Quantitative analysis of playing efficiency in squash

Resumen quantitative analysis of playing efficiency

A high-level performance in squash depends on many factors or elements of the game, among which appropriate playing tactics are clearly of great importance. It manifests itself in a variety of strokes executed by the player or group of players in a match. Given the great number of different strokes and their execution in various parts of the court, a player may select and use different strokes in identical or similar circumstances or the same strokes in different circumstances. The proper choice of stroke depends on the player’s tactical assessment that leads to the choice of the most efficient stroke in the given circumstances. The scientific literature abounds with studies dealing with playing tactics in squash. These studies have applied various data collection methodologies based on the notation of different tactical indicators obtained by analyses of video recordings. Hong et al. (1996) and Hughes and Robertson (1998) analysed the structure of strokes in the court divided into a small number of equivalent segments. Similarly, Hong, Chang and Chan (1996) and Hughes (1985, 1986) analysed the differences in patterns of play between players at different competitive levels. A more detailed analysis of playing tactics used in squash was provided by McGarry and Franks (1994). They used a stochastic Markov model as a descriptor of empirical athletic behaviour and predictor of future sport performance. McGarry and Franks (1995) used a slightly modified stochastic model in their subsequent studies. They found that the player’s tactics do not change in a match against the same opponent, which is not true when playing against different opponents. The authors reported similar findings even after they had changed their stroke tracking methodology by taking into consideration the player’s previous stroke besides the stroke of the opponent and by observing the backhand and forehand of each stroke separately (McGarry and Franks, 1996a, 1996b).

1. Introduction

A high-level performance in squash depends on many factors or elements of the game, among which appropriate playing tactics are clearly of great importance. It manifests itself in a variety of strokes executed by the player or group of players in a match. Given the great number of different strokes and their execution in various parts of the court, a player may select and use different strokes in identical or similar circumstances or the same strokes in different circumstances. The proper choice of stroke depends on the player’s tactical assessment that leads to the choice of the most efficient stroke in the given circumstances. The scientific literature abounds with studies dealing with playing tactics in squash. These studies have applied various data collection methodologies based on the notation of different tactical indicators obtained by analyses of video recordings. Hong et al. (1996) and Hughes and Robertson (1998) analysed the structure of strokes in the court divided into a small number of equivalent segments. Similarly, Hong, Chang and Chan (1996) and Hughes (1985, 1986) analysed the differences in patterns of play between players at different competitive levels. A more detailed analysis of playing tactics used in squash was provided by McGarry and Franks (1994). They used a stochastic Markov model as a descriptor of empirical athletic behaviour and predictor of future sport performance. McGarry and Franks (1995) used a slightly modified stochastic model in their subsequent studies. They found that the player’s tactics do not change in a match against the same opponent, which is not true when playing against different opponents. The authors reported similar findings even after they had changed their stroke tracking methodology by taking into consideration the player’s previous stroke besides the stroke of the opponent and by observing the backhand and forehand of each stroke separately (McGarry and Franks, 1996a, 1996b). In spite of the large number of investigated tactical indicators, such studies bring up the question of how accurate is the determination of the stroke location. Most often the problem concerning the accuracy of the result has been resolved by establishing reliability (Wells et al., 2004) and the validity of the measurement procedure (repeated determination of the stroke location) which, however, should not be interpreted as measurement accuracy. Moreover, the division of the court has failed to correspond to the playing conditions and the ensuing bouncing of the ball off all court walls. To avoid the abovementioned deficiencies, our study took into consideration specific playing conditions (bouncing of the ball off all walls), which is why the court was divided into 29 segments. The efficiency of individual playing tactics was established on the basis of the positioning of all strokes in a two-dimensional space. Therefore, the aim of this study was to establish stroke distribution and, consequently, stroke efficiency as well as to investigate differences in the percentage of strokes executed in specific segments of the court by two groups of players of different quality.

2. Methods

2.1 Design Data was collected during two competitions, the World Team Championship (Vienna, 2003) and the Slovenian National Championship (Ljubljana, 2003). Eleven matches were recorded in both competitions, and the players played until they won their third game. In total, 42 games at the World Team Championship and 44 at the Slovenian National Championship were recorded. As an individual game is in itself a separate part of the match and not related to other games in terms of time or result, all variables were examined at the level of a game and the results of both players (the winner and the loser) were considered. The sample of variables included the number and percentage of strokes in individual segments of the court. 2.2 Participants Sixteen of the world’s top squash players played in the world championship and 14 top Slovenian squash players in the national championship. 2.3 Materials All matches were recorded with a fixed SVHS video camera (JBL, UTC – A6000H, Korea) with the frequency of capturing input pictures of 25 Hz. The camera was mounted on the ceiling in the centre of the squash court and its wide-angle lens (JBL, SCV 2982D, Korea) covered the entire court.

Figure 1: The court as recorded by the wide-angle camera lens.

The wide-angle lens did not affect the measurements (Perš et al., 2002). The camera did not interfere with the play and could not be hit by the ball. The video-recordings were digitised using the Video DC30+ video digitiser hardware (Miro, Germany) with a resolution of 384 x 576 pixels at a data rate of 2 MB.s-1, while the processing was carried out at a resolution of 384 x 288 pixels. The second camera (Sony, DCR-TRV17E, Japan) was positioned outside the court, a few metres behind the back (glass) wall of the court. It was used to measure the height of individual strokes (the distance between the floor and the point of striking). The data obtained were entered manually in the Sagit/Squash software. 2.4 Procedure The SAGIT/SQUASH tracking system was used to divide the court into 29 segments and to determine the positions of the strokes (Vu?kovi? et al., 2005). Each segment represents one variable. The size of the segments corresponds to specific playing conditions (bouncing of the ball off the front, side and back walls of the court). Canonical discriminant analysis and a one-way analysis of variance with the level of significance of P<0.05 were applied to establish differences between the groups of players of different quality in terms of the percentage of strokes made in an individual segment.

Figure 2: The court divided into 29 segments.

3. Results

Table 1 shows the percentage of strokes executed by both groups of players by segment. To allow for better transparency, only those variables were taken into account whose resulting values are normally distributed. All strokes were taken into consideration, less the serves. With the initial stroke, the point of striking is often in the central part of the court and therefore recording these points (strokes) would certainly affect the results and/or the number and percentage of strokes in those segments of the court which are considered disputable from the point of view of playing quality and point to playing imprecision.

Table 1: Percentage of strokes executed by top world players and top Slovenian players by court segment.

The world’s top players executed the majority of strokes in segment 26, followed by 27, 25, 4, 2, 3 and 28. In these segments the percentage of strokes exceeded 4 percent. The top Slovenian players also executed the highest percentage of strokes in segment 26. More than 4 percent of all strokes were executed in segments 27, 25, 19 and 28. In both groups of players, the highest number of strokes was recorded in the back area of the court (segments 22, 24, 25, 26, 27, 28 and 29), namely top world players 52.7% and top national players 52.3% of the total.

Table 2: Results of discriminant analysis in terms of the percentage of strokes executed by both groups of players in various segments of the court.

Table 3: Standardised correlation coefficients.

Table 4: Classification by discriminant function.

The values of the correlation coefficients show the highest discriminant power with the function of segments 3, 4, 19, 22, 24 and 26, while the negative values seen in the variables 19, 22 and 24 show that the nationally ranked players probably executed a higher percentage of strokes in the above segments of the court. The results of the analysis of variance (Table 1) confirm this.

4. Discussion

Despite the fact that players from both groups executed the highest and an almost identical percentage of strokes in the back area of the court, a detailed analysis of the strokes in this part of the court reveals statistically significant differences. The percentage of strokes executed by the world ranked players was statistically significantly higher in segment 26 (p = .000) and that of the Slovenian players in segments 22, 24, 25, 28 and 29 (p < 0.05, see Table 1). In terms of squash playing tactics, the strokes in the back area of the court consist of the basic tactical principles of defensive play (McKenzie, 1994) which could also be named basic play. In this part of the court the player has the least possibilities of hitting a winning return. It is evident that both groups of players are well aware of this fact, nevertheless, the world ranked players play much more precisely and efficiently. Such conclusions are underpinned by the statistically significant difference (p < 0.05, see Table 1) between the strokes executed in segments 1, 3, 4 and 16 by both groups. Irrespective of the playing tactics the ball has to be hit as closely as possible to the side wall to prevent the opponent from delivering a simple return or even starting an offensive action. Moreover, these segments (3, 4 and 16) are located in that part of the court where the players often execute volleys. The higher percentage of strokes seen in these segments with top players could thus indicate more offensive tactics. In the said (central) part of the court, the nationally ranked players executed the highest percentage of strokes in segment 19. It constitutes a strategic position (T-position) which the player wishes to take at the time the opponent strikes the ball, which is very important from the point of view of playing performance (Vu?kovi? et al., 2004). This group of players recorded a statistically significantly higher percentage of strokes in segment 12 (p = .040), located in the direct proximity of the abovementioned segment. All this manifests the very inefficient employment of playing tactics by the nationally ranked players. The more aggressive tactics of the top players is manifested in the values for segment 2, which is located in the outermost front left part of the court. The strokes in this segment are correlated with offensive strokes whose purpose is either to deliver a winning return or force the opponent to make a mistake. , Clearly the higher percentage of strokes of world ranked players (p = .000) indicates their more offensive playing tactics, which is probably due to their more precise and thus more efficient basic play.

5. Conclusion

It may be concluded from the results that the playing tactics of players of different quality are quite similar. Both groups executed the highest percentage of those strokes whose aim was to hit the ball to the back area of the court. Consequently, the highest percentage of strokes was executed in segments located in the back of the court. This points to the fact that players from both groups are aware of the significance of the fundamental tactical principle for achieving a high performance, namely that the ball has to be hit as close as possible to the side wall and back corner of the court. Apparently the precision of strokes and related application of individual tactical principles and tactics are the main factors distinguishing the groups of players.

Bibliografía

• 1. Hong, Y., Chang, T.C. & Chan, D.W. (1996). A comparison of the game strategies employed by national and international squash players in competitive situation by notational analysis. Journal of Human Movement Studies, 31, 89-104.
• 2. Hong, Y., Robinson, P.D., Chan, W.K., Clark, C.R., & Choi, T. (1996). Notational Analysis on Game Strategy Used by the World’s Top Male Squash Players in International Competition. The Australian Journal of Science and Medicine in Sport, 28 (1), 18-23.
• 3. Hughes, M. (1985). A comparison of the patterns of play of squash. In I.D. Brown, R. Goldsmith, K. Coombes and M.A. Sinclair (eds.), International Ergonomics, London (pp. 139-141).
• 4. Hughes, M. (1986). A review of patterns of play in squash at different competitive levels. In J. Watkins, T. Reilly and L. Burwitz (eds.), Sport Science, London (pp. 363-368).
• 5. Hughes, M., & Robertson, C. (1998). Using computerised notational analysis to create a template for elite squash and its subsequent use in designing hand notation systems for player development. In A. Lees, I. Maynard, M. Hughes and T. Reilly (eds.), Science and Racket Sports II, London (pp. 227-234).
• 6. McGarry, T., & Franks, I.M. (1994). A stochastic approach to predicting competition squash match-play. Journal of Sports Sciences, 12, 573-584.
• 7. McGarry, T., & Franks, I.M. (1995). Modelling Competitive Squash Performance from Quantitative Analysis. Human Performance, 8 (2), 113-129.
• 8. McGarry, T., & Franks, I.M. (1996). Development, Application and Limitation of a Stochastic Markov Model in Explaining Championship Squash Performance. Research Quarterly for Exercise and Sport, 67 (4), 406-415.
• 9. McGarry, T., & Franks, I.M. (1996). In search of invariant athletic behaviour in sport: An example from championship squash match-play. Journal of Sports Sciences, 14, 445-456.
• 10. McKenzie, J. (1994). Beyond the basics. Excelling at Squash. London, Sydney, Auckland: Hadder & Stoughton.
• 11. Perš, J., Bon, M., Kova?i?, S., Šibila, M., & Dežman, B. (2002). Observation and Analysis of Large-scale Human Motion. Human Movement Science, 21, 295-311.
• 12. Vu?kovi?, G., Dežman, B., Er?ulj, F., Kova?i? S., & Perš, J. (2004). Monitoring the time and frequency of players staying on the basic T-position in squash. In: A. Lees, J.F. Kahn and I.W. Maynard (eds.), Science and Racket Sports III, New York (p. 208-213).
• 13. Vu?kovi?, G., Dežman, B., Er?ulj, F., Kova?i? S., & Perš, J. (2005). Position error analysis of Sagit/squash system in manual stroke annotation. In: 10th Annual Congress [of the] European College of Sport Science, Book of abstracts, Belgrade, Serbia (p. 265).
• 14. Wells, J., Robertson, C., Hughes, M., & Howe, D. (2004). Performance profiles of elite men’s squash doubles match play. In: A. Lees, J.F. Kahn and I. W. Maynard (eds.), Science and Racket Sports III, New York (pp. 196-201).