Effects of adaptive error-threshold practice on soccer instep kick learning

Abstract

This study examined the effects of contextual interference and algorithmic practice with 33% or 44% error thresholds on learning the soccer instep kick in novice participants. Seventy-one inexperienced students (18–25 years) were randomly assigned to Blocked, Random, algorithmic 33%, algorithmic 44%, or control groups. After pre-testing, practice involved 324 trials over two days from 5, 6, and 7 m distances. Algorithmic groups began with blocked practice and progressed to serial or random structures based on accuracy thresholds (≥ 67% for 33%; ≥ 56% for 44%). Blocked and random groups practiced according to classical random and blocked order. Retention and transfer tests occurred two days post-practice; psychological pressure was induced via financial incentives, audience, and social comparison. Acquisition results showed no group differences, but algorithmic 33% improved significantly from day 1 to 2. In retention, both algorithmic groups outperformed random and control groups. In the transfer test, algorithmic 44% surpassed all groups, including algorithmic 33%. Heart rate increased post-stress induction, confirming manipulation success, yet no group differences emerged under psychological pressure. The findings may be interpreted within the challenge point framework, although the underlying informational mechanisms were not directly assessed. As an initial application of algorithmic practice to a field-based motor skill, the present results suggest that error-threshold tuning may represent a promising avenue for future motor learning research.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-57684-y.

Introduction

Movement is the most fundamental indicator of human life. Wherever life exists, movement is present, and life is inconceivable without it. Movement in human life begins before birth and continues until the end of life. Motor learning can be considered a critical component in sustaining human vitality. Motor learning refers to relatively permanent changes in motor behavior resulting from experience and practice¹. One factor that can influence the motor learning process is the error generated during practice. The magnitude or nature of errors during practice can affect learning in various ways, and different theories offer contrasting perspectives on this issue. For instance, according to Adams’ closed-loop theory (1971)², the errors may reinforce the incorrect perceptual trace, leading the individual away from learning the optimal movement pattern.

Schmidt’s schema theory (1975)³, although informed by Adams’ (1971) earlier framework, introduced several substantive conceptual shifts. A central distinction concerns the role of movement errors in motor learning. Schmidt proposed that every movement attempt—accurate or erroneous—contributes to the development of a generalized rule that links selected movement parameters to their resulting outcomes. Through repeated practice, the learner accumulates information that supports the refinement of this rule, thereby improving the ability to estimate and adjust parameters in subsequent performances¹. Consequently, practice involving variable parameters, despite producing more errors during acquisition, enhances long-term retention and facilitates transfer by strengthening the underlying parameter-estimation schema. Within this theoretical view, errors are not detrimental; rather, they serve as essential inputs for building flexible and robust motor skills.

Aligned with schema theory³ is the contextual interference effect⁴, which pertains to practice arrangements. Contextual interference is defined as the performance disruption that arises from practicing multiple variations of a task or multiple tasks simultaneously⁵. According to this concept, contextual interference during practice may lead to poorer performance (more errors) during the acquisition phase but enhances performance in retention or transfer tests⁴. Several potential explanations for the contextual interference effect have been proposed, with research in this area suggesting two primary hypotheses: the forgetting and reconstruction hypothesis⁶ and the elaborative processing hypothesis⁴ as explanatory mechanisms for this effect. According to these hypotheses, the interference generated during practice, while potentially increasing movement errors, ultimately leads to a stronger and clearer movement representation. This enhanced representation serves as the foundation for the learner’s subsequent performance. It has been demonstrated that contextual interference can improve an individual’s mental representation of a task⁷. In addition, multiple studies provide evidence that contextual interference can play a beneficial role in motor learning⁸. However, this evidence primarily pertains to laboratory-based tasks⁹. From the contextual interference viewpoint, errors made during acquisition are not detrimental to motor learning and may, in fact, support more effective skill development.

In contrast to practice-variability and contextual-interference accounts, the implicit learning hypothesis—consistent with Adams’ (1971) framework—argues that errors hinder motor learning by drawing attention toward conscious movement control¹⁰. This shift increases reliance on working memory, limiting the capacity available for other concurrent demands. Under conditions such as psychological pressure, this cognitive load can impair performance. Supporting this view, evidence shows that learning environments designed to minimize errors lead to smaller performance declines when individuals later perform under psychological pressure¹¹.

The perspectives discussed thus far adopt a binary view of errors during practice, either deeming them entirely beneficial or detrimental. However, some newer theories propose a hybrid approach to the role of errors in motor learning. For instance, the challenge point framework¹² suggests that when an individual makes an error, the deviation from the ideal performance serves as information for the learner to process. If this information exceeds or falls below the required level, learning is impaired due to either overwhelming the learner’s processing capacity or insufficient information for task execution. According to this framework, the amount of information required by the learner varies at different stages of learning, and it is the responsibility of the practice designer to structure training to maintain a balance between the amount of information and the learner’s skill level as it progresses. Based on this theory, various studies have explored different motor learning methods. For example, progressive contextual interference¹³, computer-controlled practice^14–16 have been proposed. While these methods represent a step forward, they face challenges in real-world application. First, these methods involve conceptual complexities that make them impractical for individuals unfamiliar with motor learning principles. Second, these methods rely on an initial assessment of the individual’s performance level to design the practice structure.

A recently proposed method is the algorithmic approach. In this approach, a specific error threshold is set for learning, and if the individual experiences errors below this threshold, the practice structure is adjusted¹⁷. In the present study, the term “algorithmic practice” refers to a rule-based adaptive practice progression system grounded in established motor-learning concepts, particularly the challenge point framework, contextual interference effects, and adaptive practice scheduling approaches. Rather than representing a distinct theoretical model, the proposed approach operationalizes adaptive adjustment of practice structure through predefined performance thresholds designed to regulate functional task difficulty during learning. It has been shown that this training method leads to better performance compared to practice with high or low interference¹⁸. However, studies utilizing this method also have limitations. First, these studies have been conducted using laboratory-based tasks, and it remains unclear whether they are applicable in real-world settings. Second, this training method uses a single error percentage as the critical threshold for altering the practice structure. Although some studies suggest that an error rate of approximately 30% may be optimal for learning (reference), other effective error percentages may exist. Based on this rationale, the present study included a 33% error-threshold condition as a theoretically grounded adaptive practice parameter derived from prior challenge-based learning perspectives. In addition, a 44% error-threshold condition was included as a comparatively higher error-tolerance condition to examine whether allowing greater error tolerance—and consequently potentially earlier progression to more variable practice structures—would differentially influence learning outcomes. Importantly, the 44% threshold was not selected as a theoretically established optimal value, but rather as an experimentally higher adaptive threshold intended to explore the potential influence of increased error tolerance within adaptive practice scheduling. Furthermore, the impact of this training method on a critical variable, psychological pressure, has not been examined. Beyond acquisition and transfer performance, the present study also examined performance under psychological pressure. The phenomenon of choking under pressure, a common occurrence in sports, refers to performance below expectations¹⁹. This phenomenon is significant as it can lead to a poor throw, a missed penalty, or an error at critical moments in high-level games, determining the difference between victory and defeat. According to research evidence^19–22, contextual interference and adaptive practice conditions may contribute to the development of more flexible and stable movement representations that are less dependent on conscious (explicit) control processes during execution. According to reinvestment¹⁰ and choking-under-pressure perspectives²³, motor skills that rely less on explicit control may demonstrate greater resistance to performance disruption under stressful conditions. Therefore, if adaptive algorithmic practice promotes more functionally stable skill organization, such practice conditions may theoretically reduce susceptibility to pressure-induced performance decrements. Given the theoretical contradictions and the research limitations outlined, this study aims to investigate the effects of contextual interference and algorithmic training with different error percentages (33% and 44%) on learning soccer shooting.

Methods

Participants

A total of 71 students (47 men and 24 women- age range 18–25) were randomly assigned to five groups (each with 14–15 participants) as follows: Random (15 participants; 5 women, 10 men), Blocked (14 participants; 5 women, 9 men), Algorithmic 44% (14 participants; 4 women, 10 men), Algorithmic 33% (14 participants; 4 women, 10 men), and Control (14 participants; 6 women, 8 men). Participants had no history of formal soccer or futsal training, competitive participation, or regular structured involvement in these sports prior to the study. Informed consent was obtained in written form from all participants. The study protocol was approved by the Ethics Committee of Shiraz University (approval code: IR.US.PSYEDU.REC.1404.095). All methods were performed in accordance with the relevant guidelines and regulations.

Procedure

The target task in this study involved performing an instep soccer kick. A standard futsal ball for this age group (size 4, weight 400–440 g) was used to execute the task. Additionally, targets drawn on a wall served as the kicking targets. The general execution of the task is illustrated in the Fig. 1. The designated areas in the task were labeled as Zones 1, 2, and 3, corresponding to scores of 1, 2, and 3 points, respectively. The scoring system primarily reflected kicking accuracy rather than kicking power, as scores were determined directly by the landing location of the ball within the target areas. Similar scoring procedures have been used previously in soccer kicking and motor-learning research and have demonstrated acceptable validity for assessing kicking accuracy performance^24,25. One experimenter recorded the obtained scores throughout the study. To ensure scoring consistency across distances, the same target structure and scoring criteria (1–3 points per trial) were applied uniformly at all distances. Thus, the performance thresholds (in the algorithmic groups) reflected overall task success across distances rather than performance at a single distance.

Fig. 1.

Schematic presentation of the task execution.

Participants were individually invited to the laboratory and randomly assigned to one of the following groups based on a draw: Random, Blocked, Algorithmic 33%, Algorithmic 44%, or Control. After a brief rest and completing a written consent form, participants were shown a video of a skilled player (10 years of formal practice) performing the task, recorded from the sagittal plane. The video was played three times at 50% of normal speed. No verbal instructions regarding the execution of the movement were provided during the video. Subsequently, the scoring system for the kicks was explained to the participants, and they performed three practice trials as a warm-up. This was followed by a pre-test consisting of 15 trials conducted from three distances (5, 6, and 7 m). The order of distances was randomized, with the constraint that no distance was repeated consecutively, and each distance was repeated five times. Following the pre-test, the groups practiced the task according to their assigned conditions. The practice consisted of 18 blocks of 9 trials per day, conducted over two days (a total of 324 trials). The practice time for each group was about one hour for each day. The practice structure for each group is described below.

Blocked Group: In this group, participants performed kicks toward the targets from three distances (5, 6, and 7 m). The practice was organized in a blocked structure, such that on each day, half of the group completed the first six blocks from the farthest distance (7 m), the next six blocks from the intermediate distance (6 m), and the final six blocks from the closest distance (5 m). The other half of the group practiced in the reverse order, performing the first six blocks from 5 m, the next six blocks from 6 m, and the final six blocks from 7 m. This counterbalancing was implemented to control for potential order effects of the target distances.

Random Group: In this group, participants performed 18 blocks of 9 trials per day, with the order of trials completely randomized, subject to the constraint that no distance was repeated consecutively within a block, and each distance (5, 6, and 7 m) was repeated three times within each block.

Algorithmic 33% Group: Participants in the Algorithmic 33% group (Fig. 2A) practiced under an adaptive schedule in which progression between practice structures was determined by block-level performance. Each practice block consisted of 9 trials, with three trials performed from each distance (5, 6, and 7 m). Performance thresholds were calculated based on the total score obtained across all 9 trials within a block. The maximum possible score per block was 27 points. Practice began with a blocked structure. Half of the participants started from the closest distance (5 m→6 m→7 m), whereas the other half began from the farthest distance (7 m→6 m→5 m) to control for possible order effects.

Fig. 2.

Schematic presentation of the algorithmic practice groups. (A) Represents the practice structure for the algorithmic 33% error Group, and (B) Represents the practice structure for the algorithmic 44% error group.

If a participant achieved a total block score of 18 points or higher (corresponding to successful performance on approximately 67% of the maximum possible score), the practice structure progressed from blocked to serial practice. In the serial stage, participants performed the distances in a repeating sequential order (5–6–7 or 7–6–5, depending on the initial assignment). If performance during the serial stage again reached or exceeded 18 points, participants progressed to the random practice stage. In the random stage, trials from the three distances were presented in a randomized order, with the constraints that no distance was repeated consecutively and each distance appeared three times per block.

If participants failed to achieve the threshold score during the serial stage, they transitioned to an intermediate blocked-serial stage. In this stage, participants first performed two consecutive trials from each distance and then completed the remaining three trials in serial order. If the participant achieved the threshold score in the blocked-serial stage, they returned to serial practice. If the threshold was not reached, the blocked-serial stage was repeated. Participants who failed to achieve the threshold score during random practice returned to the serial stage, whereas those who successfully reached the threshold continued in random practice..

Algorithmic 44% Group: The Algorithmic 44% group (Fig. 2B) followed the same adaptive practice structure as the Algorithmic 33% group, with the only difference being the performance threshold required for progression between stages. Each practice block consisted of 9 trials, with three trials performed from each distance (5, 6, and 7 m). Performance thresholds were calculated using the total score obtained across all 9 trials within each block, with a maximum possible score of 27 points.

Participants began with blocked practice, and the initial order of distances was counterbalanced across participants (5–6–7 or 7–6–5). If a participant achieved a total block score of 15 points or higher (corresponding to approximately 56% of the maximum possible score), the practice structure progressed from blocked to serial practice. Successful performance in the serial stage resulted in progression to random practice, whereas failure to achieve the threshold led to the blocked-serial stage.

The blocked-serial stage consisted of two consecutive trials from each distance followed by three trials in serial order. Participants who achieved the threshold score in this stage returned to serial practice, whereas those who failed repeated the blocked-serial stage. During random practice, trials were presented in a randomized order with the constraints that no distance was repeated consecutively and that each distance appeared three times within a block. Participants who failed to achieve the threshold score during random practice returned to the serial stage, whereas those who successfully reached the threshold continued in random practice.

Performance thresholds (in both Algorithmic 33% and Algorithmic 44% groups) were evaluated at the level of each practice block, based on the total score obtained across the nine trials within that block. In addition, participant-level progression trajectories across adaptive practice stages were recorded throughout the intervention and are provided in the Supplementary Materials.

Control group: The control group did not participate in any practice sessions and only took part in the testing phases. A no-practice control group was included to provide a reference condition for evaluating potential changes associated with repeated testing, task familiarization, and natural performance variability across the experimental period. However, the primary theoretical comparisons of interest concerned differences among the active practice schedules, particularly the adaptive algorithmic conditions relative to traditional blocked and random practice structures.

Two days after the final practice day, participants were recalled to the laboratory and performed three warm-up trials. They then completed a retention test identical to the pre-test, consisting of 15 trials from distances of 5, 6, and 7 m in a randomized order, with the constraints that no distance was repeated consecutively, and each distance was repeated five times. Subsequently (10 min later), participants performed a distance transfer test comprising 15 trials from distances of 5.5, 6.5, and 8 m in a randomized order. A Polar heart rate monitor was then attached to each participant, and their heart rate was recorded for one minute, with the average serving as the baseline heart rate before the induction of psychological pressure. Next, a psychological pressure protocol was implemented, utilizing financial rewards, social comparison, and the presence of an audience to induce stress. Following this, participants’ heart rates were recorded for one minute, and the average was taken as the heart rate after the stress induction protocol. Finally, participants performed 15 trials identical to the pre-test distances (5, 6, and 7 m) under the induced psychological pressure condition. The present study included two distinct post-practice assessments targeting different aspects of motor performance adaptability. The distance-transfer test evaluated generalization of learning to modified spatial task parameters, whereas the psychological-pressure condition examined performance robustness under altered emotional and contextual demands while maintaining the original task structure. Although both assessments involved performance outside the original acquisition context, they represented conceptually different forms of post-practice evaluation.

Data analysis

For each trial, participants received a categorical accuracy score ranging from 1 to 3 based on the target zone in which the ball landed, with higher scores indicating greater kicking accuracy. The dependent variable used in the statistical analyses represented the mean score across trials within each testing phase. Consequently, reported values reflect averaged categorical performance scores. Prior to inferential analyses, data were screened for normality, homogeneity of variance, and potential outliers. Normality assumptions were evaluated using Shapiro–Wilk tests and visual inspection of distribution characteristics, while homogeneity of variance was assessed using Levene’s test. The assumption checks did not indicate substantial violations that would preclude the use of parametric analyses.

To analyze the accuracy data during the acquisition phase, a 5 (Group) × 2 (practice days) mixed design analysis of variance (ANOVA) was conducted, with repeated measures on the second factor. Similarly, for the heart rate data, a 5 (Group) × 2 (Pre- and Post-Stress Induction) mixed ANOVA was used, with repeated measures on the last factor. For the accuracy data in the pre-test, retention, and transfer phases, one-way ANOVA was used. Statistical analyses were conducted separately for theoretically distinct learning phases (acquisition, retention, transfer, and psychological pressure testing), each corresponding to specific experimental questions derived from the study hypotheses. In the presence of a significant main effect in the ANOVA, the LSD post-hoc test was applied for subsequent pairwise comparisons. The LSD post-hoc procedure was selected because the comparisons were guided by a priori theoretical expectations regarding differences among practice conditions. However, given the relatively liberal nature of LSD testing and the relatively constrained scoring range of the dependent variable, findings should be interpreted with appropriate caution.

In addition, we conducted an exploratory analysis within the algorithmic groups to examine whether initial baseline performance was related to how participants progressed through the adaptive practice schedule. To do this, we used a Spearman correlation between the pre-test performance and the percentage of trials completed under the random schedule, as the percentage data were not normally distributed. The significance level was set at 0.05. Effect sizes are reported as partial eta squared (η²_p) for the repeated‑measures ANOVA and as eta squared (η²) for the one‑way ANOVA, with values of 0.01, 0.06, and 0.14 interpreted as small, medium, and large effects, respectively²⁶.

Data availability

The data that support the findings of this study are available from the authors and have been uploaded on a digital database (10.5281/zenodo.17500896).

Results

Pre-test

Figure 3 illustrates the performance of the groups in the pre-test. To assess participants’ baseline performance prior to the intervention, pre-test data were analyzed using a one-way analysis of variance (ANOVA). The results indicated that the main effect of group was not significant, F(4, 70) = 0.26, P = 0.89, η² = 0.01.

Fig. 3.

The accuracy of different groups during the pre-test. Error bars represent the standard deviations (SD).

Acquisition

The control group was excluded from acquisition-phase analyses because participants in this condition did not undergo practice during the intervention period and therefore did not produce acquisition data comparable to those of the experimental groups. Figure 4 illustrates the performance of the groups across the two practice days. The results of the mixed analysis of variance (ANOVA) revealed that the main effect of group was not significant, F(3, 53) = 0.12, P = 0.94, η²ₚ = 0.007. However, the main effect of practice day was significant, F(1, 53) = 20.56, P < 0.001, η²ₚ = 0.28, as was the group × practice day interaction, F(3, 53) = 3.46, P = 0.02, η²ₚ = 0.16. Post-hoc tests for the group × practice day interaction indicated that the difference between the first and second practice days was significant only in the Algorithmic 33% group, P < 0.05. In the other groups, the difference between the two practice days was not significant, all P > 0.05. Comparison of means showed that in the Algorithmic 33% group, participants exhibited higher accuracy on the second day (M = 1.85, 95% CI [1.72, 1.97]) compared to the first day (M = 1.65, 95% CI [1.55, 1.75]).

Fig. 4.

The accuracy of different groups during the acquisition days. Error bars represent the standard deviations (SD).

In addition, descriptive analysis of the adaptive practice trajectories demonstrated differences in the distribution of experienced practice structures between the two algorithmic groups. Participants in the Algorithmic 44% group spent a greater proportion of total trials in serial and random practice formats, whereas participants in the Algorithmic 33% group spent relatively more trials in blocked and blocked-serial formats (Table 1). Furthermore, on the first day, in Block 5—which represents a point near the midpoint of the training session—eight participants in the Algorithmic 44% group reached a random practice schedule, whereas only one participant in the Algorithmic 33% group achieved a random practice schedule in the same block. On the second day, again in Block 5, nine participants in the Algorithmic 44% group reached a random practice schedule, while only three participants in the Algorithmic 33% group attained a random practice schedule. Taken together, these findings indicate that participants in the Algorithmic 44% group transitioned to the more complex random practice arrangement earlier.

Table 1.

Percentage of trials spent in blocked, blocked-serial, serial, and random practice formats across algorithmic practice groups.

Practice structure	Algorithmic 33%	Algorithmic 44%
Blocked	26.18	9.51
Blocked-serial	35.51	20.83
Serial	20.03	20.23
Random	18.25	49.39

Exploratory analysis of adaptive progression

An exploratory Spearman correlation analysis showed a significant relationship between baseline pre‑test performance and subsequent advancement through the adaptive practice schedule (ρ = 0.37, p = 0.049, N = 28), indicating that participants with higher initial performance tended to progress more toward the random practice structure.

Retention

Figure 5 illustrates the performance of the groups during the retention test. The results of the one-way analysis of variance (ANOVA) revealed a significant main effect of group, F(4, 70) = 3.13, P = 0.02, η² = 0.15. Post-hoc LSD tests indicated significant differences between the Random group and the Algorithmic 33% group, as well as between the Random group and the Algorithmic 44% group, all P < 0.05. Additionally, both the Algorithmic 33% and Algorithmic 44% groups showed significant differences compared to the Control group, all P < 0.05. No other group differences were significant, all P > 0.05. Comparison of means revealed that the Algorithmic groups exhibited higher accuracy than the Random and Control groups (means: Blocked = 1.68, 95% CI [1.50, 1.85]; Random = 1.58, 95% CI [1.43, 1.73]; Algorithmic 33% = 1.78, 95% CI [1.65, 1.90]; Algorithmic 44% = 1.809, 95% CI [1.69, 1.91]; Control = 1.54, 95% CI [1.41, 1.68]).

Fig. 5.

The accuracy of different groups during the retention test. Error bars represent the standard deviations (SD).

Transfer

Figure 6 illustrates the accuracy performance of the groups in the distance transfer test. The results of the one-way analysis of variance (ANOVA) revealed a significant main effect of group, F(4, 70) = 2.59, P = 0.044, η² = 0.12. Post-hoc LSD tests indicated that all groups, except the Blocked group, showed significant differences compared to the Algorithmic 44% group, all P < 0.05. Comparison of means revealed that the Algorithmic 44% group exhibited higher accuracy than the other groups in this phase (means: Blocked = 1.71, 95% CI [1.55, 1.87]; Random = 1.55, 95% CI [1.32, 1.78]; Algorithmic 33% = 1.67, 95% CI [1.46, 1.87]; Algorithmic 44% = 1.93, 95%CI [1.74, 2.12]; Control = 1.6, 95% CI [1.41, 1.78]).

Fig. 6.

The accuracy of different groups during the distance transfer test. Error bars represent the standard deviations (SD).

Manipulation check for psychological pressure

Figure 7 illustrates the heart rate results before and after the induction of psychological pressure. The results of the mixed analysis of variance (ANOVA) revealed that the main effect of group was not significant, F(4, 66) = 1.64, P = 0.17, η²ₚ = 0.09. Similarly, the group × time interaction was not significant, F(4, 66) = 1.25, P = 0.29, η²ₚ = 0.07. However, the main effect of time was significant, F(1, 66) = 9.65, P = 0.003, η²ₚ = 0.128. Comparison of means for the main effect of time indicated that the groups exhibited higher heart rates after the induction of stress protocol compared to before (means: pre-stress = 96.61 bpm, 95% CI [93.86, 99.37]; post-stress = 99.13 bpm, 95% CI [96.52, 101.74]).

Fig. 7.

The heart rate before and after the induction of psychological pressure. Error bars represent the standard deviations (SD).

Performance under psychological pressure

Figure 8 illustrates the accuracy performance of the groups under the psychological pressure. The results of the one-way analysis of variance (ANOVA) revealed that the main effect of group was not significant, F(4, 70) = 0.16, P = 0.95, η² = 0.009.

Fig. 8.

The accuracy of different groups under the psychological pressure. Error bars represent the standard deviations (SD).

Discussion

The results of this study did not demonstrate the classic contextual interference effect⁴. Contrary to expectations, no differences were observed between the Blocked and Random groups in any phase of the study. Based on findings reported in previous research, it was anticipated that the Blocked group would exhibit higher accuracy than the Random group during practice, but lower accuracy in the retention or transfer tests^7,27,28. Although this finding contradicts a substantial body of research (for review see²⁹), it is not entirely surprising within the contextual interference literature. Studies have reported no differences between blocked and random practice^30,31. Some review studies have indicated that the contextual interference effect is less pronounced in sports-related tasks^29,32. Researchers argue that in such tasks, the high level of challenge for novice learners may cause high contextual interference (random practice) to exceed the optimal challenge level, potentially explaining the absence of the contextual interference effect in these tasks^13,17.

It is argued that increasing contextual interference, when appropriately matched to the learner’s skill level, may facilitate learning by providing an interpretable amount of information during practice^13,33. Consistent with this argument, previous studies have shown that forms of practice with progressively increasing interference^13,33 or learner-adapted practice structures^16,18,34 lead to higher learning outcomes in novices. The results of this study may align with prior research^34,35, demonstrating that algorithmic practice with 33% or 44% error rates resulted in higher performance in the retention test compared to purely random and blocked practice. The likely explanation for these findings may relate to the functional difficulty of the task and the amount of information available in each practice structure¹². According to the challenge point framework, task difficulty is divided into nominal and functional difficulty. Nominal difficulty refers to difficulty within the constraints of an experimental protocol, remaining constant regardless of who performs the task or the conditions under which it is performed. In the present study, the nominal difficulty can be attributed to the distance from the starting point to the target. Functional difficulty, however, is related to the learner’s skill level and the practice structure. As learning is a problem-solving process, it depends on the amount of potential information available and the information that can be interpreted. Potential information is linked to nominal difficulty, whereas interpretable information is associated with functional difficulty. When the functional difficulty of a task increases (e.g., through practice structures that increase task complexity), the amount of potential information available rises, but this information may not be interpretable to the learner. For information to contribute to the learning process, it must be interpretable. When a learner has a low skill level, their information processing capacity is limited, and thus, only a small amount of information can be interpreted. However, as skill level increases, information processing capacity improves, allowing more information to be interpreted¹².

Furthermore, it is argued that information is transferred when it reduces uncertainty. When the actual outcome deviates from the expected outcome, information is provided to the learner. As skill level improves and performance becomes more successful, if the functional difficulty of the task remains constant, the actual performance will closely align with the expected performance, resulting in limited information available to the learner, which may be insufficient to enhance learning. Therefore, increasing functional difficulty can increase the amount of potential information by creating a discrepancy between expected and actual outcomes. Conversely, if a learner with a low skill level engages in a practice structure with high complexity, the high error rate may provide excessive information that, due to limited processing capacity, overwhelms the learner, leading to reduced learning. The challenge point framework emphasizes the importance of aligning the amount of information with the learner’s skill level to ensure interpretability¹². In this study, the blocked practice structure, being the simplest arrangement, likely failed to provide sufficient information to improve learning as participants’ performance improved, even though it may have been appropriate for participants’ initial skill level. In contrast, the random practice structure, given the learners’ low skill level, likely provided excessive information that participants could not fully interpret due to their limited processing capacity during the initial phases of practice. It is worth mentioning that in this study the attentional demand and information processing were not addressed. Consequently, interpretations based on the challenge point framework should be considered theoretical explanations rather than directly verified mechanisms. Thus, the present findings should be interpreted as being consistent with challenge point interpretations rather than as direct evidence of the underlying informational mechanisms proposed by the framework.

The algorithmic practice structures used in this study (33% and 44% error rates) began with a blocked arrangement, the simplest practice structure, which was suitable for the low skill level of participants early in practice, preventing information overload. As participants achieved a critical accuracy threshold, their practice structure shifted to a more complex arrangement. If participants failed to maintain an acceptable performance level in the new, more complex structure, they reverted to a simpler one. This approach aimed to tailor the amount of information (error rate) during practice to the learner’s skill level. Consequently, the higher performance of the algorithmic groups in the retention test compared to the blocked and random groups may be attributed to this alignment of functional task complexity (practice structure) with the learners’ performance level during practice. In addition to statistical significance, the observed effect sizes (η² = 0.15) suggested that the retention differences were of moderate-to-large practical magnitude, indicating that the adaptive practice conditions may have produced meaningfully stronger learning effects beyond short-term performance fluctuations.

Another significant finding of this study is the higher performance of the Algorithmic 44% group compared to all other groups, including the Algorithmic 33% group, in the transfer test. Moreover, the magnitude of the observed transfer effects (η² = 0.12) suggests that the performance advantage of the Algorithmic 44% condition may be practically meaningful in applied motor-learning settings, particularly for complex sport skills requiring adaptability across task variations. This is an important finding that may not align with previous research in this field. In a simulation study, an error rate of 30% was identified as a suitable error rate for motor learning, and a subsequent study using a computer-based Pong task demonstrated that a 32% error rate was the most effective for motor skill acquisition, closely aligning with the simulation results³⁵. Similarly, previous studies^17,18 showed that a 33% error rate could serve as an optimal error rate for learning a timing skill in older adults. The likely explanation for this discrepancy may be attributed to the nature of the tasks used in the current study compared to previous research. Prior studies primarily utilized laboratory-based tasks that involved limited body segments, resulting in fewer degrees of freedom and lower nominal task difficulty compared to the task in the present study.

In contrast, the current task was a sports-related task requiring coordinated movement of all body joints, thus exhibiting higher nominal difficulty. It is plausible that a 33% error rate, which requires 67% accuracy to trigger a change in practice structure, may optimize the challenge point for tasks with lower nominal difficulty. However, for the task used in this study, which has higher nominal difficulty, a 33% error rate implies greater stringency for transitioning to a more complex practice structure. Consequently, participants in the 44% error rate group may have progressed earlier to more variable practice structures. The additional descriptive acquisition analyses suggest that the adaptive threshold conditions influenced not only overall performance outcomes, but also the temporal progression of practice experiences throughout learning. As indicated by the descriptive analysis, the Algorithmic 44% group not only experienced a greater proportion of random practice compared to the Algorithmic 33% group, but also reached this practice format earlier. This change in practice structure may enhance participants’ motivation to engage more actively in practice, thereby facilitating learning. Supporting this idea, it has been shown that algorithmic practice can influence participants’ motivation³⁴. This finding is Important, as the present study is the first to examine different error rates for learning sports-related skills, serving as a starting point for future research. Although the superior transfer performance observed in the Algorithmic 44% group may suggest that a higher error tolerance may enhance participants’ motivation, this interpretation remains inferential. The present study did not directly quantify motivational responses during training. Therefore, alternative explanations cannot be fully ruled out. The 44% threshold should thus be interpreted as a promising adaptive parameter within the present task context rather than as evidence of an optimal error threshold. Future studies should directly examine the mechanisms underlying adaptive threshold-based practice designs by quantifying progression dynamics, motivational responses, and exposure to different practice structures. In addition, the observed association between baseline performance and adaptive progression suggests that initial skill level may partially influence advancement through threshold-based practice structures, an issue that warrants further investigation in future adaptive-learning research.

Furthermore, the results indicated that although the stress induction protocol increased participants’ heart rates compared to baseline, there were no significant differences in group performance under psychological pressure. Although no statistically significant group differences emerged under psychological pressure, the associated effect sizes (η² = 0.009) were generally small, further supporting the interpretation that the adaptive practice conditions did not produce a clear practical advantage in psychological pressure performance under the present experimental conditions. This finding suggests that the groups’ performance under psychological pressure conditions was comparable, indicating similar underlying mechanisms of these practice methods in high-pressure contexts. One might argue that the psychological pressure induction protocol was unsuccessful, but this argument is untenable for two reasons. First, the heart rate data demonstrated that all groups exhibited higher heart rates after the induction of the stress protocol compared to before. Second, if psychological pressure had not been induced, it would be expected that group performance in this test would resemble that of the retention test, as the two tests were identical in all conditions except for the presence of psychological pressure. The question of what led to this similar performance under psychological pressure remains open and could serve as a topic for future research. For instance, examining the underlying mechanisms of these practice methods may provide deeper insights into this question.

Although the pressure manipulation produced increased heart-rate responses, the practical magnitude of this physiological change appeared relatively modest. Therefore, the manipulation may have induced mild-to-moderate physiological arousal rather than a highly robust competitive-pressure state. In addition, the psychological pressure is inherently multidimensional and cannot be fully captured through physiological measures alone. The absence of subjective anxiety assessments in the present study limited our ability to determine whether the manipulation also elicited cognitive components of competitive anxiety, such as worry, perceived pressure, or self-focused attention. Therefore, the absence of performance deterioration under psychological pressure should be interpreted cautiously. Several alternative explanations remain possible, including limited pressure-manipulation intensity, insufficient induction of cognitive anxiety, absence of subjective anxiety assessment, relative robustness of the acquired motor patterns, substantial within-group variability, or limited statistical power associated with the present sample size. Consequently, the present findings do not allow definitive conclusions regarding the protective effects of the different practice conditions under psychological pressure.

Recent literature on mental fatigue and cognitive-performance regulation suggests that increased cognitive load, attentional demands, and perceived effort may negatively influence skilled motor performance under demanding conditions^36,37. From this perspective, psychological pressure may interact with broader cognitive and psychomotor regulation processes during sport performance. However, unlike studies reporting substantial performance disruption under cognitively demanding conditions, the present study did not observe clear between-group differences or marked performance deterioration during the psychological pressure condition. This may indicate that the present manipulation induced only modest pressure-related demands or that the learned motor performance was relatively robust under the current experimental conditions. Nevertheless, because cognitive load, mental fatigue, attentional control, and subjective pressure perception were not directly assessed, these interpretations remain speculative and warrant further investigation.

While the present findings were primarily interpreted within an information-processing and error-based learning framework, it is important to consider that learning in complex, whole-body skills such as the soccer instep kick may also involve adaptations in motor control and coordination. From a motor control and dynamical systems perspective, improvements in performance during retention and transfer may reflect not only enhanced processing of task-relevant information but also changes in movement organization, coordination patterns, and control strategies that emerge through practice^38,39. In tasks involving multiple degrees of freedom, learners may progressively develop more stable and efficient coordination patterns, reducing variability in task-relevant dimensions while allowing flexibility in others.

Furthermore, research in postural control suggests that practice and skill level are associated with changes in how stability is regulated during movement execution, with more skilled performers often demonstrating more adaptable and efficient control strategies^40,41. From this perspective, the higher transfer performance observed in the Algorithmic 44% group may partly reflect not only optimized informational conditions during practice but also emergent adaptations in coordination and postural control that support performance under novel task constraints. Importantly, these perspectives should be viewed as complementary to, rather than competing with, the challenge point framework, providing a more comprehensive account of the mechanisms underlying motor learning in complex sport tasks.

Overall, the present findings suggest that adaptive algorithmic practice with tuned error thresholds may facilitate certain aspects of motor learning in soccer instep kicking, particularly retention and transfer performance, although these effects were not uniform across all practice conditions or testing contexts. Furthermore, no clear performance advantage emerged under the present psychological pressure condition, although this finding should be interpreted cautiously given the multidimensional nature of competitive anxiety and the absence of subjective psychological measures. These findings were interpreted in light of the role of information availability and the amount of interpretable information for learners. Importantly, the present findings were interpreted not solely on the basis of statistical significance, but also in consideration of effect-size magnitude, theoretical consistency, and the overall pattern of results across learning phases. From an applied perspective, several of the observed effects demonstrated magnitudes that may be meaningful for motor-learning interventions in complex sport skills, even where statistical differences should be interpreted cautiously due to multiple testing considerations. Importantly, the control group served as a non-practice reference condition and should not be interpreted as reflecting motor-learning processes comparable to those of the trained groups. Therefore, similarities or differences in performance outcomes between the control and experimental groups do not necessarily imply equivalence in underlying learning mechanisms.

Like all research, this study has limitations. First, only outcome measures of performance were used, and performance production measures were not examined. For example, the use of electroencephalography could provide deeper insights into the underlying mechanisms of these practice methods. A major limitation of the present study is the absence of subjective measures of psychological pressure or state anxiety during the pressure condition. Although heart rate provided an objective indicator of physiological arousal, it did not fully capture the multidimensional cognitive and emotional components of competitive pressure relevant to choking-under-pressure theories. Consequently, it remains unclear whether the induced anxiety was purely somatic or whether cognitive anxiety also contributed to the effect. Future studies should incorporate multidimensional assessments of competitive pressure, including both physiological and subjective psychological measures, to better understand how adaptive practice conditions influence performance under stress. Another limitation of the present study relates to the adaptive nature of the algorithmic practice conditions. Although participant-level transition trajectories across practice stages were recorded, the exact amount of time spent in each practice structure (e.g., blocked, serial, blocked-serial, random) was not formally quantified. Consequently, it is difficult to determine the extent to which the observed learning effects were attributable solely to the intended error-threshold manipulation versus differences in relative exposure to specific practice modes. Future studies should systematically quantify exposure duration within each practice structure to further clarify the mechanisms underlying adaptive algorithmic practice. The present study also involved multiple outcome phases and statistical comparisons across learning and pressure-related conditions.

Although these analyses were theoretically differentiated and planned according to distinct experimental phases, formal multiplicity correction procedures were not applied. Consequently, some findings—particularly selective transfer effects—should be interpreted cautiously pending replication in future studies. Another limitation relates to the use of Fisher’s LSD post-hoc comparisons, which may increase the risk of Type I error relative to more conservative multiple-comparison procedures. Therefore, some statistically significant findings should be interpreted cautiously and considered in conjunction with effect sizes and theoretical consistency. Furthermore, in this study, acquisition performance was summarized at the level of each practice day, which limited our ability to track the more nuanced, within‑session learning changes that occur across individual practice blocks. Future research should retain block-level acquisition data to enable more detailed analyses of adaptive progression trajectories and temporal learning characteristics throughout practice. Another limitation of the present study is that sex distribution was not balanced across groups and sex was not incorporated analytically. Because sex-related differences may influence motor performance and kicking characteristics, future studies should examine adaptive practice effects using larger samples with balanced sex representation. Finally, the experimenter responsible for recording the performance scores was not blinded to group allocation. Although the scoring procedure was based on objectively defined target zones with minimal subjective judgment, the possibility of unintentional recording bias cannot be completely excluded.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

Hossein Taghizadeh, Davoud Fazeli, and Gholamhossein Nazemzadegan contributed equally to all aspects of the study, including conceptualization, experimental design, data collection, statistical analysis, figure preparation, and manuscript writing. All authors reviewed and approved the final version of the manuscript.

Funding

This research received no specific grant from any funding agency in the public, private, or not-for-profit sectors.

Data availability

The data that support the findings of this study are available from the authors and have been uploaded on a digital database (10.5281/zenodo.17500896).

Declarations

Competing interests

The authors declare no competing interests.