Autoregulated resistance training for maximal strength enhancement: A systematic review and network meta-analysis

Abstract

Objectives

This study aims to systematically review the effects of Autoregulating Progressive Resistance Exercise (APRE), Rating of Perceived Exertion (RPE), and Velocity-based Resistance Training (VBRT) on maximal strength through a network meta-analysis.

Methods

Forest plots and network diagrams visualized training modality differences and intervention relationships. Pooled standard mean difference (SMD) of different studies and the corresponding 95 % confidence intervals (CIs) quantified effect sizes, with inconsistency models assessing heterogeneity and surface under the cumulative ranking curve (SUCRA) values ranking protocols by optimal probability.

Results

For back squat 1RM, no moderate/large effect sizes were observed between interventions. SUCRA rankings showed APRE (93.0 %) as the most optimal intervention, followed by RPE (66.8 %), VBRT (27.0 %), and PBRT (13.2 %). In bench press 1RM, PBRT demonstrated a large effect vs APRE (SMD = −0.83, −1.22 to −0.44), while RPE showed a moderate effect vs APRE (SMD = −0.76, −1.70 to 0.19). SUCRA rankings prioritized APRE (97.1 %), followed by VBRT (57.1 %), RPE (29.9 %), and PBRT (15.9 %).

Conclusion

In this study, the network meta-analysis confirmed that APRE, VBRT, and RPE were significantly more effective than PBRT in enhancing maximum strength. Among these, APRE demonstrated the greatest effect, ranking first in the improvement of both the back squat and bench press 1RM, followed by VBRT, RPE, and PBRT.

1. Introduction

The enhancement of maximal strength is the most direct indicator of muscular strength development.¹ Resistance training is widely recognized as an effective method for improving maximal strength, muscle hypertrophy, explore power, speed, agility, and muscular endurance.² Traditionally, Percentage-Based Resistance Training (PBRT), which determines training intensity and volume based on percentages of an individual's one-repetition maximum (1RM),³ has been extensively used to enhance muscular strength and has proven effective in maximizing strength gains.⁴ The advantage of using %1RM is that personalized adjustments can be made effortlessly to the athlete's training load based on the pre-selected training intensity.^5,6 However, this approach does not account for daily fluctuations in athletes' physiological states, physical performance, and life stressors, which can lead to suboptimal load adjustments and an increased risk of injury.⁷

To address the limitations of conventional PBRT, Autoregulated Resistance Training (ART) has emerged in recent years, aligning with the trend toward digitized and intelligent sports training.^8,9 These approaches dynamically monitor and evaluate training loads based on real-time performance metrics, enabling individualized adjustments to training volume and intensity. This paradigm optimizes training stimuli according to athletes' immediate physiological states, thereby enhancing training efficacy while minimizing fatigue accumulation.¹⁰ Common ART include Autoregulating Progressive Resistance Exercise (APRE), Rating of Perceived Exertion (RPE), and Velocity-Based Resistance Training (VBRT), all of which have proven effective in controlling resistance training intensity.⁴ Current research primarily focuses on comparing APRE, VBRT, and RPE with PBRT, as well as investigating the effects of velocity loss thresholds in VBRT on strength development.¹¹ Existing evidence indicates that VBRT surpasses PBRT in maximal strength improvement,⁴ attributed to its superior neuromuscular adaptation through higher concentric velocities, lower perceived fatigue, and reduced training loads.^12,13 Similarly, APRE^14,15 and RPE^9,16,17 have demonstrated advantages over PBRT in enhancing maximal strength.

Nevertheless, comparative studies evaluating the efficacy of different ARTs on maximal strength remain limited. Traditional meta-analyses struggle to synthesize evidence from multiple interventions, while network meta-analysis (NMA) represents a significant methodological advancement in exercise science. By integrating both direct and indirect evidence, NMA allows for the simultaneous evaluation of various intervention strategies, ranks their relative effectiveness, and surpasses conventional pairwise meta-analyses.¹⁸ In this study, the RPE includes both repetitions in reserve (RIR) and RIR-based RPE (RIR-RPE), which are methods grounded in subjective feelings. In addition, during the strength training cycle, the bench press and squat are the most commonly utilized and effective exercises for enhancing maximum strength. Furthermore, 1RM of the bench press and back squat are widely regarded as the gold standard for evaluating maximum strength in the upper and lower limbs,¹⁹ respectively. Therefore, this study conducted a network meta-analysis on the bench press 1RM and back squat 1RM, derived from relevant randomized controlled trials (RCTs) to evaluate and compare the effectiveness of various self-regulated resistance training methods in enhancing the maximum strength of the participants.

2. Methods

This systematic review and network meta-analysis was registered with PROSPERO (CRD42024573857) and adhered to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses-Network Meta-Analyses (PRISMA-NMA) checklist (Supplementary: Appendix 1).

2.1. Searching strategy

The present systematic review and network meta-analysis conducted searches in several databases, including PubMed, Web of Science, Scopus, ScienceDirect, ProQuest, and China National Knowledge Infrastructure (CNKI) (Table 1). The search timeframe extended from the inception of records in each database to February 27, 2025, and the languages included were limited to Chinese and English.

Table 1.

The filters for each database.

Database	Algorithm	Language
Web of Science	Topic	English
PubMed	Title/Abstract	English
ScienceDirect	Title/abstract/author-specified keywords	–
Scopus	TITLE-ABS-KEY	English, Chinese
ProQuest	Noft	English, Chinese
CNKI	Topic	English, Chinese

Note: ABS- abstract; KET-key words.

The search was organized around a series of keywords, and the specific search strategies for the three types of ART are presented in Table 2. In addition to electronic searches, the reference lists of several review articles^6,20, 21, 22, 23, 24 were also meticulously perused, and manual searches were conducted to ensure comprehensive coverage. To ensure the accuracy of the search, two researchers cross-checked the search keywords. If there were any disagreements on keyword selection between the two researchers, a third researcher would make the final decision. If necessary, manual searches will be conducted to supplement literature.

Table 2.

Web of science literature selection strategy.

Training	Search terms with Boolean operators
APRE	(((“Autoregulatory” OR “Autoregulated” OR “auto-regulated” OR “auto-regulation” OR “autoregulation” OR “daily autoregulated”) AND (Progressive) AND (“Resistance Exercise” OR “Resistance Training”)) OR “APRE” OR “Autoregulatory Progressive Resistance Exercise")
VBRT	(“velocity-based resistance training” OR “velocity-based training” OR “velocity loss” OR “velocity threshold” OR “Velocity cut-off” OR “Loading-velocity profile” OR “Auto-regulation Method” OR “barbell velocity”)
RPE	((“Rating of Perceived Exertion” OR “RPE” OR “sRPE” OR “season RPE” OR “repetitions in reserve” OR “RIR”) AND (“resistance training” OR “strength training” OR “weight training”))

Note: APRE-autoregulating progressive resistance exercise; VBRT-velocity-based resistance training; RPE-rating of perceived exertion; RIR-repetitions in reserve.

2.2. Study selection and eligibility criteria

Two researchers conducted searches in each database using the same search strategy and independently translated and read the titles and abstracts using Google Translate to perform the preliminary screening and identify all relevant studies. Subsequently, the full texts were independently assessed against the pre-established criteria using Google Translate to determine which articles met the inclusion and exclusion criteria. Disagreements were resolved through discussion with a third expert or by consensus. After screening the literature in each database, the references were imported into EndNote X21 software (Clarivate Analytics, Philadelphia, PA, USA) for organization, and the duplicate data removal function of EndNote 21 software and manual deletion of duplicate references were utilized.

This systematic review and network meta-analysis followed the Cochrane Collaboration²⁵ and adhered to the PRISMA-NMA guidelines.²⁶ The PICOS methodology (population, intervention, comparator, outcome, study design) was applied as follows: (P) athletes, students, active men, and adolescents who have engaged in long-term, regular resistance training or sports training without experiencing injuries, illnesses, or other clinical symptoms were included; (I) implementation of APRE or VBRT or RPE; (C) comparison with PBRT or another ART; (O) the maximum strength before and after intervention; (S) RCTs. Specific inclusion and exclusion criteria are outlined in Table 3.

Table 3.

Inclusion and exclusion criteria.

Project	Inclusion criteria	Exclusion criteria
P	Athletes, students, active men, and adolescents who have engaged in long-term, regular resistance training or sports training	Experiencing injuries, illnesses, or other clinical symptoms; The elderly population
I	APRE, VBRT, RPE	Comparing the effects of different VL
C	PBRT, APRE/VBRT/RPE	Other resistance training
O	Bench press 1RM, Back squat 1RM	Inconsistent indicators: power clean 1RM, deadlift 1RM, front squat 1RM
S	RCTs	self-controlled trial, case analysis, relationship study

Note: APRE-autoregulating progressive resistance exercise; VBRT-velocity-based resistance training; RPE-rating of perceived exertion; RCT-randomized controlled trials; VL-velocity loss; PBRT-percentage-based resistance training.

2.3. Data extraction

After confirming the final inclusion of all literature in the analysis, two researchers extracted the data into a Microsoft Excel spreadsheet. The extracted data included the article title, year of publication, author(s) name, subject characteristics (e.g., age, sample size, sports item, and years of training), training program (intervention period, training frequency, and intervention means), and pre- and post-test data for outcome indicators (Bench press 1RM, and Back squat 1RM). The pre- and post-test data are as mean ± standard deviation, and all data is available from text and tables. If the data extracted by the two researchers was biased, it was reviewed and finalized by a third researcher. If the full text or study data could not be accessed, the authors of literature would be contacted via email for the content. When the original text only provided data result graphs, Getdata software was used to extract the mean and standard deviation.

2.4. Assessment of risk of bias

Two independent researchers employed the Cochrane Risk of Bias Tool within Review Manager software version 5.4 to assess the methodological rigor of each eligible RCTs. The risk of bias across the included studies was evaluated based on seven criteria: 1) generation of random sequences, 2) concealment of allocation, 3) blinding of participants and staff, 4) blinding of outcome assessment, 5) incomplete outcome data, 6) selective reporting, and 7) any other sources of bias. The quality of the literature was determined by the number of studies classified as “low risk of bias” (with scores of ≥4 considered low risk, 2–3 as moderate risk, and 0–1 as high risk). These findings were crucial in establishing the overall quality assessment of literature.

2.5. Statistical analysis

The systematic review and network meta-analysis package of STATA (version 18.0; StataCorp, College Station, TX, USA) software was used for NMA and drawing the network map, and Review Manager (version 5.4; Cochrane, London, UK) software was used to evaluate the quality of the included studies.

The systematic review and network meta-analysis was performed according to the current operation guidelines²⁷ and based on the frequentist framework. It was performed with the following steps. Initially, if there were at least two studies, we conducted a paired meta-analysis, generated a forest plot to compare the effects of one type of training with another or with a control condition, and created a network diagram.²⁸ The network diagram was generated according to NMA, where each note referred to intervention type and the line referred to studies in which interventions were compared directly. Node size was weighted by the number of participants receiving the specific intervention, while the line's thickness was weighted by the number of RCTs. In the statistical process of NMA, since the outcome measurement indicators of the included studies were continuous data and the scale scoring methods of each study were different, the standard mean difference (SMD) of different studies and the corresponding 95 % confidence intervals (CIs) were used as the effect size to merge the results. Effect sizes (ES) were classified according to Cohen's d index as small (0.2 ≤ ES < 0.5), medium (0.5 ≤ ES < 0.8) or large (ES ≥ 0.8).²⁹ Second, the collected data is tested with the inconsistency model to check whether there is good consistency between the groups and the local areas. If there is consistency, the consistency model is used for further analysis of the data. Then, the processed data were sorted using surface under the cumulative ranking curve (SUCRA) values³⁰ to obtain the ranking of the effects of various interventions. The SUCRA value refers to the area under the cumulative probability curve of an intervention, with the value ranging from 0 to 100 %. Finally, the funnel plot was drawn to identify whether there was a small sample effect.

3. Result

3.1. Identification and screening of studies

A total of 6006 studies were retrieved. Based on the information in the title and abstract, 148 citations were left to remove duplicates. After removing duplicate citations, 37 studies remained for full-text screening, and two studies were lost because the full text could not be found. Finally, 35 articles were read in full. After full-text screening, 8 studies were excluded because of inconsistent intervention methods, and 8 studies were excluded because of inconsistent outcome indicators (Supplementary: Appendix 2). A total of 19 RCTs were included.^3,9,13,15, 16, 17^,31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43 The detailed study selection process is shown in Fig. 1.

Fig. 1.

PRISMA flow chart for inclusion and exclusion of studies.

3.2. Characteristics of the included studies

After screening and study selection, 19 studies^3,9,13,15, 16, 17^,31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43 were included in the NMA, and all studies are the two-armed study (Fig. 1). Among the studies, comprising 6 in APRE, 11 in VBRT, 3 in RPE, and 17 in PBRT. The full list of selected studies, with the corresponding study details, is displayed in Table 4. Overall, 438 participants were ultimately included for the NMA. The sample size of each study participant ranged from 10 to 57, and the age range was 10–30 years old. Additionally, 11 studies reported the statistical results of training load.

Table 4.

Characteristics of study participants.

Study	Sample	Participants	Age (year)	Years of training (year)	Period (week)	Frequency (number)	Methods		Training Load	Outcome measures
Mann32 (2010)	23	Male collegiate football players	APRE: 20.2 ± 1.0 PBRT: 20.3 ± 1.6	Resistance training: APRE (2.9 ± 0.7) PBRT (2.43 ± 0.7)	6	2	APRE	10RM,6RM,3RM	Not reported	Back squat 1RM, Bench press 1RM
							PBRT	70–85 %1RM
Mann31 (2011)	57	NCAA Division I male football players	APRE: 19.62 PBRT: 19.13	–	6	1	APRE	10RM,6RM,3RM	Not reported	Back squat 1RM, Bench press 1RM
							PBRT	70–85 %1RM
Weber15 (2015)	18	Male collegiate wrestlers	APRE: 20.4 ± 1.6 PBRT: 20 ± 1.1	Resistance training: APRE (9.9 ± 3.4) PBRT (10.3 ± 2.6)	8	–	APRE	10RM	Not reported	Back squat 1RM, Bench press 1RM
							PBRT	85 %1RM
Huang43 (2024)	30	Male and female collegiate taekwondo players	APRE: 19.8 ± 1.2 VBRT: 19.7 ± 1.5	Taekwondo training: ≥3	8	3	APRE	10RM, 6RM, 3RM	Load: VBRT > APRE	Back squat 1RM
							VBRT	70 %1RM (0.48–0.72 m/s) 80 %1RM (0.4–0.6 m/s) 90 %1RM (0.32–0.48 m/s)
Bryce33 (2016)	16	Resistance-trained males	APRE: 21.57 ± 2.87 VBRT: 22.78 ± 2.73	Resistance training: ≥1	6	3	APRE	10RM,6RM,3RM	Load: VBRT ≈ APRE	Back squat 1RM, Bench press 1RM
							VBRT	LVP (MCV≥3 % average of the previous three training, increase loads; MCV≥3 % average of the previous three training, reduce loads)
Dorrell34 (2020)	16	Resistance-trained males	22.8 ± 4.5	Resistance training: ≥2	6	3	VBRT	Back squat: 0.74–0.88 m/s Deadlift: 0.51–0.65 m/s Bench press: 0.58–0.69 m/s	Load: PBRT > VBRT	Back squat 1RM, Bench press 1RM
							PBRT	Back squat: 70 %–95 %1RM Deadlift: 70 %–90 %1RM Bench press: 70 %–92 %1RM;
Orange41 (2020)	27	Academy rugby league players	<18	Resistance training: >2	7	2	VBRT	LVP (velocity±0.06 m/s, load±5 %1RM)	Not reported	Back squat 1RM
							PBRT	80 %1RM, 60 %1RM
Banyard40 (2021)	24	Resistance-trained males	VBRT: 25.5 ± 5 PBRT: 26.2 ± 5.1	Resistance training: >2	6	3	VBRT	0.66–0.88 m/s (velocity±0.06 m/s, load±5 %1RM)	Load: VBRT ≈ PBRT	Back squat 1RM
							PBRT	59 %–85 %1RM
Montalvo-Pérez36 (2021)	17	Female cyclists	26 ± 7	Resistance training: >2	6/2	2	VBRT	OPL: 65 ± 10 %1RM	Load: VBRT ≈ PBRT	Back squat 1RM
							PBRT	80 %–90 %1RM
Fisher37 (2016)	17	NCAA Division II female collegiate softball players	VBRT: 20.00 ± 0.9 PBRT: 20.67 ± 0.9	>2	6	2	VBRT	10 %VL	Load: VBRT ≈ PBRT	Bench press 1RM
							PBRT	55–95 %1RM
Ortega13 (2020)	28	Female and male children soccer players	13.6 ± 1.2	–	12	3	VBRT	0.5 m/s, 20 %VL	Load: PBRT > VBRT	Back squat 1RM
							PBRT	80 %1RM
Peta42 (2019)	10	Resistance-trained males	VBRT: 27 ± 7 PBRT: 31 ± 4	Resistance training: VBRT (7 ± 4) PBRT (5 ± 1)	5	–	VBRT	Squat jump: 2.2–2.4 m/s Back squat: 0.5–0.6 m/s Bench press: 0.5–0.6 m/s	Not reported	Back squat 1RM, Bench press 1RM
							PBRT	Squat jump: 30 %–50 %1RM Back squat: 75 %–87.5 %1RM Bench press: 75 %–87.5 %1RM
Jiménez-Reyes39 (2021)	24	Physically active male sport sciences students	23.1 ± 4.1	Resistance training: >2	8	2	VBRT	0.68–1.13 m/s	Not reported	Back squat 1RM,
							PBRT	50 %–80 %1RM
Zhang3 (2023)	15	Female college basketball player	VBRT: 21.83 ± 0.58 PBRT: 21.7 ± 2.3	Basketball training: >5	6	2	VBRT	65 %–95 %1RM	Intensity VBRT > PBRT	Back squat 1RM, Bench press 1RM
							PBRT	65 %–95 %1RM
He38 (2022)	24	Male college judo players	VBRT: 21.83 ± 0.58 PBRT: 20.17 ± 1.03	VBRT (7.58 ± 2.97) PBRT (5.5 ± 2.02)	8	2	VBRT	75 %1RM±0.06 m/s	Not reported	Back squat 1RM, Bench press 1RM
							PBRT	75 %1RM
Wang35 (2020)	20	Male college basketball players	20.1 ± 0.88	3.20 ± 0.42	8	2	VBRT	75 %1RM±5 %VL	Not reported	Back squat 1RM
							PBRT	75 %1RM
Gomes17 (2020)	20	Resistance-trained males	25.1 ± 3.5	Resistance training: >3	6	2	RPE	CR10 (RPE≤5, progressed; 6 ≤ RPE<9, same; RPE≥9, reduced)	Load: RPE ≈ PBRT	Back squat 1RM
							PBRT	2 sets of 12-15RM, 4 sets of 8-10RM, 6 sets of 4-6RM
Graham9 (2019)	31	Resistance-trained males	PBRT: 28.3 ± 5.6 RIR: 27.9 ± 5.3	Resistance training: >2	12	2	RIR-RPE	Borg's RPE: RIR (Max-4)	Load: RIR-RPE ≈ PBRT	Back squat 1RM
							PBRT	65–95 %1RM
Sinclair16 (2022)	21	male professional rugby league players	18.2 ± 0.9	Resistance training: >3	4	3	RIR	RIR (6), RIR (4), RIR (2), RIR (1)	Load: RIR ≈ PBRT	Bench press 1RM
							PBRT	65 %RM,80 %RM,90 %RM,95 %RM

Note: PBRT-percentage-based resistance training; APRE-autoregulating progressive resistance exercise; VBRT-velocity-based resistance training; RPE-rating of perceived exertion; RIR-repetitions in reserve; VL-velocity loss; LVP-load-velocity profile; OPL-optimum power load; NCAA-National Collegiate Athletic Association; MCV-mean concentric velocity; RM-repetition maximum.

3.3. Risk of bias in the included articles

The Cochrane Risk of Bias assessment tool was utilized to evaluate the quality of the literature included in this meta-analysis. All studies considered in this analysis were RCTs that clearly described their methods for allocation concealment. Among these studies, only one reported the use of blinding for both researchers and participants. Regarding attrition bias, thirteen studies were found to be free of this bias, while one study exhibited a high level of attrition bias, and six studies showed a medium level of attrition bias. Within the scope of this NMA, the body of included studies consisted of fourteen studies identified as having a low risk of bias, four studies with a moderate risk of bias and one study with a high risk of bias, as illustrated in Fig. 2.

Fig. 2.

Risk of bias assessment chart.

3.4. NMA of back squat 1RM

A total of 17 trials assessed the impact of ART on back squat 1RM. Among these, 3 trials examined APRE and PBRT, 10 trials investigated VBRT and PBRT, 2 trials analyzed RPE and PBRT, and 2 trials explored APRE and VBRT (Fig. 3A). Pairwise meta-analyses revealed that the following four comparisons presented small ES: PBRT vs APRE (SMD, −0.55; 95 % CI -0.90 to −0.20), VBRT vs APRE (SMD, −0.40; 95 % CI -0.78 to −0.02), RPE vs PBRT (SMD, 0.45; 95 % CI -0.16∼1.05), and VBRT vs RPE (SMD, −0.30; 95 % CI -0.95 to 0.36). The remaining two comparisons are revealed very small ES: VBRT vs PBRT (SMD, 0.15; 95 % CI -0.14 to −0.44) and RPE vs APRE (SMD, -0.10; 95 % CI -0.80 to 0.60) (Fig. 3B). For all the outcome metrics that form mesh evidence, we did not detect significant inconsistencies, indicating good internal consistency within the network. As node-splitting analysis revealed no significant inconsistency (Supplementary: Appendix 3, Table 1), a NMA based on the consistency model was conducted. According to the cumulative rank probabilities (Fig. 3C), APRE (93.0 %) was most likely to rank best, followed by RPE (66.8 %), VBRT (27.0 %), and PBRT (13.2 %).

Fig. 3.

Network analysis results of back squat 1RM (A: network diagram; B: pairwise meta-analyses; C: cumulative probability plot).

Note: PBRT-percentage-based resistance training; APRE-autoregulating progressive resistance exercise; VBRT-velocity-based resistance training; RPE-rating of perceived exertion.

3.4.1. NMA of bench press 1RM

A total of 10 trials assessed the impact of ART on bench press 1RM. Among these, 3 trials examined APRE and PBRT, 5 trials investigated VBRT and PBRT, 1 trial analyzed RPE and PBRT, and 1 trial explored APRE and VBRT (Fig. 4A). Pairwise meta-analyses revealed that the following one comparison presented large ES: PBRT vs APRE (SMD, −0.83; 95 % CI -1.22 to −0.44); one comparison presented medium ES: RPE vs APRE (SMD, −0.76; 95 % CI -1.7- to 0.19); three comparisons presented small ES: VBRT vs APRE (SMD, −0.48; 95 % CI -0.99 to 0.03), VBRT vs PBRT (SMD, 0.35; 95 % CI -0.04 to −0.73), and VBRT vs RPE (SMD, 0.28; 95 % CI -0.66 to 1.21). The remaining one comparison revealed very small ES: RPE vs PBRT (SMD, 0.07; 95 % CI -0.79∼0.93) (Fig. 4B). For all the outcome metrics that form mesh evidence, we did not detect significant inconsistencies, indicating good internal consistency within the network. As node-splitting analysis revealed no significant inconsistency (Supplementary: Appendix 3, Table 2), a NMA based on the consistency model was conducted. According to the cumulative rank probabilities (Fig. 4C), APRE (97.1 %) was most likely to rank best, followed by VBRT (57.1 %), RPE (29.9 %), and PBRT (15.9 %).

Fig. 4.

Network analysis results of bench press 1RM (A: network diagram; B: pairwise meta-analyses; C: cumulative probability plot).

Note: PBRT-percentage-based resistance training; APRE-autoregulating progressive resistance exercise; VBRT-velocity-based resistance training; RPE-rating of perceived exertion.

3.4.2. Publication bias

Comparing the left and right sides of funnel plot did not reveal large asymmetries, suggesting that publication bias and small study effects may have had a small impact on this study (Fig. 5).

Fig. 5.

Publication bias plots for back squat 1RM (A) and bench press 1RM (B).

Note: PBRT-percentage-based resistance training; APRE-autoregulating progressive resistance exercise; VBRT-velocity-based resistance training; RPE-rating of perceived exertion.

4. Discussion

This study employed a NMA to evaluate the effects of three ARTs on the maximum strength of participants. A total of 19 published studies, comprising 27 RCTs and involving 428 participants, were included in the NMA. Pairwise meta-analyses and NMA were conducted between the back squat 1RM and the bench press 1RM. The results of the pairwise meta-analyses indicated that APRE was more effective than PBRT in improving back squat 1RM. Additionally, the effect on bench press 1RM was found to be superior to the RPE and significantly better than PBRT. The cumulative probability ranking results demonstrated that the effectiveness on back squat 1RM was as follows: APRE > RPE > VBRT > PBRT. For bench press 1RM, the ranking was: APRE > VBRT > RPE > PBRT. Overall, APRE, VBRT, and RPE were shown to enhance maximum strength compared to PBRT.

APRE, VBRT, and RPE are ARTs that involve real-time dynamic adjustments to training loads during each session within a training cycle. APRE is a training method that adapts to an individual's daily physical condition by adjusting the training load (intensity and repetitions) based on completed repetitions.³¹ In APRE, athletes perform the first and second sets according to a predetermined training load. The intensity for the fourth set is then adjusted based on the number of repetitions completed in the third set, which is performed to the point of exhaustion. If the number of repetitions in the third set exceeds the target, the intensity is increased; if not, it is decreased. VBRT is a training method that leverages the strong correlation between movement speed, %1RM, repetitions, and fatigue to formulate, monitor, and adjust training loads.²⁰ VBRT allows for the quantitative and continuous monitoring of strength training intensity by utilizing the relationship between repetition velocity and %1RM.⁴⁴ Additionally, it can manage the fatigue level of each set within a training group by monitoring velocity loss, thereby mitigating the negative effects of excessive fatigue on practitioners and ensuring consistent stimulation levels among individuals. RPE is another training method that employs the linear relationship between perceived effort scores and %1RM⁴⁵ to subjectively assess training load based on the individual's perceived effort level. These three types of ARTs can dynamically adjust the training load based on the athlete's own condition.³ This approach allows the athlete's muscles to achieve optimal neuromuscular adaptation without surpassing the overload threshold, thereby facilitating the development of muscle strength.⁴⁶

The significant improvements in both back squat and bench press 1RM observed with APRE may be attributed to its incorporation of training-to-failure protocols during the third and fourth sets of a single session. The rationale behind training to failure is its ability to maximally recruit motor units.⁴⁷ When performed with moderate-to-high intensity loads, failure training enhances the recruitment of type IIa muscle fibers. From the perspective of functional characteristics, type IIa muscle fibers possess a greater aerobic metabolic capacity and enhanced resistance to fatigue compared to other type II muscle fibers.⁴⁸ This makes them more effective for promoting muscle strength growth and hypertrophy.⁴⁹ From the perspective of training load, only two studies related to APRE among those included reported statistical results regarding training load. One study demonstrated that the training load of VBRT was higher than that of APRE,⁴³ while another study indicated a similar finding.³³ Therefore, it remains unclear whether training load is the primary factor contributing to the development of maximum strength in APRE. Consequently, it is possible that the training mechanism of APRE is more effective in promoting the development of maximum strength.

The core principle of VBRT involves regulating load intensity through predefined target velocity ranges while monitoring fatigue and training volume via velocity loss thresholds.³ In VBRT, training loads and movement velocities are typically maintained within specified intervals, which enhances muscular contractile capacity by increasing the diameter of high-threshold motor units and recruiting a greater number of motor units, thereby promoting maximal strength development.⁵⁰ During VBRT, athletes are required to perform back squat at maximal velocity; if the concentric velocity falls below the predefined range, the session is terminated immediately. However, this protocol results in less sustained neuromuscular stimulation compared to the two sets of failure training in APRE, which may explain its comparatively inferior efficacy in enhancing maximal strength relative to APRE. Furthermore, VBRT modulates training intensity by controlling movement velocity and acceleration, optimizing strength and muscular adaptations.⁵¹ Consequently, VBRT may be more advantageous for improving intermuscular coordination and sport-specific skills,⁵² thereby enhancing an athlete's ability to sustain high-power output over extended durations.

The RPE regulates training load based on participants' subjective perception of fatigue, sharing a similar regulatory framework with VBRT. While VBRT utilizes objective measures of velocity loss to monitor fatigue, RPE depends on the subjective escalation of fatigue as its termination criterion. As a result, training cessation prompted by increased subjective fatigue may limit its effectiveness in developing maximal strength compared to APRE. Graham's study⁹ attributes RPE's superiority over PBRT to its capacity to sustain higher training intensity, a rationale that aligns with one of the mechanisms underlying VBRT's advantage over PBRT. Both RPE and VBRT, which share threshold-based termination principles (i.e., discontinuing training upon reaching predefined subjective or objective thresholds), exhibit inferior efficacy in enhancing maximal strength compared to APRE. Notably, there was no significant difference in the SUCRA scores between the two groups; RPE demonstrated superiority over VBRT in the back squat 1RM, while VBRT outperformed RPE in the bench press 1RM.

In this study, we found that although VBRT and RPE share similar regulatory mechanisms, their effects on the back squat and bench press differ. Specifically, RPE is superior to VBRT in the back squat 1RM, while VBRT outperforms RPE in the bench press1RM. Currently, only one experimental study has directly compared the long-term effects of RPE and VBRT on maximum strength, revealing that VBRT significantly surpassed RPE in enhancing both the back squat 1RM and bench press 1RM.⁸ Since the number of training sets and repetitions per set were matched between the groups in the study, it is speculated that the notable improvement in 1RM strength following VBRT, compared to RPE, was attributable to a higher average perceived effort during training (i.e., greater relative intensity). Previous studies have indicated that perceived effort within a set is often overestimated.⁵³ The inconsistency of the 1RM results for the bench press in this study may be attributed to the indirect comparison methods used and the relatively small number of studies included in the analysis. Furthermore, the inability to effectively extract data hindered the inclusion of the previously mentioned direct comparison study, which affected the overall results.

This systematic review and network meta-analysis have several limitations. First, although only 19 studies met the inclusion criteria, the stringent requirements were essential for establishing a homogeneous network. The network model showed no evidence of heterogeneity or inconsistency, which supports this methodological choice. Second, while the RPE and APRE met the minimum standards for NMA, the relatively small number of studies examining these modalities necessitates cautious interpretation of the findings. Then, the absence of comprehensive outcome measures related to athletic performance (e.g., power output, sport-specific skills) restricts the ability to evaluate the efficacy and differential effects of ART in a holistic manner. Finally, the findings of this study may be limited to the performance of back squats and bench press; therefore, caution should be exercised when generalizing these results to other forms of maximum strength performance.

5. Conclusion

This systematic review and network meta-analysis demonstrates that ART significantly outperforms PBRT in enhancing maximal strength. Among them, APRE demonstrated the highest efficacy, with the back squat and bench press 1RM ranking first, followed by VBRT and RPE. Future research should explore the application of these autoregulated training methods across diverse populations and sport-specific contexts to establish a more robust evidence base for personalized training paradigms.

Ethical statement

None declared. This work does not require ethical approval.

F unding

This study was supported by Shanghai Key Lab of Human Performance（Shanghai University of sport）（NO. 11DZ2261100）

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

The following is the Supplementary data to this article: