank (SJR) 2015: 0.288
Source Normalized Impact per Paper (SNIP) 2015: 0.358
Impact per Publication (IPP) 2015: 0.250

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Measures of tactical efficiency in water polo

James Graham1 / 2

1University of the Pacific – Athletics, Stockton, California, USA

2University of the Pacific – Mathematics, 3601 Pacific Ave., Stockton, California 95211, USA

Corresponding author: John Mayberry, University of the Pacific – Mathematics, 3601 Pacific Ave., Stockton, California 95211, USA, Tel.: +209.946.3166, e-mail:

Citation Information: Journal of Quantitative Analysis in Sports. Volume 10, Issue 1, Pages 67–79, ISSN (Online) 1559-0410, ISSN (Print) 2194-6388, DOI: 10.1515/jqas-2013-0127, February 2014

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We present a notational analysis of offensive tactics commonly employed in elite men’s water polo and address three questions related to this objective: which tactics are most effective?, which tactical performance indicators best classify the winning team?, and how accurate are predictive models based on these performance indicators? We define a new statistic, Efficiency Rating, which quantifies the importance of a tactic via a weighted average of direct and indirect goals generated by its use. By this measure, direct shot is the most efficient even strategy despite being employed far less frequently than centre or perimeter tactics. We address our second question by measuring the effect size of winning over losing teams for 25 tactical variables and find that exclusion conversion rate is the most effective discriminatory statistic in both close and unbalanced games, correctly classifying almost 90% of all contests. To address our third question, we develop and apply a simple Binomial model based on goals generated per play which correctly predicts all eight games in the medal round of the 2012 Men’s Olympics from preliminary rounds. Success probabilities are computed based on a weighted average of offensive and defensive efficiency with an optimal weight that favors defense.

Keywords: classification; notational analysis; prediction; water polo

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