Measures of tactical efficiency in water polo

Abstract

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.

The ebb and flow of official calls in water polo

“…Information transcribed about each possession included the team on offense, the offensive tactic employed (see Table 3 below), the defensive tactic employed, and the result (goal, missed shot, exclusion, penalty shot, turnover, offensive foul, or rebound). Tactics were classified according to the heuristics described in the appendix of Graham and Mayberry (2014) with the tactics drive, new center, pick, and post-up combined into a single category of movement based tactics for the purposes of analysis. Games were mostly played in neutral locations (the only exceptions were games from the 2013 Championships involving Spain), but with one team assigned to wear home caps (the Dark team) and the other to wear traditional away caps (the White team).…”

“…For penalty shots, this is equivalent to the shooting percentage, but for exclusions, the conversion rate also takes into account goals scored in the current possession after an exclusion ends. Goal conversion rates have been shown to be a better metric for measuring the effectiveness of exclusions than shooting percentage alone; see Graham and Mayberry (2014) for details dynamically evolve over the course of a game (eg. game-time, scoring momentum, whether the offensive team is losing or winning).…”

“…Considering the importance of exclusions and penalty shots in generating goals, one would expect that the number of foul opportunities received by each team is a good classifier of the outcome of water polo games with winning teams receiving more opportunities than losing teams. Recent research, however, has shown that there is no significant difference between the number of exclusion opportunities obtained by winning and losing teams in elite men's water polo with slightly more than 50% of all games ending with more opportunities for the losing team (Graham and Mayberry (2014)). This counterintuitive result may suggest that water polo referees follow the principle, stated in Askins (1978), of being "fair" (giving equal opportunities to both teams) as opposed to being "objective" (calling fouls based on severity of infractions alone).…”

“…Even situations includes all set six on six offensive configurations whereas counterattack includes all fast break or transition situations in which one or more defensive players is still returning to position after a change of possession. Escalante et al (2011); Escalante et al (2012); Lupo et al (2012); Graham and Mayberry (2014)), this is the first study which takes a dynamic look at foul calling patterns in the sport and seeks to identify situations in which a team's chances of drawing a foul may significantly differ from their baseline rates. We conclude by exploring whether statistically significant foul calling biases can be explained by differences in playing styles or whether referee bias is a more likely explanation for these effects.…”

Determining spatio-temporal metrics that distinguish play outcomes in field hockey

“…Regardless of whether statistical significance or magnitude-based methods are used, investigating metrics individually does not account for the possibility of interaction effects. Univariate methods have performed well for identifying important inputs (Haws et al 2015) but considering metrics' interactions might be more informative (Escalante et al, 2011;Graham and Mayberry, 2014).…”