Introduction

Marathon running has experienced unprecedented global growth, with millions of participants annually pursuing the challenging 42.2-kilometer distance across diverse performance levels and training backgrounds1. This surge in participation has intensified scientific interest in optimizing training methodologies, as traditional one-size-fits-all approaches increasingly demonstrate inadequate accommodation of substantial inter-individual differences in physiological responses, recovery capacity, and adaptation rates among runners2. Contemporary training prescription faces the fundamental challenge of reconciling standardized protocols with the inherent biological variability that characterizes human athletic performance, particularly in endurance sports where training adaptations unfold over extended periods and involve complex physiological systems3.

In preparing for a marathon, two notable models of training intensity distribution have become the mainstream model: tapered and polarized4. The pyramidal system involves primarily low-intensity training regimes (70%), with medium-sized doses at threshold intensities (20%) and only low high-intensity work (10%). When looked at graphically on a time-intensity scale, this creates the characteristic pyramid-shaped distribution5. Conversely, strategies of the polarized model involve substantial low-intensity training (80%) combined with targeted high-intensity sessions (15%), while little moderate-intensity training (5%) is done deliberately. Compared to just output graphs, these results are shown in contrast to that of a bimodal distribution emphasizing intensity extremes6. While controlled investigations show both theories to be effective, direct comparative studies now contradict each other: when the same experiment was repeated but for different runners or different races in between runs over a given week period and not only did no advantage from either method emerge, it appeared eventually as if effectiveness may have been dependent on aspects about the athletes themselves rather than being attributable to an inherent superiority of either method topic7.

The fact that a substantial degree of individual difference exists in the progress (i.e., speedup or slowdown) seen by different athletes on identical courses is increasingly prompting personalization of training8. Evidence suggests that approximately 10–30% of individuals fail to achieve meaningful cardiorespiratory fitness improvements following standard endurance training protocols, highlighting the substantial biological variability that characterizes human training responses9. This heterogeneity encompasses far more than basic fitness adaptations, involving intricate relationships between genetic predisposition, training background, physiological traits, and environmental factors that collectively influence optimal training methodology selection for individual athletes10. Recent methodological reviews have emphasized critical considerations when interpreting inter-individual training response variability, noting that appropriate study designs and statistical approaches are essential to distinguish genuine biological differences from measurement error and methodological artifacts11,12,13. Although our investigation demonstrates considerable individual response heterogeneity, we acknowledge the inherent challenges in definitively attributing observed variability to true biological differences versus methodological limitations. Current personalization efforts remain fragmented across various approaches without comprehensive integration frameworks14.

Machine learning has emerged as a powerful analytical tool in sports science, offering capabilities to process complex, multidimensional datasets and identify patterns that traditional statistical methods might overlook15. Applications across performance prediction, injury prevention, and tactical analysis have shown encouraging results in diverse sporting contexts16. Advanced algorithms demonstrate particular promise for detecting complex training data relationships that predict individual adaptation patterns and performance trajectories17. However, most current machine learning implementations in sports focus primarily on prediction rather than training optimization, limiting their practical utility for personalized prescription and real-time training adaptation18.

Several significant limitations impede the translation of research findings into effective training practice. Current training intensity distribution studies typically employ small sample sizes, controlled laboratory conditions with limited ecological validity, and group-level comparisons that inadequately address individual response variation19. While machine learning applications show sophisticated predictive capabilities, they often lack integration with established physiological training principles and fail to provide actionable guidance for training modifications based on individual adaptation patterns20. This disconnect between predictive accuracy and prescriptive capability represents a fundamental gap, as practitioners require dynamic, evidence-based recommendations for training adjustments rather than merely performance forecasts21. Furthermore, existing personalization approaches inadequately address how multiple individualization factors interact to optimize training outcomes across diverse athlete populations22. The absence of comprehensive frameworks integrating real-time physiological monitoring with adaptive training prescription represents a significant barrier to practical implementation23.

This investigation addresses these limitations through the development and evaluation of machine learning models that examine the comparative effectiveness of pyramidal versus polarized training methodologies for marathon performance optimization while enabling personalized training prescription based on individual athlete characteristics. Through comprehensive analysis of training and performance data integrated with physiological measurements, this research identifies optimal intensity distributions for different runner profiles while developing models capable of real-time training adaptation. The approach transcends traditional group comparisons by implementing individualized methodologies that can dynamically adjust training recommendations based on ongoing physiological responses and performance metrics, thereby bridging the gap between theoretical training science and practical coaching applications in marathon preparation.

Methods

Study design and ethics

All experimental procedures adhered to the Declaration of Helsinki standards and received approval from Hanyang University’s Institutional Review Board (Approval No. HYU-2025-001). Prior to participation, written informed consent was secured from all participants, including legal guardian consent for those under 18 years of age. The research protocol, data collection, processing, and analytical procedures followed established human subjects research guidelines. This study employed a machine learning-based methodological framework to conduct comparative analysis of marathon training models, specifically examining pyramidal and polarized training intensity distributions. The investigation focused on evaluating individualized training intensity distribution models by incorporating evidence-based training principles and personalized prescription methods to account for individual physiological characteristics, adaptation responses, and exercise intensity preferences24.

The comprehensive research framework illustrated in Fig. 1 encompasses three sequential phases: data collection and preprocessing, parallel model development, and experimental validation through comparative model analysis. A parallel-group, randomized controlled trial design was implemented, with participants allocated to either pyramidal (n = 60) or polarized (n = 60) training protocols throughout a 16-week preparation period preceding an autumn marathon event. Both experimental groups followed identical data collection protocols and physiological assessment procedures, with training intensity distribution serving as the sole differentiating factor between groups. This parallel development approach facilitated controlled comparative analysis while maintaining the distinct characteristics inherent to each training methodology. The integrated framework prioritized concurrent development and evaluation of both training models, with particular emphasis on critical methodological elements including model architecture, data management protocols, and evaluation metrics to ensure comprehensive comparative analysis of training effectiveness and individualization potential.

Fig. 1
figure 1

Research framework for comparative analysis of machine learning-based marathon.

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Participants

A total of 120 recreational and semi-elite marathon runners (68 male, 52 female) were recruited through local running clubs, online platforms, and university athletics programs. Participants represented diverse training backgrounds and performance levels, reflecting the heterogeneous nature of the modern marathon running population2. Baseline participant characteristics are presented in Table 1. The cohort was stratified by experience level: novice (< 2 years, n = 31), intermediate (2–5 years, n = 47), advanced (5–8 years, n = 28), and elite (> 8 years, n = 14), ensuring adequate representation across the performance spectrum to enable meaningful analysis of individual response patterns18.

Inclusion criteria comprised: age 18–55 years; minimum 12 months of consistent running training (≥ 3 sessions/week); ability to complete half-marathon distance within 6 months prior to enrollment; commitment to complete the full 16-week training intervention; access to GPS-enabled running watch and heart rate monitor; and no planned major competitions during the intervention period beyond the target marathon. Exclusion criteria included: history of cardiovascular disease, metabolic disorders, or musculoskeletal injuries requiring medical intervention within 6 months; current use of performance-enhancing substances or medications affecting cardiovascular response; pregnancy or planned pregnancy during the study period; elite athletes with marathon personal best times faster than 2:45:00 (male) or 3:15:00 (female); inability to attend baseline and follow-up laboratory assessments; and previous participation in structured polarized or pyramidal training programs within 12 months.

Participants were randomly assigned to either pyramidal training (n = 60) or polarized training (n = 60) groups using computer-generated randomization stratified by gender, age group (18–30, 31–40, 41–55 years), and baseline marathon experience. Group allocation was concealed until completion of baseline assessments. As shown in Table 1, demographic and physiological characteristics demonstrated no significant differences between groups at baseline (all p > 0.05), confirming successful randomization as outlined in the study framework (Fig. 1). A total of 116 participants completed the study protocol, achieving a 96.7% retention rate through regular monitoring, flexible scheduling of assessments, and comprehensive support throughout the intervention period.

Table 1 Baseline participant characteristics.
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Data collection

Data collection employed a systematic approach utilizing consumer-grade wearable technology to ensure practical feasibility and participant compliance throughout the 16-week marathon preparation period. The comprehensive monitoring framework was designed to capture essential training and physiological parameters while maintaining ecological validity for recreational marathon runners24. All data acquisition protocols prioritized non-invasive monitoring methods suitable for continuous use during normal training activities (Table 2).

The primary data collection system comprised GPS-enabled sports watches (Garmin Forerunner series) and chest-strap heart rate monitors, providing continuous monitoring of cardiovascular and movement parameters during all training sessions. This approach enabled systematic collection of approximately 50,000 data points per participant over the study duration, encompassing heart rate variability, training load metrics, and performance indicators without imposing unrealistic monitoring demands. The framework incorporated evidence-based principles for individualized training monitoring, ensuring data quality while maintaining practical implementation standards25.

Table 2 Data collection framework for marathon training analysis.
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Data preprocessing followed a standardized pipeline to transform raw sensor outputs into meaningful training variables while preserving the temporal relationships essential for machine learning model development. The preprocessing framework addressed missing data through multiple imputation techniques, applied outlier detection using interquartile range methods, and implemented temporal alignment procedures to synchronize multi-sensor data streams with varying sampling frequencies. Quality assurance protocols included weekly device calibration against laboratory standards and systematic validation of data integrity throughout the collection period (Fig. 2).

Fig. 2
figure 2

Data preprocessing and feature engineering pipeline for marathon training analysis.

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Feature engineering extracted time-domain and frequency-domain characteristics from physiological signals, emphasizing heart rate zone distributions and running dynamics parameters accessible through consumer wearable devices. The process generated 27 optimized features across five categories: cardiovascular measures, movement efficiency indicators, training load parameters, recovery metrics, and athlete profile characteristics. This feature set was specifically designed to capture the distinct physiological signatures associated with pyramidal and polarized training methodologies while maintaining compatibility with practical monitoring constraints. The resulting dataset provided robust input for machine learning model development and enabled comprehensive analysis of individual training responses across diverse athlete populations.

Physiological assessments

Comprehensive physiological assessments employed established, non-invasive laboratory protocols to characterize individual athlete profiles and monitor training adaptations. All testing utilized validated methodologies appropriate for recreational marathon runners, with emphasis on measurements directly relevant to endurance performance and training intensity prescription (Table 3)26.

Table 3 Laboratory testing protocols for physiological assessment.
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Maximal oxygen uptake (VO₂max) was determined using incremental treadmill protocols with metabolic cart analysis, representing the primary measure of aerobic capacity. Lactate threshold assessment employed incremental exercise testing with capillary blood sampling, enabling determination of first lactate threshold (LT₁ at 2 mmol/L) and second lactate threshold (LT₂ at 4 mmol/L) as critical markers for training zone prescription. Running economy was evaluated through steady-state submaximal testing at standardized speeds relevant to marathon performance.

The testing schedule comprised baseline assessments, mid-intervention evaluations, and follow-up assessments at study completion. This timeline captured meaningful physiological adaptations while minimizing participant burden and testing-related interference with training protocols27. Heart rate responses were continuously monitored during all testing to establish individual heart rate zones corresponding to metabolic thresholds, enabling precise training intensity prescription for both pyramidal and polarized protocols.

All laboratory assessments were conducted under standardized environmental conditions with consistent quality control procedures, including daily equipment calibration and validation protocols. The comprehensive assessment battery provided robust physiological characterization for machine learning model input while maintaining compatibility with the individualized training prescription framework.

Machine learning model development

Machine learning model development employed a systematic approach to capture the distinct physiological signatures associated with pyramidal and polarized training methodologies. The development framework utilized established principles for sports performance modeling while addressing the specific requirements of individualized training prescription15. Two parallel models were developed to enable direct comparison of training approaches while maintaining the unique characteristics inherent to each intensity distribution paradigm.

The model architecture selection process considered the complex, high-dimensional nature of endurance training data and the substantial inter-individual variability in training responses documented in endurance athletes18. A hybrid approach combining gradient boosting regression for performance prediction and support vector machine classification for training zone assignment was implemented, aligning with recent advances in sports analytics16.

Hyperparameter optimization employed Bayesian search methodology with five-fold cross-validation to ensure robust model performance across diverse athlete populations (Table 4). The optimization process systematically evaluated learning rates, regularization parameters, and network architecture configurations to maximize prediction accuracy while preventing overfitting. Distinct hyperparameter sets were established for pyramidal and polarized models to accommodate the fundamental differences in training intensity distributions.

Table 4 Model hyperparameter optimization for pyramidal and polarized training models.
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The fundamental mathematical framework for both models employed weighted training load calculations:

$$P(t)=f\left( {\sum\limits_{{i=1}}^{n} {{w_i}} \cdot T{L_i}(t) \cdot {e^{ - \lambda (t - {t_i})}}} \right)$$
(5)

where P(t) represents predicted performance at time t, TLi denotes training load at session i, wi represents intensity-specific weighting factors, and λ reflects the decay factor for training stimulus over time20.

The pyramidal model (P-ML) utilized progressive weighting factors reflecting the characteristic intensity distribution, while the polarized model (POL-ML) employed bimodal weighting emphasizing intensity extremes (Fig. 3). Model-specific loss functions incorporated intensity distribution constraints:

$${L_{polar}}=\alpha \cdot {L_{class}}+\beta \cdot {L_{perf}}+\gamma \cdot {L_{zone2}}$$
(6)

where α and β balance classification accuracy and performance prediction, while λ enforces training methodology-specific intensity distribution patterns.

Fig. 3
figure 3

Comparison of pyramidal and polarized training intensity distributions.

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Feature engineering generated 27 optimized variables across cardiovascular, biomechanical, training load, recovery, and athlete profile domains. Training load quantification employed both session rating of perceived exertion (sRPE × duration) and heart rate-based training impulse (TRIMP) calculations to capture training stress indicators. Model validation employed stratified cross-validation preserving performance distribution across all folds, following the systematic evaluation framework illustrated in Fig. 4. Performance evaluation incorporated multiple metrics including mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²), emphasizing generalization capability over training performance.

Fig. 4
figure 4

Structure of marathon training effect evaluation.

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Statistical analysis

All statistical analyses were conducted using R version 4.3.0 and Python 3.9.7, with statistical significance set at α = 0.05. Sample size determination followed established guidelines requiring 10–15 observations per predictor variable10. With 120 participants and 27 features, the study met the recommended ratio for robust machine learning model development. To address potential overfitting concerns given the feature-to-sample ratio, we employed several mitigation strategies: (1) feature selection using correlation analysis to reduce multicollinearity, (2) stratified 5-fold cross-validation with multiple iterations, (3) L2 regularization parameters optimized through Bayesian search, and (4) external validation procedures to assess generalization capability. Machine learning model validation employed stratified 5-fold cross-validation with performance evaluated using mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²). Feature importance was assessed using permutation-based methods to ensure ranking stability.

Inter-individual variability in training responses was analyzed using mixed-effects models to partition variance components and quantify true individual differences beyond measurement error18. Between-group comparisons utilized independent t-tests for normally distributed data and Mann-Whitney U tests for non-parametric distributions. Repeated measures ANOVA assessed changes over time, with effect sizes calculated using Cohen’s d and partial eta squared. Individual response patterns were identified through k-means clustering with silhouette analysis for optimal cluster determination. Model interpretability employed SHAP values to quantify feature contributions to predictions. Hyperparameter optimization utilized Bayesian optimization with cross-validation to prevent overfitting. Missing data (< 3% of observations) were handled using multiple imputation with chained equations. All analyses followed intention-to-treat principles with sensitivity analyses conducted using per-protocol populations to assess result robustness.

Results

Model performance evaluation

Machine learning model evaluation revealed distinct performance characteristics between pyramidal and polarized training approaches, with important implications for individualized training prescription. The pyramidal model demonstrated superior overall prediction accuracy, achieving 6.15 ± 1.12 min mean absolute error compared to 7.28 ± 1.31 min for the polarized model (Table 5). However, this advantage was primarily driven by enhanced performance for experienced runners, where pyramidal predictions achieved 24.6% lower error rates. Both models performed comparably for novice athletes, indicating that training methodology selection becomes increasingly critical with advancing experience.

Table 5 Prediction accuracy metrics for pyramidal and polarized training models.
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Feature importance analysis revealed fundamentally different predictive mechanisms underlying each approach. The pyramidal model relied heavily on training load parameters (32.4%) and cardiovascular measures (28.5%), reflecting its emphasis on systematic aerobic development (Fig. 5a). Conversely, the polarized model showed more balanced utilization across feature categories, with notable emphasis on movement efficiency (22.6%) and biomechanical factors. Cross-domain analysis confirmed these patterns, with pyramidal models deriving 52% of predictive power from physiological features compared to 38% for polarized models, while polarized models showed greater dependence on biomechanical features (41% versus 23%) (Fig. 5b).

Fig. 5
figure 5

Feature importance analysis for marathon training models.

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Model generalization performance demonstrated population-specific strengths aligned with training methodology characteristics. Cross-population analysis showed pyramidal models maintained consistent accuracy across experience levels (6.7–12.8% error range), while polarized models exhibited greater variability, performing poorly for novice runners (14.3% error) but excelling for elite athletes (6.1% error) (Fig. 6a). Temporal robustness analysis revealed distinct adaptation signatures, with pyramidal models showing stable performance throughout training cycles compared to polarized models demonstrating pronounced improvement during later phases (Fig. 6b).

Fig. 6
figure 6

Model generalization performance evaluation.

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These findings indicate that optimal training methodology selection requires consideration of individual athlete characteristics and experience levels. The superior pyramidal performance for less experienced athletes likely reflects the systematic nature of this approach, while polarized effectiveness for elite athletes suggests this methodology requires established aerobic foundations to realize full potential. The differential feature importance patterns provide mechanistic insights for personalized training prescription based on individual physiological profiles and adaptation capacity.

Comparative analysis of training methods

Performance outcomes

Polarized training demonstrated superior marathon performance, with athletes achieving 11.3 ± 3.2 min improvement compared to 8.7 ± 2.8 min for pyramidal training (p < 0.03, d = 0.81) (Fig. 7a). This 30% performance advantage emerged primarily during the latter half of the marathon, where split analysis revealed divergent fatigue patterns (Fig. 7b). Both groups performed comparably through 25 km, but polarized-trained athletes maintained pace beyond 30 km while pyramidal counterparts experienced progressive deceleration, with differences reaching 18–25 s per 5 km split. Pacing strategy analysis revealed contrasting race execution capabilities (Fig. 7c). Polarized training produced significantly more consistent pacing profiles (CV = 3.2%) compared to pyramidal approaches (CV = 5.7%, p < 0.01), indicating superior metabolic control and race management. This enhanced consistency likely contributed to late-race performance advantages, as even pacing minimizes glycogen depletion throughout the marathon distance. Cardiovascular efficiency during competition differed markedly between methodologies (Fig. 7d). Polarized-trained athletes maintained 15–20% better heart rate recovery capacity throughout the marathon, with differences increasing during later stages (p < 0.05). This enhanced cardiac efficiency may partially explain the sustained performance observed in split analysis, facilitating oxygen delivery and lactate clearance during prolonged exercise.

Fig. 7
figure 7

Marathon performance outcome comparison.

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Training load management revealed distinct periodization strategies (Fig. 8a). Polarized training demonstrated greater load variability with pronounced peaks during build phases followed by strategic recovery periods, contrasting with the linear progression characteristic of pyramidal training. This approach may better accommodate high-intensity sessions while maintaining recovery balance. Program adherence patterns provided critical implementation insights (Fig. 8b). While both approaches maintained high overall compliance, polarized training sustained superior adherence during peak phases (92.3% vs. 86.7%, p < 0.05). This enhanced compliance during intensive periods likely contributed to performance outcomes, as consistent high-intensity session execution is essential for competitive adaptation. Despite accumulating 17.3% less total training volume, polarized athletes achieved superior performance outcomes, indicating enhanced training stimulus effectiveness. This efficiency gain suggests that training quality may be more important than absolute volume for marathon optimization, with important implications for time-constrained recreational athletes.

Fig. 8
figure 8

Training load and recovery relationship.

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Physiological adaptations

Both training methodologies produced significant physiological adaptations with distinct patterns reflecting their intensity distributions (Table 6). Polarized training elicited superior VO₂max improvements (+ 12.7% vs. + 10.4%, p = 0.042), indicating enhanced maximal aerobic capacity from high-intensity training emphasis. Conversely, pyramidal training demonstrated greater lactate threshold velocity gains (+ 9.3 vs. + 6.7 km/h, p = 0.037), reflecting improved submaximal efficiency from extensive moderate-intensity volume. Running economy adaptations were intensity-specific. Pyramidal training produced superior moderate-intensity economy (+ 7.4% vs. + 5.2%, p = 0.031), while polarized training showed greater high-intensity gains (+ 6.9% vs. + 4.3%, p = 0.028). Neuromuscular adaptations strongly favored polarized approaches, with maximal sprint velocity (+ 5.8% vs. + 3.1%, p = 0.021) and leg stiffness (+ 8.2% vs. + 4.7%, p = 0.018) improvements nearly doubling pyramidal responses. Cardiovascular adaptations differed markedly. Pyramidal training produced greater cardiac stroke volume increases (+ 11.3% vs. + 8.9%, p = 0.043) from volume-mediated cardiac remodeling, supporting enhanced submaximal efficiency.

These adaptation patterns explain observed performance differences. Polarized training’s superior VO₂max and neuromuscular adaptations likely contributed to late-race advantages, as maximal capacity and elastic energy utilization become critical during glycogen depletion. The findings demonstrate that intensity distribution produces specific physiological signatures directly influencing marathon performance capacity.

Table 6 Comparative analysis of physiological adaptations following 16-week training intervention.
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Personalization effectiveness

Individual response clustering revealed substantial heterogeneity in training methodology effectiveness, with distinct responder profiles emerging across the athlete population (Fig. 9a). Four clusters characterized response patterns: polarized responders (31.5%), pyramidal responders (31.9%), dual responders (18.7%), and non-responders (17.9%). This distribution demonstrates that no single training approach optimally serves all athletes, supporting the necessity for individualized prescription strategies. Experience level emerged as the strongest predictor of training response, showing significant correlations with both pyramidal (r = 0.72, p < 0.01) and polarized (r = 0.68, p < 0.01) training effectiveness (Fig. 9b). Baseline VO₂max demonstrated additional predictive value, with higher fitness levels associated with enhanced polarized training responses. These findings indicate that simple demographic and physiological assessments can effectively guide training methodology selection.

Fig. 9
figure 9

Individual response clustering analysis.

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Systematic analysis across athlete characteristics revealed distinct optimization patterns (Fig. 10). Novice athletes demonstrated superior responses to pyramidal training (+ 32.4% advantage), while elite athletes favored polarized approaches (+ 27.6% advantage) (Fig. 10a). Age-related patterns showed middle-aged athletes (41–50 years) responding better to pyramidal training (+ 15.2% advantage), whereas younger athletes favored polarized methods (Fig. 10b). Baseline fitness levels strongly influenced optimal training selection (Fig. 10c). Athletes with VO₂max > 55 ml/kg/min achieved superior results with polarized training (+ 23.8% advantage), while those with moderate fitness (45–55 ml/kg/min) responded better to pyramidal approaches (+ 17.6% advantage). Running mechanics provided additional personalization insights, with forefoot strikers showing enhanced polarized training responses (+ 20.6% advantage) (Fig. 10d).

Fig. 10
figure 10

Training effect comparison across athlete characteristics.

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The training effect matrix quantified these relationships for practical application (Table 7). Significant advantages (p < 0.05) emerged for specific athlete-training combinations, enabling evidence-based methodology selection. These findings demonstrate that easily assessed characteristics can effectively guide personalized training prescription, potentially improving performance outcomes while optimizing training efficiency across diverse athlete populations.

Table 7 Training effect matrix by athlete characteristics.
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Discussion

This investigation demonstrated that polarized training methodology produced superior marathon performance outcomes compared to pyramidal approaches, with athletes achieving 30% greater improvement despite reduced training volume. The substantial inter-individual variability observed, with four distinct responder clusters identified, challenges the prevailing one-size-fits-all training paradigm and supports the necessity for personalized intensity distribution strategies28. Machine learning models successfully predicted individual responses based on easily assessable characteristics, particularly training experience and baseline fitness levels, providing a practical framework for evidence-based training prescription in recreational marathon runners29. Recent advances in artificial intelligence applications for marathon performance prediction have demonstrated the potential for sophisticated algorithmic approaches30.

Our findings align with research demonstrating the efficacy of heart rate variability-guided training approaches for endurance performance enhancement31, while extending these observations to recreational marathon populations previously underrepresented in controlled investigations. The superior late-race performance observed with polarized training corroborates research indicating that training adaptation monitoring through heart rate variability is essential for elite endurance athletes32. However, our results contrast with quantitative analyses of elite training programs that suggest pyramidal distributions predominate in successful marathon preparation33, indicating that optimal intensity distribution may differ between recreational and elite populations. This divergence aligns with recent perspectives emphasizing the importance of long-term training approaches over single high-intensity sessions34.

The practical implications of these findings extend beyond academic interest to address real-world training prescription challenges. The identification of training experience as the primary predictor of methodology effectiveness provides coaches and athletes with actionable guidance for training selection, supporting the development of explainable prediction systems for marathon runners35. Recent studies incorporating half-marathon performance relationships with marathon outcomes36 highlight the importance of accessible predictors, which our research extends through machine learning methodologies. The demonstrated effectiveness of consumer-grade monitoring technology addresses previous barriers to personalized training implementation37. These findings support the development of automated training recommendation systems that could democratize access to evidence-based training strategies38.

Several limitations warrant consideration when interpreting these results. Several methodological limitations warrant consideration. The complex machine learning models relative to sample size may limit generalizability, though our cross-validation approach and regularization strategies aimed to mitigate overfitting concerns. Our interpretation of individual response patterns should be considered within the context of recent methodological critiques highlighting the complexity of distinguishing true inter-individual variability from measurement error in training response studies. The 16-week intervention period, while sufficient for meaningful adaptation, may not capture long-term training responses across multiple competitive seasons, particularly considering how training intensity distributions vary across different competitive phases39. The single-marathon validation approach limits generalizability compared to approaches that incorporate broader performance prediction frameworks40. Sample size constraints prevented detailed subgroup analyses within responder clusters, potentially missing important individual characteristics. While genetic-based algorithms for personalized training have shown promise in other contexts41 and genetic testing for training personalization has been explored42, such approaches remain impractical for widespread implementation in marathon training.

Future research should prioritize larger-scale validation studies incorporating diverse competitive environments and extended follow-up periods to establish long-term methodology effectiveness. Investigation of real-time training adjustment algorithms represents a promising avenue for enhancing individualized prescription accuracy, building upon existing systematic reviews of data-guided training prescription37. Extension of these methodologies to other endurance disciplines would determine broader applicability, while current training session models in endurance sports provide implementation frameworks43. Development of more sophisticated machine learning architectures could further improve prediction accuracy and training optimization outcomes.

This investigation provides compelling evidence that personalized training intensity distribution, guided by machine learning analysis of individual athlete characteristics, can significantly enhance marathon performance outcomes. The demonstration that simple, easily assessed factors can effectively predict optimal training methodology challenges current practice patterns and supports a paradigm shift toward individualized prescription strategies. The practical framework developed offers immediate application potential for coaches and athletes while establishing a foundation for future technological innovations in personalized endurance training. These findings underscore the importance of moving beyond population-based training recommendations toward truly individualized approaches that accommodate the substantial biological diversity inherent in human athletic performance.

Conclusion

This investigation establishes that polarized training intensity distribution produces superior marathon performance outcomes compared to pyramidal approaches in recreational athletes, achieving 30% greater improvement with reduced training volume. The identification of substantial inter-individual variability, with four distinct responder clusters comprising the study population, demonstrates that optimal training methodology selection depends critically on individual athlete characteristics rather than universal prescriptions. Machine learning analysis successfully predicted individual training responses using easily accessible parameters, particularly training experience and baseline fitness levels. This finding bridges the gap between theoretical training science and practical implementation by providing coaches and athletes with evidence-based tools for methodology selection. The superior predictive accuracy achieved using consumer-grade monitoring technology addresses previous barriers to personalized training prescription, making individualized approaches feasible for recreational marathon runners.

The physiological mechanisms underlying these performance differences reveal distinct adaptation signatures between training methodologies. Polarized training enhanced maximal aerobic capacity and neuromuscular function, supporting late-race performance advantages observed during competition. Pyramidal training improved submaximal efficiency but failed to translate these adaptations into superior marathon outcomes, challenging traditional volume-focused preparation strategies. These findings have immediate practical implications for marathon training prescription. The training effect matrix developed enables evidence-based methodology selection based on athlete experience, age, baseline fitness, and running mechanics. This framework represents a significant advancement from current one-size-fits-all approaches toward truly personalized training strategies. The broader significance extends beyond marathon running to encompass personalized training prescription across endurance disciplines. The demonstration that machine learning models can effectively guide training methodology selection using non-invasive monitoring technologies establishes a foundation for future innovations in sports science. This research supports a paradigm shift toward individualized training approaches that accommodate the substantial biological diversity inherent in human athletic performance, ultimately optimizing training effectiveness while minimizing the risk of inappropriate prescription for diverse athlete populations.