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.
- 1
In basketball, it is common to distinguish between plays and possessions (Kubatko et al. 2007), the latter referring to the period of game play between which a team gains control of the ball until the time at which control passes to the opposing team. In this paper, we look only at plays because (i) we are more interested in the outcome of specific tactical choices and (ii) the proportion of plays ending in non-possession ending outcomes such as corner or rebound is relatively small anyways.
- 2
We exclude exclusions resulting from exclusions in this calculation so that ε is technically the conditional probability that a power-play situation results in a goal given that the power-play resulted in a return to an even situation or counterattack.
- 3
Exceptions included penalty shots and shooting percentage for centre and direct shots, which all received values of 0 for both teams in about 40% of contests in our sample.
- 4
There was also one game in which both teams had the same ECR.
- 5
The correlation is similar if one looks just at perimeter shooting percentage.
- 6
We excluded all games against last place finishers Kazakhstan and Great Britain as well as the Serbia vs. Romania game because it occurred after Romania was eliminated from playoff contention.
- 7
Note that we round
- 8
The two exceptions being USA vs Hungary and USA vs Montenegro.
- 9
In fact, one can compute the probability that team i beats j by k goals for any k≥0 in a similar manner.
- 10
Incorrect: Serbia vs Hungary and Montenegro vs Hungary. With α=0.03, we also incorrectly predicted Hungary vs USA so it appears that the Exclusion Model with low offensive weight does especially poorly in predicting matches involving Hungary.
- 11
... and USA vs Montenegro in the preliminary round.
Acknowledgments
We would like to thank Grant Hollis for providing tactical descriptions and valuable feedback on the original manuscript. We would also like to thank Janice Intoy whose Matlab scripts were instrumental in helping us sort through raw game logs.
Appendix
Description of Tactics
Direct Shot – An attempt by any player to get fouled outside the 5 m line to get a free throw and shoot directly to the goal. Only free throws which result from deliberate attempts to get fouled are tracked as direct shots which distinguishes this tactic from free throw statistics considered in other papers; see Lupo et<nonbrspace;al. (2010), 2011, 2012b, 2014).
Centre Forward –The centre forward is the player closest to the goal who occupies the central game area at about 2 m from the opposing goal (Lozovina et al. 2004; Lupo et al. 2012b). Any action that occurs at the centre position is logged as a centre forward tactic.
Perimeter Players –Any non-free throw shot, or attempted shot, that occurs at one of the non-centre forward positions is logged as a perimeter tactic.
Drive – A tactic performed by swimming toward the goal to get a pass (generally close to the goal to effectively shot), or a favorable game situation for a team mate (influencing the opponents defensive arrangement). This tactic may also be referred to as a cut.
Post up –A tactic exclusively executed by perimeter players and differentiated from a drive by the attempt to turn ones’ back to the defender in order to get an opponents exclusion.
Pick –Two players “cut” in an attempt to get an offensive advantage with respect to the defenders (similar to a screen in basketball).
New Centre –Similar to a post up with the added facet that the centre vacates the region in front of the goal and the perimeter player that comes in stays as a replacement.
Double Centre Forward –Similar to a post up, but distinguished by an extended period of time in which a player continues to work for position as opposed to looking for an opportunistic advantage. The offense often shifts and balances into a formation similar to that in the 4–2 MA (see below).
Counterattack –Any game situation where, the number of offensive players is larger than that of the defense relative to the ball position, determining a numerical advantage for the offensive players. This state persists until the numerical superiority is neutralized by the defense; see also Lupo et al. (2010), 2011, 2012a, 2014).
4–2 PP –An offensive team arrangement during a power-play: two centre forwards at 2-m in front of the posts of the opponent goal, and four perimeter players round the two centre forwards; see also Lupo et al. (2012a), 2014).
3–3 PP –An offensive team arrangement during a power-play: one centre forward centrally located at 2-m from the opponent goal, and five perimeter players round the centre forward.
Quick – Any game action that occurs at the start of a power-play, before a definite offensive (i.e., 4–2 PP, 3–3 PP) or defensive arrangement.
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