Dynamic systems

Modelling human behaviour is implicitly a very complex mathematical exercise, which is multidimensional, and these dimensions will depend upon two or three spatial dimensions, together with time. But the outcomes of successful analyses offer huge rewards, as Kelso (1999) pointed out:

If we study a system only in the linear range of its operation where change is smooth, it’s difficult if not impossible to determine which variables are essential and which are not.

Most scientists know about non-linearity and usually try to avoid it.

Here, we exploit qualitative change, a non-linear instability, to identify col-lective variables, the implication being that because these variables change abruptly, it is likely that they are also the key variables when the system operates in the linear range.

Recent research exploring mathematical models of human behaviour led to populist theories categorized by ‘Catastrophe Theory’ and ‘Chaos Theory’.

an overview of the development of notational analysis

67

5.5.2.1 Critical incident technique

At the First World Congress of Notational Analysis of Sport (1992), Downey talked of rhythms in badminton rackets, athletes in ‘cooperation’ playing rhyth-mic rallies, until there was a dislocation of the rhythm (a good shot or conversely a poor shot) – a ‘perturbation’ – sometimes resulting in a rally end situation (a ‘critical incident’), sometimes not. A good defensive recovery can result in the re-establishment of the rhythm. This was the first time that most of us had considered different sports as an example of a multidimensional, periodic dynamic system.

The term ‘critical incident’ was first coined by Flanagan (1954) in a study designed to identify why student pilots were exhausted at flight school.

‘The critical incident technique outlines procedures for collecting observed inci-dents having special significance and meeting systematically defined criteria’.

The critical incident technique is a powerful research tool but as with other forms of notating behaviour there are limitations inherent in the technique.

Flanagan (1954) admitted that ‘Critical incidents represent only raw data and do not automatically provide solutions to problems’. But Flanagan also pointed to the advantages of such a technique:

The critical incident technique, rather than collecting opinions, hunches and estimates, obtains a record of specific behaviours from those in the best position to make the necessary observations and evaluations.

These opinions sound very much like the debates that have surrounded nota-tional analysis within the halls of sports science over the last decade.

Research in sport has addressed some of these issues and notation and move-ment analysis systems have been developed that can overcome some of these disadvantages. Since Downey’s suggestions in 1992, some researchers have investigated the possibilities that analysing ‘perturbations’ and ‘critical incidents’

offer. McGarry and Franks (1996a, b and d) applied further research to tennis and squash. They derived that every sporting situation contains unique rhyth-mical patterns of play. This behavioural characteristic is said to be the stable state or dynamic equilibrium. The research suggested that there are moments of play where the cycle is broken and a change in flow occurs. Such a moment of play is called a ‘perturbation’. It occurs when either a poorly executed skill or a touch of excellence forces a disturbance in the stability of the game. For example, in a game of rugby, this could be a bad pass or immediate change of pace. From this

an overview of the development of notational analysis

68

situation, the game could unfold one of two ways; either the flow of play could be re-established through defensive excellence or an attacking error, or it could result in loss of possession or a try that would end the flow. When the perturb-ation results in a loss of possession or a try, it was then defined as a ‘critical incident’, sometimes the perturbation may be ‘smoothed out’, by good defen-sive play or poor attacking play, and not lead to a critical incident. A more in-depth approach is essential in order to derive a system for analysing the existence of perturbations. In order to do so, entire phases of play must be analysed and notated accordingly.

Applying McGarry and Franks’ (1995) work on perturbations in squash, Hughes et al. (1997a) attempted to confirm and define the existence of perturbations in soccer. Using 20 English league matches, the study found that perturbations could be consistently classified and identified, but also that it was possible to generate specific profiles of variables that identify winning and losing traits. After further analyses of the 1996 European Championship matches (n = 31), Hughes et al. (1997b) attempted to create a profile for nations that had played more than five matches. Although supporting English League traits for successful and unsuccessful teams, there was insufficient data for the development of a com-prehensive normative profile. Consequently, although failing to accurately pre-dict performance, it introduced the method of using perturbations to construct a prediction model. By identifying 12 common attacking and defending perturba-tions that exist in English football leading to scoring opportunities, Hughes et al.

(1997b) had obtained variables that could underpin many studies involving per-turbations. These 12 causes were shown to occur consistently, covering all pos-sible eventualities and had a high reliability. Although Hughes et al. (1997a, b) had classified perturbations; the method prevented the generation of a stable and accurate performance profile. In match play, teams may alter tactics and style according to the game state; for instance a team falling behind may revert to a certain style of play to create goal-scoring chances and therefore skew any data away from an overall profile.

In some instances, a perturbation may not result in a shot, owing to high defen-sive skill or a lack of attacking skill. Developing earlier work on British league football, Hughes et al. (2000) analysed how the international teams stabilize or

‘smooth out’ the disruption. Analysing the European Championships in 1996, attempts were made to identify perturbations that did not lead to a shot on goal.

Hughes et al. (2000) refined the classifications to three types of causes: actions by the player in possession, actions by the receiver and interceptions. Inaccuracy of pass accounted for 62 per cent of the player in possession variables and interception by the defence accounted for the vast majority of defensive actions

an overview of the development of notational analysis

69

(68 per cent). Actions of the receiver (12 per cent) were dominated by a loss of control; however these possessions have great importance because of the increased proximity to the shot (critical incident). Conclusions therefore focussed on improvements in technical skill of players, however with patterns varying from team to team, combining data provides little benefit for coaches and highlights the need for analysing an individual teams ‘signature’.

Squash is potentially an ideal sport for analysing perturbations and as such, has received considerable attention from researchers. It is of a very intense nature and is confined to a small space. The rhythms of the game are easy to see, and the rallies are of a length (mean number of shots at elite level = 14; Hughes and Robertson 1997) that enables these rhythms and their disruption, i.e. per-turbations and critical incidents. In defining perper-turbations, it may help to understand the reasons for this occurrence – consider the simplest model of a dynamic oscillating system. What are the main parameters and do the equivalent variables in sports contests conform to the same behaviour?

Squash coaches often talk about players imposing their own rhythms on the game – can this be measured by identifying specific values, the frequency of play for specific players and how does this vary against different opponents? This could be repeated in different individual and team sports (see Figures 5.4 and 5.5).

Critical incident and/or perturbation analysis seems to offer a way of making sense of all the masses of data that is available from an analysis of a team sport

Figure 5.4 Distance–time graph for squash players (from Peakman 2001)

an overview of the development of notational analysis

70

such as soccer – even a ‘simple’ sport such as squash will have 4,000–6,000 bits of data per match. The resultant data output can be so overwhelming that it leaves coaches and sports scientists struggling to see significant patterns among the thousands and thousands of bits of data. This method appears to direct analysts to those important aspects of the data that shape winning and losing models. Recent research had demonstrated that player profiles of perturbation shots are stable and differ from player to player (Hughes et al. 2007).