Is Anticipation Skill Learning Bayesian?

ABSTRACT

Purpose: The aims of this study were to examine the learning of anticipation skill in the presence of kinematic and outcome probabilities information, and to see if this learning exhibited characteristics of Bayesian integration. Method: Participants with no competitive tennis playing experience watched tennis player stimuli playing forehand tennis shots and were tasked with predicted shot outcomes. Accuracy, response times and perceived task effort were recorded, pre, post and during four acquisition blocks where outcome feedback was provided. In both Experiment 1 and 2, kinematic information about shot direction was either present in the training group stimuli or absent. In Experiment 1, left/right shot probability information remained equi-probable for both groups. In Experiment 2, both groups also trained with a bias in the shot outcome probability toward one shot direction on 80% of the trials across acquisition blocks (and were not told about this manipulation). Results: Pre-to-post anticipation performance improved in the presence of kinematic (EXP 1) or both information sources (EXP 2). Pre-to-post improvements in the presence of shot outcome probability information were congruent with the bias in the shot direction trained (EXP 2). Superior anticipation performance was found when both information sources were present. The presence of kinematic information resulted in increased perceived effort during early training (EXP 1 & 2). Bayesian odds ratios indicated that shot direction probabilities and kinematic information were integrated during anticipation skill learning. Conclusion: Learning with shot direction probabilities and kinematic information shows characteristics of Bayesian integration.

KEYWORDS:

• Advance cue
• perceptual learning
• predictive coding
• situational probabilities
• sport

Expert sportspeople are known to make use of superior memory structures to recognize and recall pattern of play, make use of situational probabilities information ranking the most likely outcomes, and to make use of advance cues arising from the players movements prior to an outcome to anticipate an upcoming event (Williams et al., 1999). However, little is known about how these information sources interact to allow one to anticipate and how one might learn to make use of multiple information sources to anticipate (Broadbent et al., 2015; Gredin et al., 2020). Here, two experiments investigate how the acquisition of anticipation skills varies when learners encounter biases in shot outcome probabilities alongside kinematic information concerning shot outcomes. In a subsequent analysis, we examine the usefulness of a Bayesian learning approach to understand the relative influence of experience of Outcome Tendencies and Advance Cue Information on learning to anticipate shot direction in tennis.

Advance cue utilization refers to experts’ skills in identifying movements of the opponents actions that indicate the outcome of the upcoming action (Williams et al., 2002). Historically, the dominant approach to examine anticipation skill is to investigate how advance cue information is perceived and guides decision making by experts (Huys et al., 2008). It has been found that experts are able to perceive whole-body dynamic patterns in the biological motion of an opponent in order to anticipate outcomes (Abernethy et al., 2001; Huys et al., 2009; Ward et al., 2002; Williams et al., 2009) and this skill can be learnt (Smeeton et al., 2013).

However, with growing interest in recent years, the question of if and how contextual information is used with advance cue information to enable anticipation of action outcomes (Cañal-Bruland & Mann, 2015) has been raised. Contextual information arises from information sources separate to advance cue information and can be available earlier in time than this latter source (Murphy et al., 2019). Using analysis of professional tennis games, Triolet et al. (Triolet et al., 2013) showed players were capable of accurately anticipated opponents shot outcomes based on information available 240–340 ms before ball-racket contact. However, in controlled laboratory conditions of shot outcome probabilities, skilled anticipation is observed closer in time to ball-racket contact (Farrow et al., 2005); also see Abernethy et al. (Abernethy et al., 2001). In fact, Murphy et al. (Murphy et al., 2019) has reviewed evidence that contextual information can be used by experts from event-related information (Gray, 2002a), strategic game information (Gray & Cañal-Bruland, 2018), opponent tendencies (Mann et al., 2014), player position (Runswick et al., 2018), and tactical initiative (Crognier & Féry, 2005).

To offer experimental control, contextual information has been provided in the form of outcome statistics prior to an event to be anticipated (Gredin et al., 2018). Gredin et al. (2018) invited expert and novice soccer players to anticipate the final action of the opponent and explicitly provided contextual information about the opponent’s action tendencies before each trial. The action in the subsequent trial was either congruent or incongruent with the contextual information After Green and Flowers (2003) they recorded cognitive effort and expected explicit integration of probabilistic information to require more cognitive effort than that provided implicitly. It has been demonstrated that providing situational probabilities explicitly improves anticipation performance when the prior probabilities align with the outcome for both skilled and unskilled football players. However, incongruent prior information negatively impacts the anticipation performance of novice players. No differences in cognitive effort were found however. These results show that explicit provision of prior probabilities differently influence perceptual and cognitive processes impacting on anticipation performance in experts and novices. However, knowledge of in-game probabilities typically emerges from specific experience with the task and domain-general knowledge. Explicit knowledge of them may be detrimental to performance (Mann et al., 2014; Murphy et al., 2019).

Other researchers have used patterns of outcomes presented prior to the upcoming outcome to be anticipated. This design has been used to examine the effect of contextual information on anticipation performance. For example, Loffing et al. (Loffing et al., 2015) conducted a study where predetermined sequences of smashes and lobs were presented in volleyball to assess the skilled and less skilled players’ ability to recognize the target shot quickly and accurately at the end of the predetermined sequence. Skilled players demonstrate the use of prior event sequences to anticipate outcomes, as indicated by their quicker and more accurate identification of congruent sequences compared to incongruent sequences (see also (Gray, 2002b).

Whilst expert-novice differences highlighted provide one line of evidence toward what is learnt, training studies offer additional evidence. Mann et al. (Mann et al., 2014) examined the learning of action preferences in skilled handball goalkeepers. The action preferences group were exposed to throws that favored the top left of the goal 75% of the time. In the no preference group the throws were distributed equally to the four corners of the goal. Those that were exposed to handballers’ throw preferences were able to learn this throw outcome bias in as little as 72 training trials. Improvements were found when action preference was present and accuracy decreased when the preference was absent. Whilst those that were not exposed to throw preferences did not improve response accuracy from pretest to posttest. The response time decreased by approximately 200 ms when the action preferences group anticipated a player with action preferences but was longer when preferences were absent. The lack of overall improvement in anticipation skill was attributed to the relatively short training period and the high skill level of the participants. But potentially learning to perceive differences in kinematic information may have been prevented by way of the relatively high informational value of player preference information negating the need to explore and discover other information such as that from a kinematic source.

An important future direction for researchers highlighted by (Murphy et al., 2019, 2019), is the need to examine how contextual and advance cue information interact when successfully anticipating action outcomes. Some have suggested that contextual information has decreasing importance as the event outcome approaches in time and therefore weights less on anticipation response. Meanwhile, the relative importance of advance cue information is thought to increase as the event outcome approaches (Müller & Abernethy, 2012). In support of this proposal, Loffing and Hagemann (Loffing & Hagemann, 2014) found that expectations were initially based on contextual information, which then decreased over time and the relative value of kinematic information increased. Whilst others have shown that contextual information is used under specific conditions (Murphy et al., 2016; Triolet et al., 2013) and sometimes cannot help, but be used even when it negatively effects performance (Runswick et al., 2019). Consistent with Beek et al. (Beek et al., 2003) experts make use of reliable information when available, and perhaps even in the case of incongruent information (i.e. negatively correlated). However, ongoing questions are how do experts learn to perceive this information, and whether other information sources compete or form higher order relationships to better predict outcomes (Jacobs & Michaels, 2007).

Recently, it has been suggested that the use of contextual information and advance cue information may follow Bayesian learning principles (Broadbent et al., 2019; Cañal-Bruland & Mann, 2015; Gredin et al., 2018, 2020; Harris et al., 2022; Helm et al., 2020; Loffing & Cañal-Bruland, 2017). However, at the time of the conception of this study, there was no explicit test of this hypothesis. Some have used this literature as a theoretical background to elucidate how skilled athletes may utilize prior statistical information about outcomes along with advance cue information to improve their ability to anticipate outcomes in sports (Gray & Cañal-Bruland, 2018; Gredin et al., 2018). However, to the best of the authors’ knowledge only one principled application of Bayesian learning for anticipation skill has been reported (Harris et al., 2022).

Heirarchial Bayesian frameworks have been used in theoretical accounts of sensorimotor learning (Körding & Wolpert, 2004) and perception (Friston & Kiebel, 2009; Friston & Stephan, 2007; Maffei et al., 2017). The proposal is that visual perception and sensorimotor systems act in a “Bayes optimal” fashion in order to resolve uncertainty and guide “beliefs” about the world (Knill & Pouget, 2004). The probable cause of the sensory data (Posterior Probability) is computed from the current sensory data (Likelihood ratio) and previous accuracy of one’s prediction about the cause of the sensory data (Prior “belief”). Inaccuracies between the latent belief in the cause of the sensory data (posterior prior) and the actual cause generate Prediction Error (PE). PE outside levels of tolerance can result information being passed up to higher levels of the hierarchy for more conscious processing. Top-down attention can drive the precision of the prior and increase the chances of information reaching more conscious levels of the hierarchy (Gredin et al., 2020; Stephan et al., 2016). Trial to trial, PE is used subsequently to update the belief in the origin of the sensory data (Prior) for future use. As a result, ones’ ability to attribute sensory information to outcomes becomes more and more accurate through experience in the task domain.

To date, there is little literature available within the anticipation skill domain to guide researchers on how to use the previously described theoretical accounts. This generalization is also made more challenging because behavioral data is used to infer internal processes in the brain. But by hypothesis, it may be possible to use Bayesian learning to understand how a left/right decision about a throw or strike direction of a projectile in sport from an opponent is made. The sensory information from the visual system can be attributed to the Likelihood. The previous probability of an outcome being observed can be attributed to the Prior. The probability that the sensory data will be attributed to the correct outcome forms the Posterior probability. In other words, the posterior probability is calculated from the likelihood (e.g., probability of matching a left shot divided by the probability there will be a left shot) multiplied by the prior probability (e.g., probability there will be a left shot) divided by the marginal likelihood (probability of matching any shot [overall shot anticipation accuracy]).

Here, we operationally define situational probability information as the probability there will be a shot in a left or right direction in a set of trials (i.e. the Likelihood). The Prior is defined as the Prior/anticipated “belief” the resulting shot direction will be left or right before the shot is seen. The sensory data, i.e. the Likelihood is defined as the kinematic information sensed by the action of the tennis player’s shot. We measure anticipation skill based on the posterior probability, the ability to attribute sensory data correctly to shot outcome.

In two experiments, participants undertook a tennis anticipation training programme designed to improve their ability to anticipate the left/right shot direction of upcoming tennis shots. Participants learned under conditions where shot outcome probabilities information (i.e., situational probabilities) was present or absent in the training stimuli by manipulating the frequency of left to right shot present in the training blocks and manipulated the training stimuli by presenting tennis shots with either advance cue (kinematic) information present or absent (by neutralizing or preserving the shot-direction specific information in the movement of the tennis player stimuli). Based on previous research into anticipation skill (Broadbent et al., 2019; Gray, 2002a; Gredin et al., 2018; Mann et al., 2014; Murphy et al., 2016), it was expected that participants would use shot outcome probabilities information with advance cues to learn to anticipate tennis shot direction. If learning behaved according to Bayesian learning principles, then we expected that learning under the presence of an informative prior (shot outcome probabilities information present) would lead to a bias in the frequency of responses toward the congruent shot direction even in posttest conditions where there is no difference in the frequency of left and right shots, whereas such a bias would not be seen when learning without an informative prior (situational probabilities information absent).

Secondary aims related to the simple Bayesian model of anticipation skill learning. They were to 1) examine whether learning with the addition of shot outcome probabilities information lead to a faster rate of acquisition than with only kinematic information and lead to superior anticipation performance in the posttest than with just learning with kinematic information. That is, whether learning with both information sources were additive (e.g. (Müller & Abernethy, 2012), and optimised (Knill & Pouget, 2004); and 2) test predictions from a simple Bayesian model by examining bias in the anticipation data from these two experiments. Specifically, the effect of having a highly informative prior formed from a relatively small sample size (such as early in acquisition) would be that the posterior probability will closely represent the prior probability. In order words, if there was a high probability the player played a shot to the right in the past then this would influence their choice and would likely respond right. However, having a non-informative prior means the posterior probability will represent the likelihood more closely. In other words, if there is equal probability the shot will go to the left or right then the choice about left or right will be based on the advance cue information (sensory evidence). Finally, learning with an informative prior and sensory evidence would lead to “Bayes optimal” learning where prediction error is minimized and learning with no sensory evidence would lead to the development of a posterior probability that closely reflects the prior (probability of a shot being left or right).

Experiment 1

The aim of Experiment 1 was to examine the learning effect when only kinematic information about shot direction was present in the training stimuli. That is, was the training protocol was sufficient to demonstrate increases in anticipation performance from pre-to-posttest (cf Mann et al., 2014)? Consistent with previous studies (Smeeton et al., 2005, 2013; Williams et al., 2002, 2004), it was expected that individuals will learn to anticipate an outcome from kinematic information of a tennis shot direction (Kinematic Information Present [KIP]) with outcome feedback and subsequent presentation of the tennis shot after outcome feedback. Furthermore, the experiment was used to record the natural bias to respond left or right in the absence of a bias in the shot outcome probability information (Shot outcome Probability Information Absent [SPA]).

Method

Ethics statement

All experimental and ethical approval procedures used in the three experiments were approved by the lead Institutions’ Ethics Committee. All participants gave informed written consent before participating in the study. All participants were over the age of 18 years old. Consent was documented via a signature on the consent form.

Sample size estimation

Based on previous research examining the learning of kinematic information in tennis anticipation skill (Smeeton et al., 2013), a minimum total sample size of 12 was calculated using G*Power (Faul et al., 2009). This calculation was based on the interaction effect of group (kinematic information present vs. Kinematic information absent) on response accuracy in the mentioned previous study to achieve a power of .95, having an effect size (${\eta }^2$) of .27.

Participants

Thirty participants (16 male, 14 female) who have played recreationally or at amateur club-level and did not receive professional tennis coaching in the last two years participated in the study (Tennis Skill Self-rating on a scale from beginner 1–10 professional player: M = 2.62; SD = 2.24). Participants (26 right-handed, 4 left-handed) were recruited from the sport science student population and were randomly allocated to the two intervention groups: Kinematic Information Present Shot outcome Probability information Absent (KIP-SPA) and Kinematic Information Absent Shot outcome Probability information Absent (KIA-SPA).

Apparatus and stimulus production

The simulations were based on kinematic data collected and analyzed in (Huys et al., 2008), which allowed us to be able to experimentally add or remove kinematic differences (i.e. neutralize kinematic information) between left and right shots. In that study, retroflective markers were placed on 18 body and racket locations (left and right shoulder, elbow, wrist, hip, knee, ankle, and toe, and four racket positions) to record the kinematics of six right-handed tennis players as they performed forehand groundstrokes to four different target locations (forehand inside-out and cross-court shots to near and far targets). One inside-out and one cross-court shot were included from each of the six players in the pretest, training and posttest stimuli. Where neutralized shots were used, two shots from each player were included in the pretest, training and posttest stimuli. Inside-out and cross-court shots are defined here as forehand shots directed toward the left-hand or right-hand side of an opponent’s court, respectively (from the perspective of the opponent). The recorded players were between 15 and 18 years of age and played tennis at the national competition level. The stimuli were constructed using MatLab (MatLab 6.5, MathWorks, Natick, MA). Each simulation was saved in audio-video interlaced format at a rate of 30 frames/s and lasted 1.8 s. The simulations started at the first backward movement of the right wrist from the ready stance and ended at the moment of ball-racket contact (no ball was visible throughout).

A tennis anticipation training protocol similar to Smeeton et al. (2013) was used. The stick-figure simulations of tennis shots were presented to participants on a notebook computer (Dell, Latitude 5410, Round Rock, USA) playing shots to either left or right using PsychoPy2 software (Peirce et al., 2019). Participants’ responses were registered with a Qwerty keyboard by pressing the backslash (for anticipating shots to the left) or slash (for anticipating shots to the right) key. Response time and accuracy were recorded.

Pre-test consisted of four test conditions; and 2080RIGHT, 8020LEFT, 5050KIP and 5050 KIA. Both the 2080RIGHT and 8020LEFT conditions consisted of 60 test stimuli and either contained 12 leftward shots and 48 rightward shots (2080RIGHT) or 48 leftward shots, 12 rightward shots (8020LEFT). Both 5050KIP and 5050KIA conditions consisted of 36 test stimuli (18 leftward shots, 18 rightward shots). In the 5050KIP condition shot direction kinematic information was preserved, whereas this information was neutralized in the 5050KIA condition. The Post-test contained the same four test conditions. All stimuli were randomized for shot direction within each condition.

Experimental design

To measure learning, a pre-posttest design with four sessions during the acquisition phase was applied. Sixty trials were presented during each of the four acquisition blocks (30 leftward and 30 rightward tennis stimuli); the order was randomized for shot direction. During the pretest and posttest phase, all participants were presented with the same four different tests (2080RIGHT, 8020LEFT, 5050KIP, 5050KIA). The condition presentation order for each participant was assigned using a 4 × 4 Latin square design to control for condition order effects during pretest and posttest for the participant. No shot direction feedback was given at any point during or after pretest and posttest sessions.

The participants were randomly assigned to two learning groups, with kinematic information for shot direction present and shot outcome probability information absence (KIP-SPA) or a control condition with both kinematic and shot outcome probability information absence (KIA-SPA) during their respective acquisition phase. Left/Right shot direction probability was 50:50 over each acquisition block (i.e., shot probability absent, SPA).

Procedure

For all experimental phases: pretest, acquisition phase, and posttest participants sat in front of the computer screen at a distance of approximately 0.5 m. They were informed that they would be shown forehand shots of stick figures “playing” strokes to either their left- or right-hand side. They were tasked with determining the resultant shot direction by pressing the backslash (left) or slash (right) key on the keyboard. Before the pretest, participants were familiarized to the test by being presented with an example shot from each player and for each shot direction (12 total shots) in a randomized order. The pretest and posttest each took approximately 15 minutes to complete.

During the acquisition phase, groups were given feedback about the correctness of their decision after each trial through a written message that appeared on the screen after they gave their response. For the KIA-SPA group “correctness” was based on whether or not the participant’s response happened to match labeling of a neutralized shot entered into the stimulus presentation computer programme. Immediately after the feedback message, participants were shown a replay of the same video. An inter-trial interval of 3.5 s was used between each trial. At the end of each acquisition block participants were asked to rate their task effort on a scale of 1–10, with 10 being the greatest amount of effort available to them at the time and 1 being the least amount. This measure was taken as a validation check for engagement in the learning task. Each acquisition block took approximately 25 min to administer for each participant.

Data analysis

Anticipation accuracy (%) was calculated as the percentage of correct responses within a condition or block. Response time(s) was calculated as the time between the stimulus onset and the depression of the response key. To establish if participants can learn to perceive shot outcomes from kinematic information, pre-to-post accuracy and response times were analyzed with separate three-way mixed design ANOVA with Group (KIP-SPA, KIA-SPA) as the between-participant variable and Test (Pre, Post) and Condition (2080RIGHT, 8020LEFT, 5050KIP, 5050KIA) as the within-participant variables. To examine the rate at which participants improved, acquisition accuracy and response times were analyzed with separate two-way mixed design ANOVAs with Group (KIP-SPA, KIA-SPA) as the between-participant variable and Block (1, 2, 3, 4) as the within-participant variables. Significant effects of ANOVAs were followed up using Bonferroni-corrected t-tests. Effect sizes are reported as partial eta squared (η_p²) for main effects and interactions. Effort scores between the groups on experimental block were compared using Mann-Whitney U tests.

Results and discussion

Pre- to post-test

Response accuracy

Response accuracy results are plotted in Figure 1. There was a main effect of Group, F_(1,28) = 10.237, p = .03, η_p² = .268. Accuracy was greater for the KIP-SPA than the KIA-SPA group.

Figure 1. Anticipation accuracy scores for the pre- and posttests of the KIP-SPA and KIP-SPA group per condition (2080 R, 5050KIA, 5050KIP, 8020 L). Error bars represent standard error.

Additionally, there was a main effect of Test, F_(1,28) = 6.985, p = .013, η_p² = .200, demonstrating an average increase in accuracy from pretest to postest across both groups. There was a main effect of Condition, F_(3,84) = 9.694, p = 1.5 × 10⁻⁴, η_p² = .257. Accuracy for the 8020LEFT and 5050KIP was significantly greater than the 5050KIA and 2080RIGHT, whilst accuracy for the 5050KIP was not different to the 8020LEFT and 2080RIGHT was not different to the 5050KIA condition. The lower order interaction between Test and Condition demonstrated that learning with kinematic information present in the stimuli during acquisition resulted in pre- to posttest increases in accuracy. However, it was superseded by a Group × Test × Condition interaction, F_(3,84) = 6.094, p = .001, η_p² = .179. For the KIP-SPA group, pre- to posttest increases in accuracy were seen in the 2080RIGHT, 8020LEFT and 5050KIP groups only. No significant increases in accuracy were seen in the KIA-SPA group. Because kinematic information is available in these former three conditions only, it shows this information is being used to anticipate shot direction.

Response time

There was a main effect of Test, F_(1,28) = 21.351, p = 7.8 × 10⁻⁴, η_p² = .433, demonstrating an average decrease in response time(s) from pretest to posttest across both groups (Pre: M = 2.248, SE = .052; Post: M = 2.069, SE = 0.48). No other significant effects were found.

Acquisition

Response accuracy

Response accuracy results are plotted in Figure 2. There was a main effect of Group, F_(1,27) = 17.641, p = 2.6 × 10⁻³, η_p² = .395. Accuracy was greater for the KIP-SPA compared to the KIA-SPA. Additionally, there was a main effect of Block, F_(3,81) = 5.062, p = .003, η_p² = .158, demonstrating an average increase in accuracy from Block 1 to 4. There was a Group x Block interaction, F_(3,81) = 5.803, p = .001, η_p² = .177 demonstrating this protocol was effective in training anticipation skill. During acquisition, as predicted kinematic information resulted in a more rapid acquisition rate earlier in the acquisition blocks and a more stable performance was observed later in acquisition. For the KIP-SPA group, accuracy significantly increased from Block 1 to Block 3 and 4 only. For the KIA-SPA group accuracy was only different from Block 3 to 4.

Figure 2. Anticipation accuracy scores of the KIP-SPA (red squares) and KIP-SPA (purple circles) group per each acquisition block (1–4). *indicates significant (p < .05) differences for the KIP-SPA group between the respective acquisition blocks. Error bars represent standard error.

Response time

There was a main effect of Block, F_(3,81) = 4.096, p = .009, η_p² = .132, demonstrating an average decrease in response time between Block 1 and 4 only (Block 1: M = 2.188, SE = .073; Block 4: M = 2.062, SE = .054). A decrease in response time was found over acquisition blocks as well as from pre- to posttest (approximately 180 ms decrease on average) suggesting participants became more aware of the timeliness of the response constraints (Runswick et al., 2020). It is interesting to note that kinematic information about shot direction was absent in one of the groups, yet RT still decreased in this group.

Effort during training

Effort scores have been plotted in Figure 3. A significant difference between the KIP-SPA and KIA-SPA group was found in Block 2 only, Z = 2.252, p = .025. During the conceptualization of the study effort scores were recorded to ensure participants engaged in the task. However, more recently effort has been measured as a measure of cognitive load and processing efficiency (Gredin et al., 2018; Runswick et al., 2018). As a tentative explanation greater effort during the earlier stages of learning suggesting that attentional processes in the KIP-SPA group may have been greater than the KIA-SPA group and have been hypothesized in some heirachical Bayesian frameworks to increase the precision of the prior (Greenhouse-Tucknott et al., 2022; Stephan et al., 2016).

Figure 3. Effort scores of the KIP-SPA (red squares) and KIP-SPA (purple circles) group per each acquisition block (1–4). *indicates significant (p < .05) differences between the groups on the respective acquisition blocks. Error bars represent standard error.

Experiment 2

Previously it has been shown that contextual and advance cue information interact to influence skillful anticipations of outcomes (Murphy et al., 2019). However, the characteristics of this learning are unclear. Mann et al. (2014) showed that action preferences can be learnt over a relatively short acquisition period, but there was little evidence that kinematic information was also learnt. Therefore, the primary aim of Experiment 2 was to further examine if the learning of shot outcome probabilities and investigate if kinematic information can be learnt to be perceived alongside shot direction probabilities information with a longer acquisition period. Understanding the characteristics of this learning will help evaluate if anticipation skill learning is a Bayesian process an endeavor not yet reported on. In Experiment 2, two groups followed the same training protocols as used in Experiment 1. However, both groups trained with a bias in the shot outcome frequency. That is, one group trained in the presence of kinematic and shot direction probability information (KIP-SPP), whilst in the other group, kinematic information was absent and shot direction probability information was present (KIA-SPP). Both groups were expected to improve because of the presence of reliable information in the training stimulus (Beek et al., 2003). Additionally, accuracy was predicted to increase and response time to decrease in the congruent shot direction in both groups (Gray, 2002b; Gredin et al., 2018; Loffing et al., 2015; Mann et al., 2014; Murphy et al., 2016). Evidence for learning only prior shot probability information would be seen if the KIP-SPP group accuracy was reduced to chance when accuracy performance is averaged across congruent and incongruent shot directions. However, evidence for prior shot direction probability integration with kinematic information would be seen if the performance of the KIP-SPP group was greater than the KIA-SPP group (Müller & Abernethy, 2012; Murphy et al., 2016). Two predictions were made regarding effort scores. Based on the results from Experiment 1 and the studies by Gredin et al. (2018) and Runswick et al. (2018), it was hypothesized that if precision required for perception during acquisition increased, perceived effort would also increase (Friston & Kiebel, 2009; Friston & Stephan, 2007). Therefore, it was expected that the KIP-SPP group would report higher levels of effort due to the increased precision needed to perceive kinematic information and incorporate shot outcome probability information. However, if the use of shot outcome probability information engages more conscious processes, then effort scores were expected to increase when only shot outcome probability information was available (i.e., in the KIA-SPP group).

Method

Participants

Thirty-five participants (18 male, 17 female) who had not participated in Experiment 1 and had played recreationally or at amateur club-level during the time of the data collection took part. They did not receive professional tennis coaching in the last two years (Tennis Skill Self-rating on a scale from beginner 1–10 professional player: M = 2.62; SD = 2.24). Participants (30 right-handed, 5 left-handed) were recruited from the sport science student population and were randomly allocated to the two intervention groups: Kinematic information present shot outcome probabilities present (n = 19, KIP-SPP) or kinematic information absent shot outcome probabilities present (n = 16, KIA-SPP). Statistical power and ethical approval followed the same process as Experiment 1.

Experiment design

Participants followed the same protocol as in Experiment 1. The only difference were the stimuli presented to them during acquisition. Both the group with kinematic information present (KIP-SPP) and kinematic information absent (KIA-SPP) were split into two subgroups, one of the subgroups was presented with a left shot outcome probability bias (8020LEFT) and the other subgroup was presented with a right shot outcome probability bias (2080RIGHT) to control for the possibility of any shot direction bias in the training stimuli.

Data analysis

Anticipation accuracy (%) was calculated as the percentage of correct responses within a condition or block. Response time (s) was calculated as the time between the stimulus onset and the depression of the response key. Pre-to-post accuracy and response times were analyzed with separate four-way mixed design ANOVAs with Kinematic Information Group (KIP-SPP, KIA-SPP) and Shot Outcome Probability group (Left, Right bias) as the between-participant variables and Test (Pre, Post) and Condition (2080RIGHT, 8020LEFT, 5050KIP, 5050KIA) as the within-participant variables.

Acquisition accuracy and response times were analyzed with separate three-way mixed design ANOVAs with Kinematic Information Group (KIP-SPP, KIA-SPP) and Shot Outcome Probability group (Left, Right bias) as the between-participant variables and Block (1, 2, 3, 4) as the within-participant variables. Significant effects of ANOVAs were followed up using Bonferroni-corrected t-tests. Effect sizes are reported as partial eta squared (η_p²) for main effects and interactions.

Results and discussion

Pre- to post-test

Response accuracy

Response accuracy results are plotted in Figure 4. There was a main effect of Kinematic Information, F_(1,31) = 24.997, p = 2.8 × 10⁻⁴, η_p² = .446. Accuracy was greater for the KIP-SPP than for the KIA-SPA group. Additionally, there was a main effect of Test, F_(1,31) = 12.156,

Figure 4. Anticipation accuracy scores for the pre- and posttests of the KIP-SPP and KIA-SPP group per condition (2080 R, 5050KIA, 5050KIP, 8020 L). Error bars represent standard error.

p = .001, η_p² = .282, demonstrating an average increase in accuracy across the groups. Both shot outcome probabilities and combined information sources resulted in improving anticipation skill. There was a main effect of Condition, F_(3,93) = 12.529, p = 5.96 × 10⁻⁷, η_p² = .288. Accuracy was greater for the 5050KIP, 8020LEFT and 2080RIGHT compared to the 5050KIA. 5050KIP was different to the 8020 L, but was not different to the 2080 R. Lower order interactions were superseded by a Kinematic Information × Test × Condition interaction, F_(3,93) = 4.224, p = .008, η_p² = .120. When Kinematic information was present during training, accuracy improved from pre- to posttest in the 5050KIP, 2080RIGHT and 8020LEFT condition, but not the 5050KIA condition. When Kinematic information was absent, no pre- to posttest increases in accuracy were seen. Additionally, lower order interactions involving only Shot Direction Probability, Test, and Condition were superseded by a Shot outcome Probability × Test × Condition interaction, F_(3,93) = 10.387, p = 6.0 × 10⁻⁵, η_p² = .251. When Shot outcome Probability information was biased toward the right shot direction, significant increases in accuracy were found in the 5050KIP (M_pre = 53.00, SE = 2.90; M_post = 73.80, SE = 3.40) and 2080RIGHT (M_pre = 48.60, SE = 2.90; M_post = 65.30, SE = 3.70) condition. When this bias was toward the left shot direction then accuracy only significantly increased in the 8020LEFT (M_pre = 57.00, SE = 2.70; M_post = 71.10, SE = 2.70) condition. Increases in accuracy were found when shot outcome probabilities information was present, but were specific to the congruent (left or right) shot direction bias in the training.

Response time

Response time(s) results are plotted in Figure 5. There was a main effect of Test, F_(1,31) = 23.627, p = 3.2 × 10⁻⁴, η_p² = .433, demonstrating an average decrease in response time across the groups. Finally, lower order interactions were superseded by a Kinematic Information × Left-Right Shot outcome Probability × Condition × Test interaction, F_(3,93) = 3.144, p = .029, η_p² = .092. When Kinematic Information was present and a right bias in the training stimuli, response time decreased from pre- to posttest in all conditions. However, when Kinematic Information was present and a left bias in the training stimuli, no change in the response time was found from pre- to posttest across all conditions. Conversely, when Kinematic Information was absent and a left bias in the training stimuli, response time decreased from pre- to posttest in all conditions. Furthermore, when Kinematic Information was absent and a right bias in the training stimuli, no change in the response time was found from pre to posttest across all conditions.

Figure 5. Response times [s] for the pre- and posttests of the KIP-SPP and KIA-SPP group per condition (2080 R, 5050KIA, 5050KIP, 8020 L). Error bars represent standard error.

Of particular note is an additional effect kinematic information with shot outcome probability information had on the learning of anticipation of shot direction. Here, there is good evidence that the addition of kinematic information lead to increased learning compared to learning without kinematic information. Increases from pre- to posttest were seen. It may be the case that both prior expectations about shot directions were integrated with kinematic information when anticipating shot directions. As a result, the influence of prior expectations when learning with kinematic information and shot outcome probabilities information is different and potentially performance enhancing when learning with kinematic and shot outcome probabilities information. Furthermore, different effects were seen depending on the left-right shot outcome probability information, with superior learning being seen when there was a rightward bias.

Acquisition

Response accuracy

Response accuracy results are plotted in Figure 6. There was a main effect of Kinematic Information, F_(1,30) = 90.763, p = 1.39 × 10⁻¹⁰, η_p² = .752. Accuracy was greater for the KIP-SPP than the KIA-SPP group. Additionally, there was a main effect of Block, F_(1,90) = 2.807, p = .044, η_p² = .086, demonstrating an average increase in accuracy across the Blocks. There was a Kinematic Information × Block interaction, F_(3,90) = 4.361, p = .006, η_p² = .127. When Kinematic information was present during training, accuracy improved from Block 2 to 3 and 2 to 4. No other differences between the blocks were found. The Left-right Shot outcome Probability × Shot Direction interaction was superseded by the Kinematic Information × Left-right Shot outcome Probability × Shot Direction interaction, F_(1,30) = 5.918, p = .021, η_p² = .165, which showed that the negative effect of incongruence on accuracy was reduced when kinematic information was present in the training stimuli. Finally, there was a Left-Right Shot outcome Probability × Block × Direction interaction, F_(3,90) = 12.349, p = 7.73 × 10⁻⁷, η_p² = .292. Accuracy increased in the congruent shot direction over acquisition but not in the incongruent direction.

Figure 6. Response accuracy for the left and right shot directions when learning with 2080 R and 8020 L shot probabilities during acquisition blocks 1–4. Error bars represent standard error.

Response time

Response time(s) results are plotted in Figure 7. There was a main effect of Block, F_(3,90) = 16.569, p = 1.18 × 10⁻⁸, η_p² = .356, demonstrating an average decrease in response time across the Blocks. The Left-Right Shot outcome Probability × Block × Shot Direction interaction, F_(3,90) = 3.301, p = .024, η_p² = .099, showed the rate of response time decrease was faster for the subgroups training with a right Shot outcome Probability bias regardless of shot direction, whereas subgroups with a left bias showed a faster rate of decline for rightward compared to leftward shots.

Figure 7. Response time for the left and right shot directions when learning with 2080 R and 8020 L shot probabilities during acquisition blocks 1–4. Error bars represent standard error.

Effort scores

When kinematic information was present during training effort scores were significantly greater during training Block 2 and 4 (Z = 2.073 and Z = 2.207, ps <.05 respectively). There were no differences in effort scores when Left-Right Shot outcome Probability information was compared. As predicted the presence of kinematic information in the training stimuli led to an increase in effort required. This increased in effort is thought to result from the increase in precision of the prior required to perceive information about shot direction from the shot kinematics (Gredin et al., 2018; Greenhouse-Tucknott et al., 2022; Runswick et al., 2018). Although, it is not clear why these effects are specific to acquisition block 2 and 4.

The superior learning effects for rightward compared to leftward bias raising an interesting question about the process of anticipation. The tennis player stimuli in the experiment were always depicted with a racket in their right hand. Action preferences of an opponent have been described as stable priors because they do not change during the action of the opponent (Gredin et al., 2020). As a post hoc explanation, if anticipation skill was based on a one- to two-stage process, stage one would involve the expectation (strong and stable prior) of the congruent (“percentage shot”) first. If not, then stage two would default to “belief” the sensory evidence is in fact a shot in the incongruent shot direction, then experimental evidence for this would be seen in the speed of responses. Faster responses would be seen for congruent stimuli. However, if anticipation skill results from competition between information-action outcomes (e.g. Huys et al., 2008) then it can be expected that there would be no difference in the response times between shot directions responses for congruent and incongruent stimuli because the kinematic information available is the same. Faster RTs were typically seen for rightward, but not leftward bias shots and are frequently seen for congruent shot compared to incongruent shots, indicating that anticipation of incongruent stimuli may require an additional stage of processing. Existing Bayesian models of anticipation skill in sport draw on accuracy data (Gredin et al., 2020; Harris et al., 2022; Runswick et al., 2020) and highlight the importance of a timely response (Runswick et al., 2020). It may be the case that response time data may provide evidence of the use of prior knowledge-based and integration processes.

In Experiments 1 and 2, accuracy scores and response times were used to evaluate if participants are able to learn shot outcome probabilities information. One potential consequence of learning the shot direction probabilities information is that there may have been a response bias in their learning, resulting in increased frequencies of responses to congruent shot directions even when kinematic information was available. This issue was examined in the analysis of response bias using Bayesian statistical analysis in the next section.

Bayesian analysis of responses in experiment 1 and 2

Contextual information and advance cue information may act according to Bayesian learning principles (Broadbent et al., 2019; Cañal-Bruland & Mann, 2015; Gredin et al., 2018; Loffing & Cañal-Bruland, 2017). Howeverto date, an application of Bayesian learning for anticipation skill learning has not been reported (see Helm et al. (2020) and Harris et al. (2022)) for examples in anticipation skill performance. Therefore, the primary aim of this analysis was to examine if anticipation skill learning behaved according to Bayesian learning principles. It was expected that learning in the presence of shot outcome probability information during acquisition and in the absence of kinematic information would allow an informative prior to develop, leading to a biased response toward the larger shot outcome probability during acquisition, as the evidence for the prior would become increasingly stronger than the sensory evidence from perception of the unfolding kinematic movements (i.e. likelihood), and as a consequence the subsequent posterior probability would more strongly reflect the prior shot outcome probabilities. Such prior expectations have been argued to exert a “top-down” bias in the anticipation response toward the congruent shot direction in anticipation performance (Harris et al., 2022). However, where neither shot outcome probabilities information nor shot direction kinematic information was present then, no bias was expected to develop in the left/right response frequency bias. Additionally, where no shot outcome probabilities information was present, but shot direction kinematic information was present then it was expected that the development of the prior would be based on kinematic information with sensory information dominating over a non-informative shot outcome prior when updating the posterior probabilities and subsequent prior development. As a consequence, no evidence of a response bias was expected in this group. Importantly, when shot outcome probabilities information and kinematic information were present during acquisition, evidence for Bayesian learning would be seen if the response bias lay in between that seen for the KIA-SPP and KIP-SPA groups demonstrating both information sources were integrated during anticipation skill learning rather than individuals using one information source over another. At the level of the outcome, the posterior probability forming the subsequent prior would be influenced by the perception of the kinematic information and the shot outcome probabilities information in the congruent shot direction.

To examine response tendencies posterior odds ratios were calculated using Bayes rule for left and right shot directions,

(1) $\mathit{P}(\mathit{Model}|\mathit{Data})=\frac{\mathrm{P}\left(\mathrm{Data}|\mathrm{Model}\right)\mathit{\hspace{0.17em}}\cdot \mathrm{P}\left(\mathrm{Model}\right)}{\mathit{P}\left(\mathit{Data}\right)}$(1)

The probability of the Model represented the number of shot outcomes to a direction divided by the number of shots, whereas the Data represented the probability of matching left or right responses with a left or right shot outcome.

Posterior probabilities were calculated for left and right shots separately and were then used to calculate posterior odds ratios (also known as Bayes Factor), by dividing the congruent shot outcome with the incongruent outcome. Posterior odds ratios were recalibrated for ease of interpretation. If the congruent training shot direction had a higher probability of eliciting a response than the incongruent shot direction, a positive value (greater than 0) is indicated. Conversely, a negative value (less than 0) is indicated when the incongruent shot direction elicits a response with a higher probability than the congruent shot direction.

Odds ratios were calculated for each participant separately and were based on all of the participants’ trials within a pre- or posttest condition or acquisition block. Pre-to-post odds ratios were analyzed with a three-way mixed design ANOVA with Group (KIP-SPA, KIA-SPA, KIP—SPP, KIA-SPP) as the between-participant variable and Test (Pre, Post) and Condition (Congruent, Incongruent, 5050KIP, 5050KIA) as the within-participant variables. To construct congruent and incongruent conditions it was necessary to combine some of the results. Odds ratios for the congruent conditions were calculated from the 8020LEFT SPP subgroups on the 8020LEFT pre and posttest condition and the 2080RIGHT SPP subgroups on the 2080RIGHT pre and posttest condition. However, the odds ratios for incongruent conditions calculated from the opposed bias condtion to the training group (i.e., 2080LEFT condition for the 8020RIGHT SPP subgroup). This step was necessary to examine biasing of responses resulting from the anticipation skill training. Note a priori power analysis was not calculated due to the novelty of this approach. Acquisition odds ratios were analyzed with separate two-way mixed design ANOVAs with Group (KIP-SPA, KIA-SPA, KIP-SPP, KIA-SPP) as the between-participant variable and Block (1, 2, 3, 4) as the within-participant variables. Significant effects of ANOVAs were followed up using Bonferroni-corrected t-tests. Effect sizes are reported as partial eta squared (η_p²) for main effects and interactions.

Results

Pre- and post-test

Posterior odds ratio for each group are plotted in Figure 8. There was a main effect of Test, F_(1,61) = 10.525, p = .002, η_p² = .147, demonstrating greater odds ratios post-compared to pretest. There was a main effect of Condition, F_(3,183) = 18.480, p = 1.62 × 10⁻¹⁰, η_p² = .233. Odds ratios for the Incongruent condition were greater than the 5050IA and 5050IP and the Congruent condition overall. The lower order interactions between Test and Condition and Test and Group were superseded by a Group × Test × Condition interaction, F_(9,183) = 14.903, p = 5.04 × 10⁻¹⁸, η_p² = .423. In the pretest, no differences between the odds ratios for groups or condition were found. In the posttest, odds ratios were greater for the KIP-SPP and KIA-SPP groups than the KIP-SPA and KIA-SPA groups in the Congruent and 5050IP and 5050IA condition, but this effect was reversed for the Incongruent direction. No differences were found between KIP-SPP and KIA-SPP and between KIP-SPA and KIA-SPA in any of the posttest conditions.

Figure 8. Rescaled odds ratio (bayes factor) comparing of each condition (2080 R, 5050KIA, 5050KIP, 8020 L) per each of the four groups (KIP-SPA, KIA-SPP, KIP-SPP, KIP-SPA) for the pre- and post- tests. For ease of interpretation results have been rescaled such that equi-probable responses have a value of 0 and both positive and negative integers represent the number of times more likely a congruent (positive) and incongruent (negative) response was seen. Error bars represent standard error.

Acquisition phase

Posterior odds ratio for each group are plotted in Figure 9. There was a main effect of Block, F_(3,183) = 8.357, p = 3.1 × 10⁻⁴, η_p² = .120, demonstrating odds ratios increased on average between Blocks 1 and 2 but no other adjacent blocks. There was a main effect of Group, F_(1,61) = 35.659, p = 1.94 × 10⁻¹³, η_p² = .637. The odds ratios were greater for the KIA-SPP compared to all other groups. The KIP-SPP was greater than the KIP-SPA group, but not the

Figure 9. Rescaled odds ratio (Bayes Factor) comparing of each condition of the four groups (KIP-SPA, KIA-SPP, KIP-SPP, KIP-SPA) across each of the four acquisition blocks. For ease of interpretation results have been rescaled such that equi-probable responses have a value of 0 and both positive and negative integers represent the number of times more likely a congruent (positive) and incongruent (negative) response was seen. Error bars represent standard error.

KIA-SPA, which was not different to the KIP-SPA group. There was a significant Group x Block interaction, F_(3,183) = 8.653, p = 8.86 × 10⁻¹¹, η_p² = .299. In Block 1, KIA-SPP odds ratios were greater than all other groups. In Block 2, both KIA-SPP and KIP-SPP odds ratios were greater than KIP-SPA and KIA-SPA, but neither were different from each other. In Block 3 and 4, KIA-SPP odds ratios were greater than all other groups.

Discussion

The primary aim of this analysis was to examine if anticipation skill behaved according to Bayesian learning principles. As predicted, learning under the presence of informative shot probabilities and no kinematic information led to bias in the anticipation response toward the congruent shot direction. Presumably, the shot outcome prior dominated future decisions because there was only strong evidence for the prior shot outcome probabilities than the sensory evidence from perception of the unfolding kinematic movements and as a consequence the subsequent posterior probability reflected the prior shot outcome probabilities. In fact, the extent of the response bias far exceeded the shot outcome bias (80% v 20%). Even by the end of the first acquisition block participants were approximately 11 times more likely to respond in the congruent shot direction on average. Additionally, where neither shot outcome probabilities information nor kinematic information was present, no bias was seen (odd ratios were close to zero). When shot outcome probabilities information was absent, but kinematic information was present then no evidence of a response bias was found either. Over acquisition, the prior development was presumably based on kinematic information. With sensory information initially dominating in the absence of prior shot outcome information when updating the posterior probabilities. Importantly, strong evidence was seen for information integration, as predicted by Bayesian learning, because when shot outcome probabilities information and kinematic information were present during acquisition, the response bias lay in between that seen for the KIA-SPP and KIP-SPA groups rather than being similar to either of the two groups, which would indicate one source of information was being used over another. During anticipation skill learning, the posterior probability forming the subsequent prior would be shaped by the sensory evidence from the kinematic information and the shot outcome probabilities information in the congruent shot direction to optimize the correct shot direction being perceived (Gredin et al., 2020).

As predicted, the rate at which the odds ratios changed were different between the groups. Early in acquisition, a response bias developed fastest when only shot outcome probabilities information was present (KIA-SPP), faster than the KIP-SPP group, which also had kinematic information even though both groups had the same reliability of outcome probability information available. Additionally, later in acquisition, learning with only shot outcome probabilities information led to the development of a response bias that was greater than learning with the same outcome probability and kinematic information. Presumably, the absence of kinematic information reduced the certainty in the sensory evidence leading to the prior dominating the response. Similar effects have been seen when the bowling action of cricketers has been temporally occluded reducing the availability of kinematic information but preserving contextual priors leading to a response that reflects information in the contextual prior (Runswick et al., 2018).

General discussion

Overall, in two experiments it was found that shot outcome probability information (Mann et al., 2014) can be combined with kinematic information about shot direction during the learning of anticipation skill (Cañal-Bruland & Mann, 2015). In Experiment 1, it was shown that training with kinematic information resulted in anticipation skill learning but training without kinematic information did not. But both KIP-SPA and KIA-SPA groups reduced response time. In Experiment 2, training with both shot direction probabilities and kinematic information lead to greater anticipation skill learning compared to learning in the presence of shot outcome probabilities information alone. Evidence for integration of shot probabilities and kinematic information was found when learning to anticipate shot direction.

Training with shot outcome probability information only led to specific congruence effects influencing response time and accuracy. It is apparent that shot outcome probabilities can be learnt rapidly. Similar to Mann et al. (2014) this bias can be learned over a relatively small number of training trials. Presumably, the bias in the shot outcome led to the development of a strong prior expectation for a shot direction outcome. Because no information about shot direction was present in the kinematics here, the posterior probabilities were influenced only by the prior containing shot outcome probability information and would explain the congruence effect seen.

If shot outcome probabilities act as priors in Experiment 2, then the question of what may act as a prior in Experiment 1 arises where only kinematic information was present. Here, it is argued that kinematic information present acts to inform a prior about the kinematics of a shot outcome (Gredin et al., 2020). It was hypothesized here that during early learning events, the kinematic information in the form of sensory evidence (i.e. the likelihood) and is thought to have a greater influence on the posterior probability than the prior because there is weaker evidence for the prior than the sensory evidence at this phase of learning. As more learning events occur the development of the prior must only be based on expectations about tennis shot kinematics because information about shot outcomes is not present. Later in learning, according to Bayesian learning frameworks, it is expected that the influence of the prior will be greater, where performance will be more stable when the prior is more precise. In fact, more stable performance was seen between Block 3 to 4 in the KIP-SPA group. This hypothesis could be examined by changing shot outcome probabilities during acquisition and examine how odd ratio change in response. In fact, Thomas et al. (2022) have changed dribble and shoot probabilities during a soccer anticipation task for skilled and less skilled soccer players. It was found that dramatic changes in the dribble/shoot probabilities reduced anticipation accuracy in the skilled group more than the less skilled group. But the skilled group adapted more quickly to the new outcome probabilities. An important question to be addressed in the future is what effect does expertise have on the prior during changes in outcome probabilities. An additional effect found here was that effort was greater for the KIP-SPA group than the KIA-SPA group during the earlier stages of learning suggesting that attentional processes were engaged in the task to a greater degree. According to Feldman and Friston (Feldman & Friston, 2010) attention is thought to drive precision of the prior.

There was a decrease in response times from the pre- to the posttest for both groups (i.e. when kinematic information was present or absent in the training stimuli). Furthermore, response times reduced in both groups during the acquisition blocks. Presumably, the reduced response time may reflect faster information resolution. According to Friston and Stephan (2007), greater neural processing results from lack of resolution a between a “top-down” prior and “bottom-up” sensory evidence in the form of prediction error. Figure 10 presents a conceptual diagram for how this process may act for anticipation of congruent and incongruent tennis shots. Here, faster response times may reflect a reduction in prediction error when less information is passed up to higher layers and not reaching a greater state of awareness resulting in less processing time (Feldman & Friston, 2010). However, a decrease in response time was not predicted for the KIA-SPA group. From a Bayesian modeling perspective, the credibility of the prior is specified by the Highest Density Interval width (Kruschke, 2015). This interval will be broad (i.e., platekurtic) early in learning, but quickly narrows as the prior is updated by the posterior probability and is thought to reflect the precision or certainty in the “belief” of the prior. It may be the case that the narrowing of the HDI reflects belief in the prior and facilitates the reduction in response time, albeit in the case of the KIA-SPA group, the prior may represent a belief in a lack of knowledge about shot outcome, rather than kinematic information about shot direction and more rapid response time results.

Figure 10. Hierarchical Information Integration Model of Skilful Anticipation (HIIMSA). The HIIMSA model depicts how prior shot outcome probabilities information may be integrated with kinematic shot direction information during a left to right direction decision about a shot outcome. An example of congruent information integration is presented in the left half of the figure (shot outcome probability—rightward shot, kinematic information—rightward shot) and incongruent information integration in the right side (shot outcome probability—rightward shot, kinematic information—leftward shot). Shot outcome probability (9 right, 2 left) is represented in the blue bars in the top layer of the hierarchy and forms the initial top-down prior belief about the actual shot outcome before the shot has begun. The bottom layer represents the sensory evidence (i.e. likelihood) from the kinematic information about a shot outcome over time. Note the left-right probability changes over time as the shot evolves toward ball contact, with a higher peak representing greater probability and the skewness of the distribution curve representing the left-right shot direction. The kurtosis representing the certainty. Initially, the middle layer represents the integration of sensory evidence (i.e. The likelihood, brown distribution line) and the shot outcome probability (i.e. prior, blue distribution line) forming the posterior probability (red distribution lines). As shots evolve over time toward ball racket contact (see millisecond values before ball contact) the previous posterior probability distribution forms the subsequent prior distribution, which could be determined by pick up of kinematic information from a fixation for example. This new sensory evidence is then integrated with the new prior to form the new posterior probability for each information pick up iteration. In the case of congruent information, a higher posterior probability peak is reached with fewer iterations (i.e. earlier in time, approximately 180 ms). When a response window (i.e. A window in time when a timely response can be initiated, blue shaded box) is reached and the posterior probability is above a decision threshold, a response is initiated. In the case of incongruent information, at 360 ms the kinematic information about shot direction in the sensory evidence conflicts with the shot outcome probability prior, which results in a sufficient amount of prediction error to engage the next upper layer of the hierarchy and is reflected in increased awareness. More iterations are required for the posterior probability to reach the decision threshold. This results in a longer response time for the incongruent case. The sensory evidence at the later stage of the shot carries greater probability and weights more heavily onto the posterior probability and subsequent prior iterations. Effort can drive top-down attentional processes by narrowing the distribution width of the prior and increases the likelihood that there will be mismatch between the sensory evidence and the prior, resulting in increased prediction error and engagement of the higher layers thereby increasing awareness and shifting of the subsequent prior, which may facilitate the acquisition of skill.

It has been shown here that integration of kinematic information and shot outcome probabilities occurs during the learning of anticipation skill and influences response bias. However, it is unclear how that integration occurs and future research should address this issue. Potentially, contextual information could be integrated with kinematic information in the same prior—likelihood interaction, or they can inform different prior—likelihood interactions presumably acting in a hierarchical fashion (see Figure 10). Predictive coding models of perceptual learning make reference to Bayesian statistics and are characterized by hierarchical generative process models where expectations are projected down to lower layers of the hierarchy about the predicted sensory information (see e.g. (Greenhouse-Tucknott et al., 2022)). Sensory information is passed up into the model and evaluated against the top-down predicted sensory information. When the predicted sensory information is within acceptable levels of tolerance of the sensory information then no further processing occurs. Perception is deemed to be accurate. However, if the predicted sensory information is not within tolerable levels, then prediction errors are passed up the hierarchy for further processing, attention is drawn to them and greater degrees of awareness. Prediction errors can be attenuated by either updating predictions to match sensory information more closely, by driving sensory information to align with prediction or modifying the precision weighting to change the tolerance that predictions can align to sensory information. These three processes are argued to result in perception that informs action (Friston & Kiebel, 2009; Friston & Stephan, 2007) and has been likened to perception-action coupling. Presumably, in a hierarchical process, predictive processes about contextual information acts as a prior for higher layers whereas predictive processes about kinematic information acts as a prior for lower layers of the multi-layered hierarchy.

The practical implications of this work are not certain. Any implications should be considered with caution. Learning with kinematic information and a bias in the shot outcome may facilitate anticipation. Learning in the presence of kinematic information about shot direction may develop a more precise prior about the biological motion pattern for left and right tennis shot resulting in improved accuracy scores and greater effort compared to training without kinematic information. From a theoretical perspective, there is an increased need for understanding how precision in the prior predictions for kinematic information may drive attention and increase effort. Later in acquisition, the reduction in prediction error would lead to less information being passed up and reduce awareness, resulting in decreased response times, and awareness of contextual and kinematic information. In the future, researchers should aim to build more complex models of anticipation behavior. A more complex Hierarchical Bayesian framework may have a greater explanatory value when applied to integration of sensory and other information integration for anticipation skill (Gray & Cañal-Bruland, 2018; Klatt & Smeeton, 2020), cognitive load (Runswick et al., 2018), deception (Jackson et al., 2006; Smeeton & Williams, 2012), and learning (Williams et al., 2002).

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Additional information

Funding

The author(s) reported there is no funding associated with the work featured in this article.