This study focused on a trial-by-trial error correction to decrease the variability in the release angle, which is the only factor affecting the variability of pitch locations in high-speed baseball pitching (Kusafuka et al., 2021). The results of the autocorrelation analysis suggested that pitchers with a small variability in the release angle made a correction that led to a small variability. On the other hand, pitchers with large variability in the release angle tended to make over-corrections in the vertical direction but made no corrections in the horizontal direction. These findings indicate that trial-by-trial error correction can be a strategy to decrease variability; however, there are different reasons for incorrect correction depending on the direction of errors.
In the azimuth release angle, the ACF1 of the pitcher with a small variability was close to 0, indicating a near-optimal error correction that led to a small variability, whereas the ACF1 of the pitcher with a large variability was positive, indicating a smaller than optimal error correction. This result suggests that pitchers with larger variability in the release angle repeated similar release angles without error correction between trials in the azimuthal direction. However, the inter-trial changes in the azimuth release angle showed that the pitchers with large variability had an average drift, where the value of the release angle increased or decreased as the trial progressed (Fig. 2). It is possible that the pitchers with large variability in pitching angle made trial-by-trial error corrections that changed the values of the pitching angle on average rather than reducing the variability of the pitching angle, and that they made no trial-by-trial error correction. The two largest pitchers’ azimuth release angle variability was separated from those of the other pitchers, which may have affected the correlation analysis.
However, there was no significant correlation between the variability and ACF1 in the elevation release angle. This could be attributed to the small variability in the release angles of the pitchers. The variability of the release angle was generally smaller than that of the azimuthal release angle, and this study compared pitchers with small variabilities in the release angle. The azimuth release angle in this study and arrival position in the previous study, for which there was a significant correlation between variability and ACF1, did not appear to have a significant correlation between variability and ACF1 when comparing participants with small variability (although this was a qualitative observation of the graphs). This suggests that trial-by-trial error correction of release angles in pitching may effectively reduce variability when considering a wide range of pitchers’ skill levels, but not for relatively small improvements that would fill in the differences among skilled pitchers.
The results of this study differed from those of a previous study that evaluated trial-by-trial error correction by autocorrelation analysis performed on the intertrial changes of the dart throwing positions (van Beers et al., 2013). The study showed that the lag-1 autocorrelation of experienced players with less variability was near zero, implying near-optimal error correction. In contrast, it was negative for beginners with more variability, suggesting an over-error correction. One of the reasons for this is that all the participants in this study were skilled. Regarding the elevation release angle, the participants may have been skilled at reducing the variability and were generally able to make appropriate corrections.
This study also analyzed the inter-trial changes in the elevation/azimuth release angle together by transition probability analysis in addition to separate autocorrelation analysis. As a result, there is a difference in the correction of skilled baseball pitchers depending on their state and direction. Moreover, the difference was not simply dependent on the direction (No, Elevation, Azimuth, and Both) of labeling. This result was first obtained by analyzing the trial-by-trial error correction in two dimensions. One factor in which the difference in correction was not dependent on the direction was the physical characteristics of baseball pitching. A previous study showed that the direction of the probabilistic structure in the pitch location is influenced by the trajectory of the throwing arm (e.g., right overarm pitchers pitched along a right-up-left-down ellipse) (Shinya et al., 2017). However, if the release angle is influenced only by the trajectory of the throwing arm, the transition probabilities to states 1 and 3 are always greater than those to states 2 and 4. The results that do not follow suggest that there are more complicated factors that cannot be explained only by physical characteristics in the two-dimensional error correction of the release angle.
Considering the lack of correlation between ACF1 and the variability in the elevation release angle, it is possible that all participants focused on and were skilled at reducing the variability in the elevation release angle and were generally able to make appropriate corrections. This interpretation is supported by the fact that all the participants’ variability in the elevation release angle was less than 2° (those of the azimuth release angle were not). In addition, the pitchers who frequently made no error corrections had more variability in the azimuth release angle (and the ratio of the variability of the azimuth release angle to the elevation release angle). This result is consistent with the result of the autocorrelation analysis that in the azimuth release angle, the pitcher did not make as much error correction as the pitcher who had a large variability. These results indicate that one of the reasons for the large variability in the azimuth release angle is the lower error correction.
The results of this study suggest that trial-by-trial error correction can be a strategy for decreasing variability in high-speed motor tasks. How humans correct errors has been investigated in the context of adaptation or response to new tasks or environments created by various tools, which change the feedback the executors can receive (Helmholtz, 1867; Shadmehr & Mussa-ivaldi, 1994). However, this study aimed to clarify the error correction by directly analyzing the inter-trial changes of the elements in the actual movement. This is because, in tasks such as pitching, where the object is moving away from the participant’s own hand rather than on a monitor, it is more difficult to manipulate errors (i.e., the object's motion trajectory and arrival position) than in simple tasks. However, it should be mentioned that if a new experimental system can be constructed using simulation technology or virtual space (VR) technology, it will be possible to reproduce the same experimental protocol that changes the feedback that executors can receive for the pitching task. For example, by reproducing the ball trajectory in VR according to the released ball (or simply the pitching motion) by simulation and analyzing the motion in the next trial when occasional perturbations are added, it will be possible to study error correction, as in the reaching study. It would also be possible to clarify how, and which part of the body, is corrected during pitching and whether the correction is possible.
In addition, it is important to note the large number of release parameters involved in determining the ball’s arrival position during pitching. When the number of parameters that determine the outcome is large (redundancy exists), as in the case of pitching, the release angle required to reach the target is not always uniquely determined to have the same value, although the variability in the pitching angle alone can explain the variability in the ball arrival position. In other words, depending on the values of the other release parameters, the ideal release angle for the ball to reach the target varied each time. Therefore, even if we could reproduce a release angle value in the next trial that completely corrects the error with the target at the ball arrival position (and the ball trajectory obtained up to that point), it would not be an optimal correction if the values of the other release parameters were changed. The extent to which the relationship with the changes in the values of other parameters affects the results of this study is not clear; however, it will be necessary to examine this issue in the future.
This study analyzed the intertrial changes in the elevation/azimuth release angle by transition probability analysis and a separate autocorrelation analysis. Consequently, several new findings promote an understanding of the error correction of the release angle in high-speed baseball pitching. However, several issues remain to be resolved. Two issues related to the methods used in this study, which should be considered in future studies, are presented. The first was whether the participants were trying to correct their errors. As the participants were instructed to perform the movements accurately, it was assumed that the changes in movements were the result of attempts at correction. However, humans are sometimes misguided and have cognitive biases, and their movements and outcomes do not always reflect participants’ intentions. This means that participants’ intentions and outcomes did not always correspond. Although humans learn and adapt both explicitly and implicitly (Albert et al., 2021; Avraham et al., 2020; Huberdeau et al., 2019; Schween et al., 2020; Taylor et al., 2014; Taylor & Ivry, 2012), the contribution of error correction to these processes requires further investigation.
The second issue is the index for quantifying the error correction. For example, an ACF1 close to zero does not necessarily mean that the trial-by-trial error correction (error sensitivity) is close to optimal, which is an assumption for interpreting the autocorrelation used in this study. Therefore, trial-by-trial error correction has been studied mainly in error manipulation protocols, such as those used in previous studies. Even when the autocorrelation is close to zero, the motor plan may always be accurate and not change from trial to trial. In this case, the intertrial variability was due to noise. This possibility was discussed in a previous study that used a dart-throwing task (van Beers et al., 2013) by comparing it with another study that used a reaching task (van Beers, 2009). In a study using the reaching task, visual manipulation was performed such that the error was half the actual error. A comparison was made with the case in which the error was displayed as usual. If there had been no error correction, the ACF1 would have been similar (close to zero) in both cases, but it would have been larger when the error was manipulated by half, suggesting that the intertrial variability changed based on error correction. The authors thought that this interpretation might also be possible in the dart-throwing task. However, there are many differences between tasks, and it is necessary to carefully discuss whether the conclusions obtained from one task can be applied to another. In addition, it is not clear how much of the value needs to be regarded as an error correction. It is necessary to examine how to determine the error correction that may only be shown through comparison, as this is a major issue concerning the definition of the concept of error correction. Furthermore, it is highly possible that not only the previous trials but also the previous trials were used to make decisions on the correction of motor planning. Because the number of trials in this study (30 balls) was quite small compared to those in previous studies, the number of previous trials yielding information that is considered for these processes and the relationship with the number of trials should be investigated in the future.