RESULTS AND DISCUSSION

Distance affordances

From the data several characteristics concerning decision-making behaviour in boxing are readily apparent. In particular, it was noted that specific boxing action patterns emerged as affordances of the individually-scaled distance to the target. We observed significant differences between the bounded regions of scaled distances for first time appearances and disappearances of specific boxing action patterns in the boxers. A one-way repeated measures analysis of variance revealed a significant distance main effect for the initial emergence scaled distances of the boxing action modes F(5,35) = 44.58; p < 0.00001. Kolmogorov-Smirnov D statistics of the critical scaled distance distributions for the first time activation of the whole set of the boxing action modes were not significant (p > 0.20). In similar vein Lilliefors probabilities (p > 0.20) as well as Shapiro -Wilk W statistics (all larger than p < 0.62) showed no significant departure from normal distribution.

In almost all comparisons of distances we obtained significant differences (see Table 1) except for comparisons between the initial emergence of the right and left jabs (180, -180), right and left hooks (90xz, -90xz) and left hooks and right uppercuts (-90xz, 90yz).

Even the more stringent criteria such as Bonferroni corrections for alpha levels preserved these distance effects. In similar vein, boxer - target distance dependency was revealed by a repeated - measures analysis of variance on the distances at which disappearance of previously formed action patterns occurred F(3,21) = 2467.93; p < 0.00001). Post - hoc tests yielded significant scaled distance differences between the annihilation of the jab (180, -180) and uppercut (90yz, -90yz) punching activity (see Table 2). Kolmogorov-Smirnov D statistics of the critical scaled distance distributions for the annihilation of the jab action modes were not significant (p > 0.20). In similar vein Lilliefors probabilities (p > 0.20) as well as the Shapiro - Wilk W statistics (p < 0.72) showed no significant departure from normal distribution. The critical scaled distances of the disappearance of uppercut punches possessed delta distributions. However, this violation of normality assumption did not affect the conclusions since the differences between the jab annihilation critical distance means (DC = 0.45) and the uppercut annihilation critical distances (DC = 0) are much larger than their internal distribution variability. See Figure 2 A for illustration.

Even the more stringent criteria such as Bonferroni corrections for alpha levels preserved these distance effects. In similar vein, boxer - target distance dependency was revealed by a repeated -measures analysis of variance on the distances at which disappearance of previously formed action patterns occurred F(3,21) = 2467.93; p < 0.00001). Post - hoc tests yielded significant scaled distance differences between the annihilation of the jab (180, -180) and uppercut (90yz, -90yz) punching activity (see Table 2). Kolmogorov-Smirnov D statistics of the critical scaled distance distributions for the annihilation of the jab action modes were not significant (p > 0.20). In similar vein Lilliefors probabilities (p > 0.20) as well as the Shapiro - Wilk W statistics (p < 0.72) showed no significant departure from normal distribution. The critical scaled distances of the disappearance of uppercut punches possessed delta distributions. However, this violation of normality assumption did not affect the conclusions since the differences between the jab annihilation critical distance means (DC = 0.45) and the uppercut annihilation critical distances (DC = 0) are much larger than their internal distribution variability. See Figure 2 A for illustration.

Overall, boxers revealed the following behavior: At scaled distances D > 1.2 the only observed state for the performers was the guard (i.e. the quiescent) state (0 deg.). At scaled distances of D around 1.2 the previously quiescent jab modes of action (180 deg. and -180 deg.) emerged. We observed that, in all performers, right and left jab action modes emerged for the same individual values of D (see Figure 2 A and C).

The obtained Pearson product - moment correlation coefficient r = 1.00 between the right and left jab initial action emergence corroborated this finding. For values around D = 0.9 the hooks (90xz deg. and -90xz deg.) action modes emerged. In only one out of eight performers the hook patterns emerged at different values of the scaled distance D. All of the other performers activated the hook patterns at the same individual D values. This finding was verified by the significant Pearson product - moment correlation coefficient between the right and left hook action modes r = 0.86; p = 0.006. Interestingly, uppercut action patterns did not show this kind of relationship. Right uppercut action modes emerged around greater D values (D = 0.8) than the left uppercuts (D = 0.65). The Pearson product - moment correlation coefficient between the right and left uppercut first time emergence D values was r = - 0.09; p = 0.826. This result signified that the initial emergence of uppercuts was the least coupled of events to scaled distance information. Taking into account that left and right jabs as well as left and right hooks emerged for the first time at the same individual scaled distances D, which was not the case for the left and right uppercuts, it can be assumed that scaled distances at which left and right uppercuts emerged for the first time might reveal the specific boxing handedness of the performers.

Generally, the full set of boxing actions was active in the region 0.65 < D <0. 45.

At the scaled distance D = 0.45 a spontaneous disappearance of the jab action patterns occurred. The Pearson product - moment correlation coefficient between the right and left jabs r = 1.00 confirmed that this disappearance occurred for the same individual D values (see Figure 2 A and C). Another abrupt disappearance, this time for uppercuts, arose at D = 0. At this scaled distance only the hooks remained active. Overall, these results showed that the initial emergence of the jab and hook punching modes of action showed a strong tendency to be related to scaled distance from the target, whereas uppercuts were much more variable in this respect.

These data suggested that decisions emerged as boxers picked up and exploited information about specific types of actions afforded at specific distances scaled for each individual. Significant differences between the mean group relative distances of the initial activation of different action patterns depended on the interaction between environmental constraints (absolute distance from the target) and the structural anatomical constraints of each individual boxer (effective length of upper limbs). The initiation of jab punches enabled the use of full arm length, making the effective limb length equal to its real length in extension, whereas hooks and uppercuts, depending on the degree of flexion in the elbow joint, always had a shorter effective length at the moment of collision with the target. Consequently different critical relative distances for the emergence of different action patterns were identified in the experiment. In other words, changes to the perceived context led the motor system of each boxer into and out of different functional coordination states. This feature of performance is depicted in Figure 2B where a clear polarized structure of bounded regions in the perceptual-motor landscape of the boxers is visible as a function of the scaled distance to target. At greater distances jabs were much more frequent, and hooks and upper cuts at shorter distances. Thus, participants activated specific punches at distances that fitted the effective length of their arms, signifying that they exploited a kind of body-scaled distance information in constraining this action, as reported elsewhere in the motor behaviour literature (Konczak, 1990; Konczak et al., 1992).

The results support the expressed view that, in picking up affordances of target strikeability, information on perceived reachability to a target plays a crucial role. Hence, it could be tentatively assumed that the perceived strikeability by participants is merely a special case of this early acquired affordance reported in the motor development literature. However, our data revealed that reachability is not solely responsible for the observed decision-making behaviour of the boxers. First, at the point of jab annihilation the target was reachable, although at that very point jabs ceased to be active. Second, at the point of disengagement of uppercuts the target was also reachable, although uppercut actions were being annihilated at this point. These data imply that besides reachability, other performer and task constraints, perhaps specifically related to the intended intensity of collision between the fists and target, are considered by boxers for the target to be perceived as strikeable. From a constraints-led perspective, these data confirm that handstrike selection is an emergent phenomenon dependent on the continuing interaction of intentionality, perceptual information and body-scaled affordances for each individual boxer (see Newell, 1986; Davids et al., 2003).

Movement-information coupling

As reported in Table 3, the values of the partial correlation coefficients revealed strong positive relationships between the perceived efficiency of each type of punch (taken as an independent variable) and the associated probability of occurrence of a punch, treated as dependent variable. Also, strong inverse relationships between the perceived efficiency of hooks and the probability of occurrence of jabs and between the perceived efficiency of jabs and uppercuts and the probability of occurrence of hook punches were obtained.

Similarly, Table 4 shows the relations between the differences of the perceived efficiency of punches (taken as independent variables) and differences in the probability of occurrence of each type of action mode, treated as dependent variables. High positive relationships were obtained. These data showed that, as long as boxers perceived some type of actions as more efficient, they tended to use them more often than other modes of action.

Significant partial correlations between the probabilities of occurrence of action patterns and perceptual judgments of their efficiency suggest that the dynamic perceptual-motor landscape formed by boxers during performance is particularly sensitive to the perception of punching efficiency. The positive and negative influences of perceived efficiencies exemplify how the distance-dependent reciprocal enhancements and suppressions of action patterns were shaping the perceptual-motor landscape of individual boxers (see Table 3 and 4). In other words, boxers were simultaneously exploring and modifying their distance-dependent perceptual-motor landscapes by increasing the probability of the most successful types of punches, i.e. those which afforded punching efficiencies of greater magnitude, while suppressing those with efficiencies perceived as less functional. This interpretation suggests that boxers do not perceive targets solely as strikeable or not, but these perceptions interact with intentions and cognitions to continuously regulate decisions about how a target can be most efficiently punched (which action pattern to activate more frequently at specific locations). These findings demonstrated how decision-making is an emergent phenomenon which can be considered context- and individual-dependent, as the interaction of cognitions, intentions and perceptions of individual boxers modifies the functional coupling between perceived efficiencies and actions. In this way, combat sports like boxing can be characterized as a continuous search for the essential relationship between performer, task and environmental constraints, leading to the discovery of the most efficient action patterns, manifest in distance-dependent changes of the action probability landscape.

Keywords : Martial arts, boxing, affordances, decision-making, action selection

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