Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter February 21, 2014

Measures of tactical efficiency in water polo

  • James Graham and John Mayberry EMAIL logo


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.

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

  1. 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. 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. 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. 4

    There was also one game in which both teams had the same ECR.

  5. 5

    The correlation is similar if one looks just at perimeter shooting percentage.

  6. 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. 7

    Note that we round nijα to the nearest integer.

  8. 8

    The two exceptions being USA vs Hungary and USA vs Montenegro.

  9. 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. 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. 11

    ... and USA vs Montenegro in the preliminary round.


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.


Description of Tactics

  1. 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).

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. Pick –Two players “cut” in an attempt to get an offensive advantage with respect to the defenders (similar to a screen in basketball).

  7. 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.

  8. 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).

  9. 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).

  10. 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).

  11. 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.

  12. 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.


Argudo Itturiaga, F., J. Roque, P. Marin, and E. Lara. 2007. “Influence of the Efficacy Values in Counterattack and Defensive Adjustment on the Condition of Winner and Loser in Male and Female Water Polo.” International Journal of Performance Analysis in Sport 7(2):81–91.10.1080/24748668.2007.11868398Search in Google Scholar

Argudo Itturriaga, F., J. Arias, E. Ruize, and J. Alonso. 2009. “Were there Differences in Tactical Efficacy Between the Winning and Losing Teams and the Final Classification in the 2003 Water Polo World Championship?.” Journal of Human Sport and Exercise 4(2):142–153.10.4100/jhse.2009.42.07Search in Google Scholar

Argudo Itturriaga, F., J. Arias, E. Ruize, and J. Alonso. 2011. “Effect of First Ball Possession on Partial and Final Scores in 2003, 2005 and 2007 Water Polo Championship.” Perceptual and Motor Skills 112(2):349–352.10.2466/05.PMS.112.2.349-352Search in Google Scholar PubMed

Delen, D., D. Cogdell, P. Marin, and E. Lara. 2012. “A Comparative Analysis of Data Mining Methods in Predicting Ncaa Bowl Outcomes.” International Journal of Forecasting 28(2): 543–522.10.1016/j.ijforecast.2011.05.002Search in Google Scholar

Dixon, F. and W. Massey. 1951. An Introduction to Statistical Analysis. New York: McGraw-Hill.Search in Google Scholar

Durrett, R. 2009. Elementary Probability for Applications. New York: Cambridge University Press.10.1017/CBO9780511841521Search in Google Scholar

Enomoto, I., M. Suga, M. Takahashi, M. Komori, T. Minami, H. Fujimoto, M. Saito, S. Suzuki, and J. Takahashi. 2003. “A Notational Match Analysis of the 2001 Women’S Water Polo World Championships.” Proceeding of Biomechanics and Medicine in Swimming IX, Saint-Etienne, University of Saint Etienne 487–492.Search in Google Scholar

Escalante, Y., J. Saavedra, M. Mansilla, and V. Tella. 2011. “Discriminatory Power of Water Polo Game-Related Statistics at the 2008 Olympic Games.” Journal of Sports Sciences 29(3): 291–298.10.1080/02640414.2010.532230Search in Google Scholar PubMed

Escalante, Y., J. Saavedra, V. Tella, M. Mansilla, A. García-Hermoso, and A. Dominguez. 2012. “Water Polo Game-Related Statistics in Women’s International Championships: Differences and Discriminatory Power.” Journal of Sports Science and Medicine 11:475–482.Search in Google Scholar

Escalante, Y., J. Saavedra, V. Tella, M. Mansilla, A. García-Hermoso, and A. Dominguez. 2013. “Differences and Discriminatory Power of Water Polo Game-Related Statistics in Men in International Championships and their Relationship with the Phase of the Competition.” The Journal of Strength and Conditioning Research 27(4):893–901.10.1519/JSC.0b013e318260ed85Search in Google Scholar PubMed

Hughes, M., R. Appleton, C. Brooks, M. Hall, and C. Wyatt. 2006. “Notational Analysis of Elitemen’s Water-Polo.” Proceeding of 7th World Congress of Performance Analysis, Szombathely, Hungary 137–159.Search in Google Scholar

Kubatko, J., D. Oliver, K. Pelto, and D. T. Rosenbaum. 2007. “A Starting Point for Analyzing Basketball Statistics.” Journal of Quantitative Analysis in Sports 3:516–525.10.2202/1559-0410.1070Search in Google Scholar

Lorenzo, A., A. Gomez, E. Ortega, S. Ibanez, and J. Sampaio. 2010. “Game Related Statistics which Discriminate between Winning and Losing in Under 16 Male Basketball Games.” Journal of Sports Science and Medicine 9:664–668.Search in Google Scholar

Lozovina, V., L. Pavii, and M. Lozovina. 2004. “Analysis of Indicators of the Load During the Game in the Activity of the Centre in Waterpolo.” Nae More 135–141.Search in Google Scholar

Lupo, C., G. Condello, L. Capranica, and A. Tessitore. 2014. “Women’s Water Polo World Championships: Technical and Tactical Aspects of Winning and Losing Teams in Close and Unbalanced Games.” Journal of Strength and Conditioning Research 28(1):210–222.10.1519/JSC.0b013e3182955d90Search in Google Scholar PubMed

Lupo, C., G. Condello, and A. Tessitore. 2012a. “Notational Analysis of Elite Men’s Water Polo Related to Specific Margins of Victory.” Journal of Sports Science and Medicine 11: 516–525.Search in Google Scholar

Lupo, C., C. Minganti, C. Cortis, F. Perroni, L. Capranica, and A. Tessitore. 2012b. “Effects of Competition Level on the Centre Forward Role of Men’s Water Polo.” Journal of Sports Sciences 30(9):889–897.10.1080/02640414.2012.679673Search in Google Scholar PubMed

Lupo, C., A. Tessitore, C. Cortis, A. Ammendolia, F. Figura, and L. Capranica. 2009. “A Physiological, Time-Motion, and Technical Comparison of Youth Water Polo and Acquagoal.” Journal of Sports Sciences 27(8):823–831.10.1080/02640410902946477Search in Google Scholar PubMed

Lupo, C., A. Tessitore, C. Minganti, and L. Capranica. 2010. “Notational Analysis of Elite and Sub-Elite Water Polo Matches.” Journal of Strength and Conditioning Research 24(1):223–229.10.1519/JSC.0b013e3181c27d36Search in Google Scholar PubMed

Lupo, C., A. Tessitore, C. Minganti, B. King, C. Cortis, and L. Capranica. 2011. “Notational Analysis of American Women’s Collegiate Water Polo Matches.” Journal of Strength and Conditioning Research 25(3):753–757.10.1519/JSC.0b013e3181cc245cSearch in Google Scholar PubMed

Platanou, T., G. Grasso, B. Cufino, and Y. Giannouris. 2007. “Comparison of the Offensive Action in Water Polo Games with the Old and New Rules.” Proceeding of the 12th European Collegiate of Sport Sciences, Jyvaskyla, Finland.Search in Google Scholar

Published Online: 2014-2-21
Published in Print: 2014-1-1

©2014 by Walter de Gruyter Berlin/Boston

Downloaded on 2.12.2023 from
Scroll to top button