Exploring the Dose-Response Relationship Between Estimated Resistance Training Proximity to Failure, Strength Gain, and Muscle Hypertrophy: A Series of Meta-Regressions

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Exploring the Dose-Response
Relationship Between
Estimated Resistance
Training Proximity to
Failure, Strength Gain, and
Muscle Hypertrophy: A
Series of Meta-Regressions
Supplementary materials:
https://osf.io/7knsj/
For correspondence:
zrobinson2019@fau.edu
Zac P. Robinson1, Joshua C. Pelland1, Jacob F. Remmert1,
Martin C. Refalo2, Ivan Jukic3, James Steele4, Michael C. Zourdos1
1 Department of Exercise Science and Health Promotion, Florida Atlantic University
2 Institute for Physical Activity and Nutrition (IPAN), School of Exercise and Nutrition Sciences,
Deakin University, Geelong, VIC, Australia
3 Sport Performance Research Institute New Zealand (SPRINZ), Auckland University
of Technology, Auckland, New Zealand
4 Faculty of Sport, Health, and Social Sciences, Solent University, Southampton, UK
Please cite as: Robinson ZP, Pelland JC, Remmert JF, Refalo MC, Jukic I, Steele J, and Zourdos MC, (2023).
Exploring the Dose-Response Relationship Between Estimated Resistance Training Proximity to Failure,
Strength Gain, and Muscle Hypertrophy: A Series of Meta-Regressions.

1
ABSTRACT
Background:
The proximity to failure in which sets are terminated has gained attention in the
scientific literature as a potentially key resistance training variable. Multiple meta-analyses have
directly (i.e., failure versus not to failure) or indirectly (e.g., velocity loss, alternative set
structures) evaluated the effect of proximity to failure on strength and muscle hypertrophy
outcomes categorically; however, the dose response effects of proximity to failure have not
been analyzed collectively in a continuous manner.
Objective:
To meta-analyze the
aforementioned areas of relevant research, proximity to failure was quantified as the number
of repetitions in reserve (RIR). Importantly, the RIR associated with each effect in the analysis
was estimated based on the available descriptions of the training interventions in each study.
Data were extracted and a series of exploratory multi-level meta-regressions were performed
for outcomes related to both strength and muscle hypertrophy. A range of sensitivity analyses
were also performed. All models were adjusted for the effects of load, method of volume
equating, duration of intervention, and training status.
Results:
The best fit models for both
strength and muscle hypertrophy outcomes demonstrated modest quality of overall fit. In all of
the best-fit models for strength, the confidence intervals of the marginal slopes for estimated
RIR contained a null point estimate, indicating a negligible relationship with strength gains.
However, in all of the best-fit models for muscle hypertrophy, the marginal slopes for
estimated RIR were negative and their confidence intervals did not contain a null point
estimate, indicating that changes in muscle size increased as sets were terminated closer to
failure.
Conclusions:
The dose-response relationship between proximity to failure and strength
gain appears to differ from the relationship with muscle hypertrophy, with only the latter being
meaningfully influenced by RIR. Strength gains were similar across a wide range of RIR, while
muscle hypertrophy improves as sets are terminated closer to failure. Considering the RIR
estimation procedures used, however, the exact relationship between RIR and muscle
hypertrophy and strength remains unclear. Researchers and practitioners should be aware
that optimal proximity to failure may differ between strength and muscle hypertrophy
outcomes, but caution is warranted when interpreting the present analysis due to its
exploratory nature. Future studies deliberately designed to explore the continuous nature of
the dose-response effects of proximity to failure in large samples should be considered.

2
1 INTRODUCTION
It is well established that the configuration of resistance training variables, such as set volume
[1,2], load (percentage of one-repetition maximum (% of 1RM)) [3,4], and frequency [6] can
impact resistance training outcomes. The impact of another variable, proximity to failure,
operationally defined as the number of repetitions in reserve (RIR) prior to momentary failure
(i.e., the inability to complete the concentric phase of a repetition despite maximal effort to do
so) following set termination has gained recent attention in the scientific literature [7,8].
Despite the recent attention on this topic, the specific proximity to failure that maximizes
various resistance training outcomes (i.e., muscular hypertrophy and strength gain) remains
unclear. Indeed, recent meta-analyses from Grgic et al. [9] and Vieira et al. [10] reported no
significant difference for muscle hypertrophy [SMD: 0.15 (p = 0.237); SMD: 0.59 (p = 0.239)],
and strength gain [SMD: 0.01 (p = 0.860); SMD: 0.16 (p = 0.566)] when comparing volume-
equated resistance training interventions in which sets were performed to or not to failure.
Moreover, meta-analyses from Jukic et al. [11] and Davies et al. [12] show equivocal outcomes
for muscle hypertrophy [SMD: -0.03 (p = 0.708); SMD: -0.05 (p = 0.73)] and strength gain [SMD:
-0.06 (p = 0.291); SMD: -0.05 (p = 0.56)] when comparing the effects of traditional and
alternative set structures; which alter proximity to failure via the manipulation of intra-set rest
intervals [13].
Although the data from these meta-analyses [9–12] provide valuable insight into the influence
of proximity to failure on resistance training outcomes, they investigate proximity to failure in a
categorical (e.g., to failure versus not to failure; traditional versus alternative set structures)
fashion despite its continuous nature. This is primarily due to the uncertainty of the proximity
to failure achieved across relevant studies; for example, it is difficult to know the RIR upon set
termination in non-failure groups due to a lack of reporting, individual differences, and set-to-
set fatiuge. Additionally, there is ambiguity in the criteria for set termination [14] in failure
groups, further limiting the applicability of these categorical comparisons. Fisher et al. [15]
recently suggested investigating proximity to failure in a categorical fashion fails to inform the
overall dose-response relationship between proximity to failure and resistance training
outcomes. In other words, previous meta-analyses [9–12] have not attempted to ascertain the
relationship between the number of RIR per set with muscle hypertrophy and strength gain,
which limits the ability to make practical recommendations regarding proximity to failure.
Specifically, if proximity to failure in resistance training is only examined in a categorical

3
fashion, it cannot answer the question “how far from failure should someone train to optimize
muscle hypertrophy and strength gain?”. To our knowledge, no meta-analysis to date has
examined proximity to failure as a continuous variable on muscle hypertrophy and strength
gain.
The most commonly used method that aims to rectify the limitations of categorically examining
proximity to failure is intra-set velocity loss (VL). Intraset VL controls for proximity to failure by
prescribing set termination once the concentric velocity of a repetition has declined by a
predetermined percentage from a set’s fastest (usually first) repetition (e.g., 70% of 1RM to
20%VL). In this way, higher VL thresholds terminate sets closer to failure, while lower VL
thresholds terminate sets with a greater number of RIR. Recent meta-analyses [16–20], have
indeed included meta-regressions examining the dose-response relationship between intra-
set VL and various resistance training outcomes. However, while different VL thresholds lead to
a different number of RIR, this method of set termination does not control for the number of
repetitions performed in a set or the relative volume (repetitions x sets x % of 1RM) [21,22],
which limits conclusions that can be made since training volume is related to muscle
hypertrophy and strength gain [1,2]. For example, Pareja-Blanco et al. [23] compared the
effects of training the Smith-machine squat to either a 20% or 40% VL threshold for eight
weeks with the total number of sets and load equated. These intra-set VL thresholds resulted
in the 20% and 40% groups training at an average mean propulsive velocity of 0.69 and 0.58
m·s-1, respectively, suggesting the groups trained at different proximities to failure. However,
the 40% VL group performed an average of 40% more repetitions throughout the study (40%
VL: 310.5 ± 42 vs. 20% VL: 185.9 ± 22.2 repetitions); thus, the relative volume load was not
equated. Studies exist [24,25] that have compared different VL thresholds and controlled for
relative volume load but have only been included in one meta-analysis to date [16].
Therefore, this exploratory meta-analysis aimed to investigate the effect of resistance training
proximity to failure on muscle hypertrophy and maximal strength gain by combining all of the
aforementioned areas of research. To best investigate the effect of proximity to failure
continuously and explore potential dose-response relationships, RIR was estimated for the
training intervention associated with each effect.

4
2 METHODS
This exploratory meta-analysis was performed without a systematic search and was not
preregistered. First, all studies from the existing relevant meta-analyses [9–12,16–20] were
collected. Then, any additional studies we were aware of, or were discovered during data
extraction, that met the inclusion criteria were also collected. To be included in this meta-
analysis, studies had to: (1) be published in English and either published in a peer-reviewed
journal, on a pre-print repository, or as a MSc or PhD thesis; (2) ensure participants had no
known medical conditions or injuries; (3) include either set and/or repetition volume-equated
conditions; (4) include load-equated conditions (i.e., ± 5% of 1RM); (5) compare at least two
different proximities to failure; (6) include measurement(s) of maximal strength (i.e., isometric,
isotonic, or isokinetic) and/or direct measurements of muscle hypertrophy (i.e., ultrasound,
magnetic resonance imaging [MRI], etc.). Studies that were initially gathered but did not meet
these inclusion criteria were excluded. This process was performed by ZR.
Data describing the population studied, specifications of the training intervention, and the
outcomes of interest (e.g., muscle hypertrophy and strength) were extracted from studies
found to be eligible. In the case that any necessary data were not reported, ZR emailed the
authors of the manuscripts requesting the raw or mean values. If the authors did not reply
within three months, we resorted to calculating the desired data based on the figures and
tables (data was digitized using WebPlotDigitizer; v4.3, Ankit Rohatgi;
https://apps.automeris.io/wpd/).
RIR Estimation
To operationally define proximity to failure as a continuous variable, the primary predictor in
this meta-analysis was the estimated RIR to which training was performed by each group.
Because self-reported RIR was not reported in almost all studies, specific procedures were
followed to estimate RIR for every group included in the analysis. A detailed breakdown of the
estimation of each study included in the analysis and all estimation equations utilized can be
found in supplementary file 1 (https://osf.io/dwbx3). All initial estimations were performed by
ZR, and these estimations were subsequently verified by JP, MZ, MR, and IJ. All conflicting
predictions were due to manual error and were resolved upon re-estimation. The estimation
process categorized studies into one of the following five subgroups: 1) groups training to

5
failure, 2) groups reporting velocity, 3) groups reporting RIR, 4) groups reporting load and
repetitions performed, and 5) groups training with alternative set structures.
Groups Training to Failure
The first category of studies consisted of those that included a group training to failure [26–
53]. Groups that trained to failure were estimated, by definition, to have trained to 0 RIR.
However, due to the ambiguity of the terminology utilized to describe “failure” [7], studies that
provided a clear definition (e.g., momentary failure, concentric failure, etc.) and did not indicate
participants terminated sets upon their own volition (i.e., volitional failure) were separately
coded with an RIR of “-1” for the linear-spline meta-regression model to potentially tease out
differences associated with failure definition. All other groups with RIR estimates of 0, including
volitional failure, were coded as “0.”
In studies that included a group training to failure, if a group did not train to failure but
performed sets at an equivalent load, subtraction of the repetitions performed per set was
used to estimate RIR. For example, if the group training to failure (i.e., 0 RIR) performed 10
repetitions with 75% of 1RM and the group not training to failure performed 5 repetitions with
75% of 1RM, the number of RIR was estimated to be 5. This was also applied for groups
training with a repetition maximum (e.g., 10RM). For example, if a group performed sets of 8
repetitions with a 10RM load, then the estimated RIR was 2.
Groups Reporting Velocity
The second category of studies reported velocity data that allowed for RIR estimations [23–
25,54–66]. Utilizing the most representative citations available [67–70], equations were utilized
or created to predict the maximum possible number of repetitions at a given load based on
the repetitions performed and the intra-set VL. These equations were matched by exercise,
loading range, training status, sex, and concentric intended velocity as closely as possible. After
the maximum possible number of repetitions was estimated, subtraction could be performed
from the repetitions per set provided.
For example, Pareja-Blanco and colleagues [23] reported a mean velocity loss of 41.9 ± 1.9% in
the VL40 group. Using the reported average number of repetitions per set (6.5 ± 0.9) and load
used (75% of 1RM), the maximum possible number of repetitions was predicted using the
regression equations for the Smith-machine squat published by Rodriguez-Rosell et al. [67].

6
Specifically, at 70% of 1RM, the predicted maximum possible number of repetitions was 8.31.
When subtracting the average number of repetitions performed per set reported by Pareja-
Blanco et al. [23], the estimated RIR was 1.81. However, because the average load reported
was 75% of 1RM, we averaged the estimated RIR created from the equations for 70% and 80%
of 1RM from Rodriguez-Rosell [67], resulting in the final estimated RIR for the VL40 group of
1.67. The prediction equations that were used for each velocity loss study can be found in
supplementary file 1 (https://osf.io/dwbx3).
Groups Reporting RIR
The third category of studies directly reported RIR, and these values were utilized verbatim for
the RIR estimations [38,71–73]. For example, if a group reported the average RIR throughout
the study was 2.3, the estimated RIR was also 2.3. If a study reported RIR but also fell into one
of the two prior categories (i.e., training to failure or provided velocity data), the other method
was used to predict RIR due to its objectivity.
Groups Reporting Load and Repetitions Performed
The next category of studies reported the load and repetitions performed from which RIR
estimations were derived [29,30,74–80]. Once again, prediction equations were utilized from
the most representative citations available [67–69,81–83] to establish the maximum possible
number of repetitions at a given load, to which subtraction of the repetitions performed per
set could estimate RIR. These equations were matched by exercise, loading range, training
status, sex, and concentric intended velocity as closely as possible. For example, Carneiro et al.
[78] had untrained women perform sets of 4 repetitions at 90% of 1RM on the bilateral knee
extension. Using the prediction equation created from the data of Hoeger et al. [84], it was
estimated that approximately 4.65 repetitions are possible at 90% of 1RM. Thus, subtracting 4
repetitions per set from that estimation led to an estimated RIR of 0.65.
Alternatively, some studies reported load as a percentage of a repetition maximum (RM) other
than a 1RM. In this case, the load relative to a 1RM (i.e., % of 1RM), was first predicted. Next,
utilizing the predicted percentage of 1RM, the same steps could be followed as previously
outlined. For example, Drinkwater and colleagues [74] had trained men perform sets of bench
press with percentages of 6RM loads. Therefore, using the prediction equation from Chapman
et al. [69] the percentage of 1RM associated with 100% of 6RM was predicted, which equated
to 89% of 1RM. Then, the percentages of this value used in Drinkwater et al. [74] were applied

7
to calculate the load per set (e.g., 70% of 89% (6RM) = 62.3% of 1RM). The same steps outlined
in the previous paragraph were then followed to predict the maximum possible repetitions at
the given load. Finally, the number of repetitions performed per set was subtracted from the
predicted maximum possible number of repetitions to estimate RIR.
Groups Training with Alternative Set Structures
For groups training with alternative set structures [27,29–32,34,36,39,41,42,51,65,66,74–
80,85], a determination needed to be made as to what constitutes a “set” from which proximity
to failure could be evaluated. We decided to treat each group of repetitions performed with
any intra-set or inter-set rest between them as an individual set. For rest-pause groups, each
of these sets was performed to failure, making the RIR estimation simple (i.e., 0 RIR) [77]. For
cluster and rest redistribution groups, this RIR estimation method was chosen because of
these set structures’ ability to maintain repetition performance, and thus RIR, compared to
traditional set structures.
For example, Iglesias-Soler et al. [86] compared the total number of repetitions performed with
a 4RM load on the Smith-machine squat between traditional and cluster set structures in a
crossover design. The traditional set condition performed 3 sets to failure, whereas the cluster
set condition performed as many repetitions as possible with an individualized inter-repetition
rest period (i.e., single-repetition sets). The authors observed that participants were able to
increase the total number of repetitions performed by approximately 5-fold with a cluster set
structure (Cluster: 45.5 ± 32 repetitions; Traditional: 9.33 ± 1.87 repetitions), indicating RIR was
likely maintained for many of the early repetitions. Due to this evidence, along with variability in
the initial proximity to failure of each set, intra- and inter-set rest intervals, the load used, sex
of the participants, and exercise selection, we determined this estimating RIR for cluster and
rest redistribution groups in this manner to be the best course of action.
To illustrate, Farinas et al. [41] investigated the effects of set structure within a unilateral knee
extension training program. Participants in the traditional group performed 4 sets of 8
repetitions with a 10RM load and 3-minute inter-set rest periods. Using an equivalent load (i.e.,
10RM), the alternative set structure group instead performed 1 repetition every 17.4 seconds
until 32 total repetitions were completed. The estimated RIR for each group was calculated by
subtracting the number of repetitions performed in each single-repetition set from the

8
maximum possible number of repetitions. Thus, the RIR estimation for the traditional group
would be 2 and the alternative set structure group would be 9.
Special Cases
Throughout the estimation process, special case rules were applied to a few groups.
Specifically, in these cases, even though a group fell into one of the aforementioned categories,
the estimation approach led to subjectively implausible RIR values. These alternative
approaches are outlined in supplementary file 1 (https://osf.io/dwbx3).
Additional Details
For each group in the analysis, the estimated RIR was used to represent the average proximity
to failure at which sets were terminated. Specifically, averages were developed for both the
“muscle” and the “exercise.” For the “muscle” RIR, if a study included multiple exercises, those
that primarily trained the muscle site measured or were prime movers in the exercise or joint
action tested counted towards the estimation. For example, if a lower body training program
included the barbell back squat, knee extension machine, and knee flexion machine, only the
RIR estimations of the barbell back squat and knee extension machine would be averaged for
quadriceps specific outcomes (i.e., strength or muscle hypertrophy). Alternatively, for the
“exercise” RIR, only sets performed on the same exercise that was tested were counted
towards the estimation; thus, this is only relevant for dynamic strength outcomes. For example,
in the same lower body training program that included the barbell back squat, knee extension
machine, and knee flexion machine, only the RIR estimations of the barbell back squat would
be used for the exercise RIR. When applicable, the RIR estimations of multiple sets performed
by a single group were averaged for the final estimation. Finally, if a RIR estimate was negative,
it was recorded as “0.”
3 STATISTICAL ANALYSIS
This exploratory meta-analysis was performed using the ‘metafor’ package [87] in R language
and environment for statistical computing (v 4.0.2; R Core Team, https://www.r-project.org/).
The extracted dataset, analysis scripts, models summaries, and supplementary materials are
available on the Open Science Framework (https://osf.io/7knsj/). Given the goal of this analysis,
we have opted to avoid dichotomizing our findings and therefore did not employ traditional
null hypothesis significance testing [88]. Rather, we took an estimation-based approach in

9
which effect estimates and their precision were interpreted cautiously and probabilistically
[89]. As the included studies had multiple groups and reported effects within these groups for
multiple outcomes, we opted to calculate effect sizes in a nested structure. Therefore, multi-
level mixed-effects models [90] with cluster-robust variance estimation [91] were performed
with study, group, and observation included as explicitly nested random intercepts in the
model (i.e., observations were nested within groups which were nested within studies).
Moreover, a range of models were fit and compared including with (1) random intercepts only,
(2) the addition of a single random slope for estimated RIR on the study level, (3) the addition
of random slopes for estimated RIR on the study and group level to account for potential
heterogeneity in the relationship of estimated RIR on these levels. Effects were weighted by
inverse sampling variance to account for the observation-level, within-study, and between-
study variance. Models were constructed with effect sizes, and variances thereof, calculated as
both standardized mean change and response ratio using the ‘escalc’ function [92,93].
Specifically, standardized mean changes were calculated as the difference between post-test
and pre-test means, divided by the pre-test standard deviation with an adjustment (i.e., C) for a
small sample bias. In addition, response ratios were calculated as the sum of the natural
logarithm of the ratio of post-test and pre-test means and an adjustment for small sample bias
(i.e,. C), which were later exponentiated (i.e., ex) and thereby converted to percentage change
scores to aid practical interpretation. Formulas for each effect size and their variances can be
seen below:
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No studies reported the pre-intervention to post-intervention correlations required to
determine the variance. Therefore, the available data were used to retroactively calculate pre-
to-post correlations if possible [94]. Then, we meta-analyzed these approximated correlation
coefficients (i.e., Fishers r-to-z transformed correlation coefficient) and imputed this estimate
for the studies where we were unable to obtain the required data. Since all meta-analytic
models included moderators, statistical heterogeneity was evaluated using I2, which
represents the remaining variance that is not already accounted for by the moderators [95].
This heterogeneity was then partitioned across the three levels of the nested random effects
(i.e., study, group, and observation). Additionally, marginal and conditional R2 were calculated
to quantify the proportion of variance explained by only the fixed effects and the sum of the
fixed and random effects, respectively [96]. Both I2 and R2 were calculated using the ‘orchaRd’
package for multi-level models [97]. To account for potential non-linear dose-response
relationships between proximity to failure and resistance training outcomes the following
functional forms for all model structures described above were fit and subsequently compared
using the ‘bayestestR’ package [98], utilizing BIC approximated Bayes factors to determine
under which model the observed data are the most probable for each outcome (i.e., strength
and muscle hypertrophy):
1) Linear
2) Linear Spline (knot at 0 RIR)
3) Linear-log
4) Quadratic
5) Cubic
6) Restricted Cubic Spline (4 knots at 5, 35, 65, and 95% quantiles)
All models included the following fixed effects: 1) Estimated RIR, 2) Load per set, 3) Method of
volume equating (set, repetition, or both), 4) Duration (i.e., weeks) of the training intervention
(continuous), and 5) Training status of the participants (binary categorical). Estimated marginal
means (and their slopes) with 95% compatibility intervals (confidence and prediction) were
extracted for the main effect of RIR (adjusted proportionally for all other predictors) using the
‘emmeans’ package [99]. For RIR, estimates were extracted at 0 to 23 RIR to represent the range
of values observed in the dataset.

11
Following the determination of the best fit models for each outcome (i.e., strength or muscle
hypertrophy) and effect size (i.e., SMC or RR), interaction moderator analyses were performed
to evaluate the influence of a variety of factors related to study design and participant
characteristics (supplementary file 2: https://osf.io/3tcwx). Specifically, separate models were fit
for each moderator that maintained the same structure as the best fit models from the main
analysis, but also included main effects and an interaction term between estimated RIR and the
moderator of interest. Finally, after inspecting the data, it appeared that some studies with very
high RIR estimations may have been disproportionately influencing the models. Thus, a
sensitivity analysis was performed where all models were refit only with effect sizes from
groups that were estimated to train with less than or equal to 10 RIR.
4 RESULTS
Study Characteristics
A breakdown of all 55 studies included in this analysis can be found in supplementary file 0
(https://osf.io/wpx92). On average, training interventions lasted 8.28 ± 2.35 weeks and
participants were 27.83 ± 12.84 years old. A visual summary of the training interventions from
the included studies can be seen in Figure 1. Additionally, tables summarizing study
characteristics can be seen in supplementary file 2 (https://osf.io/3tcwx). The most frequently
occurring (i.e., mode) values of the primary training variables for effects included in the
strength models were: volume- 6 sets per week; load- 75% of 1RM; and frequency- 2 sessions
per week. The average values for these metrics were 9.58 ± 4.48 sets per week, 72.06 ±
13.27% of 1RM, and 2.23 ± 0.48 sessions per week. For the effects in the muscle hypertrophy
models, the most frequently occurring values were 6 sets per week, 85% of 1RM, and 2
sessions per week. The average values for these metrics were 9.69 ± 4.61 sets per week, 72.27
± 14.53% of 1RM, and 2.08 ±0.39 sessions per week.

12
Figure 1
: Visual summary of training interventions included in the analysis. Data are presented as raincloud plots with each data point
representing an effect. Direct adjusted sets per week per muscle group = Number of direct sets performed per week per muscle group while
alternative set structure groups were adjusted to the same number of sets as the traditional set structure group in the same study.
Primary Analysis
The following sections will present the results of all meta-regression models. Specifically, for
each model, we will evaluate the overall quality of model fit (i.e., R2 and I2) and the marginal
slope for the main effect of estimated RIR (i.e., the slope at the mean of RIR after adjusting for
load, method of volume equating, intervention duration, and training status). Full model
summary tables, comparisons thereof, and all extracted estimates are located at
https://osf.io/7knsj/.
Strength Outcomes
The multi-level meta-regression models for strength included 243 total effects from 55 studies.
Model comparisons revealed that the linear-log model was the best fit with effects as a
standardized mean change (Figure 2). The fixed effects of the model explained less than a
quarter of the total variance (
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of remaining variance occurring at the study level (
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21.17%). The marginal slope of estimated RIR was positive but contained a null point estimate
Hypertrophy Strength
0 4 8 12 16 20 24 28 32
Direct Adjusted Sets Per Week Per Muscle Group
Density
30 40 50 60 70 80 90
Load (% of 1RM) Per Set
123
Direct Frequency (Sessions Per Week Per Muscle Group)
Visual Summaries of Training Interventions Included in Meta−regression Models

13
within the confidence interval (
?
= 0.003 [95% CI: -0.012, 0.018; 95% PI: -0.675, 0.682]). The
slope indicates that strength gains improve negligibly as sets are terminated farther from
failure.
Figure 2
: Best fit (linear-log) multi-level meta-regression for maximal strength outcomes analyzed as a standardized mean change. Data
are presented as estimated marginal means (solid line) with 95% compatibility intervals (dark band = confidence, light band = prediction)
after adjusting for load, method of volume equating, intervention duration, and training status of the participants. Colored circles
represent the effect size of each observation included in the analysis, with the size of each circle representing its weight determined by
inverse variance weighting. The main effect for estimated RIR is presented at the mean of continuous fixed effects (i.e., load and intervention
duration) and proportionally marginalized across categorical fixed effects (i.e., method of volume equating and training status).
Model comparisons revealed that the linear model was the best fit with effects as a response
ratio (Figure 3). The fixed effects of the model explained less than a third of the total variance
(
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occurring at the observation level (
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0.0
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Estimated Proximity to Failure (RIR)
Standardized Mean Change in Strength (Hedge's g)
Marginal Effects from Linear−log Multilevel Model for Maximal Strength (Standardized Mean Change)

14
confidence interval (
?
= -0.059 [95% CI: -0.304, 0.186; 95% PI: -12.944, 14.732]). The slope
indicates that strength gains decrease negligibly as sets are terminated farther from failure.
Figure 3
: Best fit (linear) multi-level meta-regression for maximal strength outcomes analyzed as an exponentiated response ratio. Data
are presented as estimated marginal means (solid line) with 95% compatibility intervals (dark band = confidence, light band = prediction)
after adjusting for load, method of volume equating, intervention duration, and training status of the participants. Colored circles
represent the effect size of each observation included in the analysis, with the size of each circle representing its weight determined by
inverse variance weighting. The main effect for estimated RIR is presented at the mean of continuous fixed effects (i.e., load and intervention
duration) and proportionally marginalized across categorical fixed effects (i.e., method of volume equating and training status).
Muscle Hypertrophy Outcomes
The multi-level meta-regression models for muscle hypertrophy included 140 total effects from
26 studies. Model comparisons revealed that the linear model was the best fit with effects as a
standardized mean change (Figure 4). The fixed effects of the model explained less than a
quarter of the total variance (
5*+%,-.+/
'
= 19.2%;
50".1-$-".+/
'
= 72.09%) with the primary source
of remaining variance occurring at the study level (
>#$213
'
= 55.57%;
>,%"2!
'
= 2.29%;
>"4#&%5+$-".
'
=
30.53%). The marginal slope of estimated RIR was negative and did not contain a null point
0
10
20
30
40
50
60
0 2 4 6 8 10 12 14 16 18 20 22
Estimated Proximity to Failure (RIR)
Exponentiated Response Ratio for Muscle Size (% Change)
Marginal Effect from Linear Multilevel Model for Maximal Strength (Response Ratio)

15
estimate within the confidence interval (
?
= -0.019 [95% CI: -0.035, -0.004; 95% PI: -0.551,
0.513]). The slope indicates that muscle hypertrophy improves as sets are terminated closer to
failure.
Figure 4
: Best fit (linear) multi-level meta-regression for muscle hypertrophy outcomes analyzed as a standardized mean change. Data are
presented as estimated marginal means (solid line) with 95% compatibility intervals (dark band = confidence, light band = prediction) after
adjusting for load, method of volume equating, intervention duration, and training status of the participants. Colored circles represent the
effect size of each observation included in the analysis, with the size of each circle representing its weight determined by inverse variance
weighting. The main effect for estimated RIR is presented at the mean of continuous fixed effects (i.e., load and intervention duration) and
proportionally marginalized across categorical fixed effects (i.e., method of volume equating and training status).
Model comparisons revealed that the linear model was the best fit with effects as a response
ratio (Figure 5). The fixed effects of the model explained less than a third of the total variance
(
5*+%,-.+/
'
= 26.38%;
50".1-$-".+/
'
= 63.24%) with the primary source of remaining variance
occurring at the observation level (
>#$213
'
= 38.65%;
>,%"2!
'
= 5.84%;
>"4#&%5+$-".
'
= 44.35%). The
marginal slope of estimated RIR was negative and did not contain a null point estimate within
−0.75
−0.50
−0.25
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
0 2 4 6 8 10 12 14 16 18 20 22
Estimated Proximity to Failure (RIR)
Standardized Mean Change in Muscle Size (Hedge's g)
Marginal Effects from Linear Multilevel Model for Muscle Hypertrophy (Standardized Mean Change)

16
the confidence interval (
?
= -0.48 [95% CI: -0.78, -0.179; 95% PI: -9.811, 9.817]). The slope
indicates that muscle hypertrophy improves as sets are terminated closer to failure.
Figure 5
: Best fit (linear) multi-level meta-regression for muscle hypertrophy outcomes analyzed as an exponentiated response ratio. Data
are presented as estimated marginal means (solid line) with 95% compatibility intervals (dark band = confidence, light band = prediction)
after adjusting for load, method of volume equating, intervention duration, and training status of the participants. Colored circles
represent the effect size of each observation included in the analysis, with the size of each circle representing its weight determined by
inverse variance weighting. The main effect for estimated RIR is presented at the mean of continuous fixed effects (i.e., load and intervention
duration) and proportionally marginalized across categorical fixed effects (i.e., method of volume equating and training status).
Sensitivity Analyses
Strength Outcomes
Upon refitting the multi-level meta-regression models for strength only with the effects with an
RIR estimate of <10, they included 232 total effects from 54 studies. Model comparisons
revealed that the linear-log model was the best fit with effects as a standardized mean change
−20
−15
−10
−5
0
5
10
15
20
25
0 2 4 6 8 10 12 14 16 18 20 22
Estimated Proximity to Failure (RIR)
Exponentiated Response Ratio for Muscle Size (% Change)
Marginal Effects from Linear Multilevel Model for Muscle Hypertrophy (Response Ratio)

17
(Figure 6). The fixed effects of the model explained less than a quarter of the total variance
(
5*+%,-.+/
'
= 12.68%;
50".1-$-".+/
'
= 75.81%) with the primary source of remaining variance
occurring at the study level (
>#$213
'
= 51.63%;
>,%"2!
'
= 11.03%;
>"4#&%5+$-".
'
= 24.01%). The marginal
slope of estimated RIR was positive but contained a null point estimate within the confidence
interval (
?
= 0.004 [95% CI: -0.014, 0.022; 95% PI: -0.658, 0.666]). The slope indicates that
strength gains improve negligibly as sets are terminated farther from failure.
Figure 6
: Best fit (linear-log) multi-level meta-regression for maximal strength outcomes analyzed as a standardized mean change after
effects with >10 estimated RIR were removed. Data are presented as estimated marginal means (solid line) with 95% compatibility intervals
(dark band = confidence, light band = prediction) after adjusting for load, method of volume equating, intervention duration, and training
status of the participants. Colored circles represent the effect size of each observation included in the analysis, with the size of each circle
representing its weight determined by inverse variance weighting. The main effect for estimated RIR is presented at the mean of continuous
fixed effects (i.e., load and intervention duration) and proportionally marginalized across categorical fixed effects (i.e., method of volume
equating and training status).
Model comparisons revealed that the linear model was the best fit with effects as a response
ratio (Figure 7). The fixed effects of the model explained less than a third of the total variance
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 2 4 6 8 10
Estimated Proximity to Failure (RIR)
Standardized Mean Change in Strength (Hedge's g)
Marginal Effects from Linear−log Multilevel Model for Maximal Strength with <10 RIR (Standardized Mean Change)

18
(
5*+%,-.+/
'
= 29.15%;
50".1-$-".+/
'
= 57.69%) with the primary source of remaining variance
occurring at the observation level (
>#$213
'
= 34.55%;
>,%"2!
'
= 3.13%;
>"4#&%5+$-".
'
= 55.87%). The
marginal slope of estimated RIR was positive but contained a null point estimate within the
confidence interval (
?
= -0.011 [95% CI: -0.411, 0.39; 95% PI: -13.085, 15.029]). The slope
indicates that strength gains increase negligibly as sets are terminated farther from failure.
Figure 7
: Best fit (linear) multi-level meta-regression for maximal strength outcomes analyzed as an exponentiated response ratio after
effects with >10 estimated RIR were removed. Data are presented as estimated marginal means (solid line) with 95% compatibility intervals
(dark band = confidence, light band = prediction) after adjusting for load, method of volume equating, intervention duration, and training
status of the participants. Colored circles represent the effect size of each observation included in the analysis, with the size of each circle
representing its weight determined by inverse variance weighting. The main effect for estimated RIR is presented at the mean of continuous
fixed effects (i.e., load and intervention duration) and proportionally marginalized across categorical fixed effects (i.e., method of volume
equating and training status).
Finally, upon refitting all models with the RIR and load per set of the specific exercise evaluated
as a dynamic strength outcome, a linear-log model was the best fit, regardless of effect size. All
estimates were similar to the primary and secondary models.
0
10
20
30
40
50
60
0246810
Estimated Proximity to Failure (RIR)
Exponentiated Response Ratio for Muscle Size (% Change)
Marginal Effects from Linear Multilevel Model for Maximal Strength with <10 RIR (Response Ratio)

19
Muscle Hypertrophy Outcomes
Upon refitting the multi-level meta-regression models for muscle hypertrophy only with the
effects with an RIR estimate of <10, they included 137 total effects from 26 studies. Model
comparisons revealed that the linear model was the best fit with effects as a standardized
mean change (Figure 8). The fixed effects of the model explained less than a quarter of the
total variance (
5*+%,-.+/
'
= 18.65%;
50".1-$-".+/
'
= 73.3%) with the primary source of remaining
variance occurring at the study level (
>#$213
'
= 57.55%;
>,%"2!
'
= 2.31%;
>"4#&%5+$-".
'
= 29.25%). The
marginal slope of estimated RIR was negative and did not contain a null point estimate within
the confidence interval (
?
= -0.023 [95% CI: -0.042, -0.004; 95% PI: -0.572, 0.526]). The slope
indicates that muscle hypertrophy improves as sets are terminated closer to failure.
Figure 8
: Best fit (linear) multi-level meta-regression for muscle hypertrophy outcomes analyzed as a standardized mean change after
effects with >10 estimated RIR were removed. Data are presented as estimated marginal means (solid line) with 95% compatibility intervals
(dark band = confidence, light band = prediction) after adjusting for load, method of volume equating, intervention duration, and training
status of the participants. Colored circles represent the effect size of each observation included in the analysis, with the size of each circle
representing its weight determined by inverse variance weighting. The main effect for estimated RIR is presented at the mean of continuous
−0.25
0.00
0.25
0.50
0.75
1.00
1.25
1.50
0 2 4 6 8 10
Estimated Proximity to Failure (RIR)
Standardized Mean Change in Muscle Size (Hedge's g)
Marginal Effects from Linear Multilevel Model for Muscle Hypertrophy with <10 RIR (Standardized Mean Change)

20
fixed effects (i.e., load and intervention duration) and proportionally marginalized across categorical fixed effects (i.e., method of volume
equating and training status).
Model comparisons revealed that the linear model was the best fit with effects as a
standardized mean change (Figure 9). The fixed effects of the model explained less than a third
of the total variance (
5*+%,-.+/
'
= 25.52%;
50".1-$-".+/
'
= 64%) with the primary source of
remaining variance occurring at the observation level (
>#$213
'
= 39.71%;
>,%"2!
'
= 6.48%;
>"4#&%5+$-".
'
= 43.22%). The marginal slope of estimated RIR was negative and did not contain a
null point estimate within the confidence interval (
?
= -0.544 [95% CI: -0.929, -0.158; 95% PI: -
10.074, 9.996]). The slope indicates that muscle hypertrophy improves as sets are terminated
closer to failure.
Figure 9
: Best fit (linear) multi-level meta-regression for muscle hypertrophy outcomes analyzed as an exponentiated response ratio after
effects with >10 estimated RIR were removed. Data are presented as estimated marginal means (solid line) with 95% compatibility intervals
(dark band = confidence, light band = prediction) after adjusting for load, method of volume equating, intervention duration, and training
status of the participants. Colored circles represent the effect size of each observation included in the analysis, with the size of each circle
representing its weight determined by inverse variance weighting. The main effect for estimated RIR is presented at the mean of continuous
−20
−15
−10
−5
0
5
10
15
20
25
0246810
Estimated Proximity to Failure (RIR)
Exponentiated Response Ratio for Muscle Size (% Change)
Marginal Effects from Linear Multilevel Model for Muscle Hypertrophy with <10 RIR (Response Ratio)

21
fixed effects (i.e., load and intervention duration) and proportionally marginalized across categorical fixed effects (i.e., method of volume
equating and training status).
Interacting Moderators
The following sections will present the results of the interaction moderator analyses. We
evaluated the interaction contrasts of the two-way interactions between estimated RIR and the
moderators of interest. Specifically, we will identify moderators that alter the qualitative
inference of the relationship between estimated RIR and the outcome variable (i.e.,
directionality, magnitude, and uncertainty). These analyses should be cautiously interpreted, as
the number of observations that contribute to the effects could be substantially reduced when
compared to the main models, thereby reducing the precision of the estimates. Data
visualization from all interaction moderator analyses are located at https://osf.io/7knsj/.
Strength Outcomes
For strength outcomes, interacting moderators were identified that altered the qualitative
inference. When effects were analyzed as a standardized mean change in the primary analysis,
upper body outcomes (n=104) demonstrated a more positive slope than lower body outcomes
(n=139). Additionally, training programs that used multi-joint exercises (n=150) demonstrated a
more positive slope than programs that included both multi- and single-joint exercises (n=27).
In the sensitivity analysis of the effects with an RIR estimate of <10, training programs that used
multi-joint exercises (n=150) demonstrated a more positive slope than programs that included
both multi- and single-joint exercises (n=27).
When effects were analyzed as a response ratio in the primary analysis, training programs that
used multi-joint exercises (n=150) demonstrated a more positive slope than programs that
included both multi- and single-joint exercises (n=27). In the sensitivity analysis of the effects
with an RIR estimate of <10, training programs that used multi-joint exercises (n=150)
demonstrated a more positive slope than programs that included both multi- and single-joint
exercises (n=27). Within-participant designs (n=32) also demonstrated a more positive slope
than between-participant designs (n=211).

22
Muscle Hypertrophy Outcomes
For hypertrophy outcomes, interacting moderators were identified that altered the qualitative
inference. When effects were analyzed as a standardized mean change in the primary analysis,
training programs that did not employ progressive overload (n=5) exhibited a positive slope
while those that included progressive overload (n=135) exhibited a negative slope. In the
sensitivity analysis of the effects with an RIR estimate of <10, within-participant designs (n=18)
demonstrated a positive slope, while between-participant designs (n=122) exhibited a negative
slope.
When effects were analyzed as a response ratio in the primary analysis, training programs that
did not employ progressive overload (n=5) exhibited a positive slope while those that included
progressive overload (n=135) exhibited a negative slope. In the sensitivity analysis of the effects
with an RIR estimate of <10, training programs that used heavier loads demonstrated a more
positive slope than programs that used lighter loads. Within-participant designs (n=18) also
demonstrated a more positive slope than between-participant designs (n=122). Finally, training
programs that did not employ progressive overload (n=5) exhibited a positive slope while those
that included progressive overload (n=135) exhibited a negative slope.
5 DISCUSSION
The present meta-analysis explored the dose-response relationship between proximity to
failure (quantified as estimated RIR), strength gains, and muscle hypertrophy. Our results
showed that strength gains are minimally influenced by proximity to failure, while muscle
hypertrophy tends to increase as sets are terminated closer to failure. These relationships can
inform future research and potentially improve the conceptual understanding of practitioners
in regards to how proximity to failure influences muscular hypertrophy and strength outcomes,
respectively.
Strength
In all of the best-fit models within the present analysis, the confidence intervals of the marginal
slope for estimated RIR contained a null point estimate, suggesting a negligible relationship
between proximity to failure and strength gains. There are multiple potential explanations for
these findings. In the following sections, we will discuss the principle of specificity in regards to

23
force production and opposing advantages of training far from and close to failure for strength
gain to explain the observed relationship.
Force Production and The Principle of Specificity
The main estimates from the statistical models were extracted after adjusting for both load,
the method in which volume was equated, intervention duration, and training status. Other
meta-analytic data suggest that load, in particular, exhibits a positive dose-response
relationship with strength gains [3,4]. These data, in concert with the present findings, suggest
that load is a better predictor of strength outcomes than proximity to failure. Importantly, as
load increases, the furthest obtainable proximity to failure decreases. For example, when
training with a 10RM load (~75% of 1RM) a set could be terminated after a single repetition
resulting in 9 RIR. However, a set terminated after a single repetition with a 2RM load (~95% of
1RM) will be much closer to failure (i.e., 1 RIR). This example illustrates the difference between
a load-mediated and intra-set-fatigue-mediated change in proximity to failure. The present
analysis would suggest that intra-set-fatigue-mediated changes in proximity to failure have a
negligible influence on strength gains, while there is more research in support of load-mediated
changes.
The contrast between load-mediated and intra-set-fatigue mediated changes in proximity to
failure and their impact on strength outcomes could be potentially explained by the principle
of specificity [100] in regards to force production. To align with the principle of specificity, one
would expect that training with similar forces to the strength assessment of interest would
result in favorable outcomes such as training with loads >85% of 1RM to maximize
performance on a 1RM test. Importantly, however, force production declines as sets are taken
closer to failure [101] but increases proportionally with load (i.e., % of 1RM) [102], thereby
supporting the contrast between load-mediated and intra-set-fatigue mediated changes in
proximity to failure and their impact on strength gains. Moreover, a recent meta-analysis by
Zhang et al. [20] concluded that lower velocity loss thresholds resulted in higher strength gains
per repetition than higher velocity loss thresholds. These results indicate that repetitions
performed early in the set, which have the highest force production, lead to the greatest
relative strength gain.

24
Advantages of Training Far From Failure for Strength
There are a number opposing advantages of training far from and close to failure for strength
gains that may effectively counterbalance one another, leading to a negligible overall
relationship. The first potential advantage of conditions training farther from failure is fatigue
management. Multiple acute studies have demonstrated that training closer to failure results
in greater indices of neuromuscular and perceptual fatigue compared to training farther from
failure [33,103,104]. Since resistance training interventions often do not employ a formal
tapering period in which training stress is reduced temporarily to allow for an improvement in
acute performance [105], training farther from failure may allow participants to perform
strength assessments in the absence of training-related fatigue compared to conditions
training closer to failure.
Additionally, there may be proximity-to-failure-specific adaptations to rate of force
development (RFD), which may contribute to the attenuation of maximal strength gains. While
maximal strength (i.e., absolute force production measured in a specific context) is by
definition a time-independent characteristic, the rate at which force is produced could
influence an individual’s ability to generate sufficient absolute force i) prior to the onset of
fatigue, and ii) reaching the position in the range-of-motion with the greatest force
requirements. Pareja-Blanco et al. [55] reported that training the Smith-machine squat to a
40% velocity loss threshold resulted in a reduction in the RFD measured from 0-50ms while
lower velocity loss thresholds (i.e., 0, 10 and 20%) improved RFD, suggesting training closer to
failure may harm RFD. However, differential adaptations seem to occur in the early (<200 ms)
and the late (>200 ms) phases of RFD, with the latter being suggested as more predictive of
maximal strength [106].
In an additional investigation, Pareja-Blanco et al. [56] reported that only groups training the
Smith-machine bench press to higher velocity loss thresholds (i.e., 25 and 50%) saw
improvements in RFD measured from 0-400ms, suggesting training closer to failure may harm
early but not late phase RFD. However, as previously mentioned, these studies cannot
delineate if the proximity to failure or relative volume load (i.e., % of 1RM × repetitions × sets)
mediates effects on RFD, as both are manipulated via velocity loss thresholds. In studies that
equate relative volume load and measure RFD, conditions training farther from failure usually
result in superior changes in RFD, regardless of the phase examined [24,31,32,36,43]. Finally, a
recent cross-sectional examination of strength-trained individuals demonstrate significant

25
differences in earlier, but not later phases of RFD compared to untrained controls, potentially
indicating that all phases of RFD may contribute to maximal strength [107]; however, this area
lacks sufficient evidence to confidently describe the relationship between proximity to failure
and phase-specific alterations to RFD.
Advantages of Training Close To Failure for Strength
In contrast to the potential advantages of training farther from failure, training closer to failure
may offer exposure to motor patterns and psychological experiences more specific to a
maximal strength assessment. It is well established that motor patterns change with increases
in load, which require that single repetition sets are terminated closer to failure, in exercises
with many degrees of freedom (e.g., barbell back squat) [108]. As maximal strength
assessments occur at the threshold of failure - conditions training closer to failure may be
more regularly exposed to similar motor demands, thereby aligning with the principle of
specificity. Similarly, there seem to be psycho-physiological inputs to maximal strength (e.g.,
visualization) in which greater exposure to the subjective experience of performing resistance
training near or to failure could be beneficial [109]. Practically, training closer to failure also
allows for greater accuracy in subjectively reported RIR [110]. Given that loads are often
selected via the perception of RIR (i.e., RIR-based RPE) [111], inaccuracy in this perception of
RIR could also lead individuals to train with lower loads unnecessarily and potentially harm
strength outcomes.
The second advantage of training closer to failure is greater increases in muscle size, as
supported by the present meta-analysis. Although the contribution of changes in muscle size
to changes in strength has been a topic of debate in the scientific literature [112,113], it is
plausible that some relationship exists, though the degree of which is uncertain. Given this
assumption, training closer to failure would benefit from greater muscle-size mediated
strength gain than conditions training farther from failure.
Taken collectively, these opposing advantages of training far from and close to failure may
explain the negligible dose-response relationship between estimated proximity to failure and
strength gain in the present meta-analysis.

26
Hypertrophy
In contrast to results from the analysis of strength outcomes, the confidence interval of the
marginal slope for estimated RIR did not contain a null point estimate in all best-fit models for
muscle hypertrophy. In other words, the findings suggest a meaningful relationship between
proximity to failure and changes in muscle size whereby muscle hypertrophy tends to increase
as sets are performed closer to failure. In the following sections, we will discuss the
mechanistic support for this relationship, potential explanations of the directionality of the
observed effects, and other important considerations of the present findings.
Mechanistic Support of the Observed Relationship
The linear relationship observed in the present meta-analysis seems to support the proposed
mechanistic models of resistance-training-induced muscle hypertrophy [114]. Specifically,
Henneman’s size principle suggests that motor units, and the muscle fibers they innervate, are
recruited sequentially based on their size as force requirements rise [115]. As higher threshold
motor units tend to innervate more type II fibers, which may have a greater potential for
hypertrophy [116], the goal becomes to create the necessary and sufficient conditions to
recruit these motor units allowing the muscle fibers they innervate to experience mechanical
tension [117]. Critically, training to failure seems to allow for a stimulus to be delivered to these
muscle fibers independent of load [118], while heavier loads may allow for greater motor unit
recruitment farther from failure [119]. This rationale seems to be somewhat supported by our
data as greater changes in muscle size were observed close to failure but this pattern was less
pronounced as load increased (although only considered a “meaningful” interaction in the
response ratio sensitivity analysis). Thus, the proximity to failure necessary to maximize muscle
hypertrophy may be load-dependent, where that heavier loads may not require as low of RIR.
Explaining the Directionality of the Observed Effects
It is unclear why our findings suggest a linear increase in changes in muscle size while
terminating sets closer to failure. While training to or close to failure is associated with
increased acute fatigue [103,104] and performance decrements [120,121], there is a paucity of
studies that examine fatigue longitudinally. It could be that the repeated bout effect strongly
diminishes the fatigue associated with training to or close to failure as one habituates to the
stimulus [122]. Alternatively, ambiguity in failure definitions could be playing a role. Halperin et
al. [110] demonstrated that participants often under-predict the number of repetitions they

27
are able to perform, thus, potentially training farther from failure than intended. If
underprediction does occur, studies that state participants trained to “failure” without a clear
definition of criteria for set termination would result in RIR estimations that were too low (i.e.,
estimated to be too close to failure) in the present meta-analysis. However, the failure
definition interacting moderator analysis suggests that studies which provided a failure
definition resulted in greater changes in muscle size than those that did not. Because both
models suggest that gains in muscle size increase the closer to failure a set is terminated,
ambiguity in failure definition does not seem to influence the shape of the dose-response
relationship. Although, the magnitude of the expected effects may differ between studies
providing explicit failure definitions and those that do not. Ultimately, it is difficult to explain the
directionality of the observed relationship and future research should aim to explore its
origins.
Other Findings
Another interesting finding of the present meta-analysis was that the marginal slopes for RIR
were not meaningfully influenced by the method in which volume was equated (i.e., set or
repetition volume-equated). In all of the recent velocity loss meta-analyses [16–18] the authors
report positive linear dose-response relationships between the velocity loss threshold in which
sets are terminated and changes in muscle size. However, as previously mentioned, velocity
loss thresholds influence both proximity to failure and relative volume load, which makes it
difficult to utilize the positive linear dose-response relationships to inform RIR prescriptions for
muscle hypertrophy. With the present meta-analysis in mind, it seems that the method in
which volume was equated (i.e., set or repetition volume-equated) does not meaningfully alter
the dose-response relationship between estimated proximity to failure and changes in muscle
size. Thus, a particular type of volume-equated study design (i.e., either set or repetition
volume-equated) does not seem to be necessary to inform the relationship between proximity
to failure and muscle hypertrophy.
Finally, it is important to mention that the present analysis predominantly focuses on the
proximity to failure that optimizes the average muscle hypertrophy of the prime movers of a
given exercise (e.g., a training intervention that features a leg press means that the quadriceps
are the prime mover). There are considerably fewer studies that examine the effect of
proximity to failure on synergistic muscle groups (e.g., triceps brachii in the bench press), thus
the present findings should not be generalized blindly. Moreover, very few studies measure

28
hypertrophy of multiple regions within a given muscle (e.g., proximal, middle, distal) which
could exhibit differential relationships to the proximity to failure at which training is performed.
To provide more context for these relationships, future research should aim to measure
synergistic muscles and regional hypertrophy of all the sites of interest.
Limitations and Considerations
Several limitations exist with this meta-analysis. While considerable thought and collaboration
were put into constructing the highest quality process of estimating RIR, the accuracy of these
estimations is unknown. Previous research suggests that the number of repetitions performed
at a given load is highly individual [123–126]. Thus, estimating RIR based on homogeneous RM
values may be representative of the group-level RIR but likely only applies to some participants
within a study. Additionally, multiple other factors that influence proximity to failure were not
directly addressed. First, as participants perform multiple sets, set-to-set performance declines
due to fatigue. Specifically, if the load is not adjusted from set to set and sets are performed to
the same repetition target (e.g., 10 repetitions), there may be fewer RIR on later sets.
Therefore, the estimated RIR values, on average, could be overestimated (i.e., the estimations
are too far from failure) - although the exact extent to which this may occur is influenced by
various factors (e.g., sex, exercise selection, load, rest period, and initially prescribed proximity
to failure); thus, this could not be adequately accounted for.
Another factor that may influence RIR is strength gain. Specifically, if the load is not adequately
adjusted as participants gain strength (i.e., progressive overload), and sets are performed to
the same repetition target (e.g., 10 repetitions), there may be greater RIR in later sessions of
the training program. Therefore, the estimated RIR values, on average, could be
underestimated (i.e., the estimations are too close to failure) - although, again, the extent to
which this may occur is influenced by various factors (e.g., exercise selection, load, weight
increments available, and frequency of load progression); thus, this could not be adequately
accounted for. Another limitation comes from the decision to average RIR values across all sets
performed to describe each group. Therefore, this analysis does not take into account the
variability in RIR throughout a training program. For example, at an average estimated RIR of 2,
the group could have performed all sets at 2 RIR or an even proportion of 1 and 3 RIR sets.

29
From a practical perspective, the observed relationships between estimated RIR and strength
or muscle hypertrophy outcomes may not hold on the individual level. For example, in the
context of training volume, Damas et al. [127] demonstrated that some participants saw more
favorable outcomes in a limb training with <10 sets per week compared to a limb training with
>10 sets per week. Crucially, these findings contradict a well-cited meta-analysis by Schoenfeld
et al. [1], which suggests that >10 sets per week are optimal for muscle hypertrophy outcomes,
on average. This example demonstrates that training recommendations derived from meta-
analytic estimates may be inappropriate for some individuals; however, in the absence of
robust individual-level evidence (e.g., N of 1 trials) average effects may be the best estimate
[128,129]. Moreover, applying these relationships outside the context of the volumes, loads,
frequencies, and study designs included in this analysis should be done with caution (see
Figure 1 and supplementary file 2: https://osf.io/3tcwx). For example, only volume-equated
studies (i.e., either set or repetition equated) were included in the present analysis. While
training closer to failure resulted in superior muscle hypertrophy outcomes, these results may
change if participants could modify the number of sets performed to align with their recovery
capacity. As training to failure results in greater acute fatigue [103,104], training with a greater
number of RIR could allow for more weekly sets and could impact longitudinal strength and
muscle hypertrophy outcomes. Finally, many studies did not provide the necessary data for the
analysis, so much of it had to be estimated (e.g., pre- to post-test correlation coefficients).
Our goal with this analysis was to provide reasonably precise population average RIR estimates
that, in the absence of better evidence, can describe the relationship between proximity to
failure and resistance training outcomes. However, it is critical to mention that the quality of
model fit is modest, suggesting that proximity to failure is only one piece to explain training
outcomes. Further, the uncertainty intervals of all estimates are wide, indicating many dose-
response shapes are compatible with the current analysis (particularly upon the addition of
future high-quality data). While the limitations are notable, this analysis may be useful to
explore the directionality of these relationships and identify potential RIR thresholds of interest
for future research.
6 CONCLUSION
The dose-response relationships between estimated proximity to failure and strength gain
appears to be different from that with muscle hypertrophy. Strength gains seem to be

30
negligibly impacted by the proximity to failure in which sets are performed at a given load,
while muscle hypertrophy improves as sets are terminated closer to failure. However, the
quality of overall model fits was modest and the width of the uncertainty intervals of all
estimates suggest many dose-response shapes are compatible with the current analysis,
particularly upon the addition of future data. Considering these results and the RIR estimation
procedures used, the exact relationship between RIR and muscle hypertrophy and strength
remains unclear. Researchers and practitioners should be therefore be cautious interpreting
the findings of the present analysis.
Data and Supplementary Material Accessibility
All materials, data, and code are available on the Open Science Framework project page.
Author Contributions
ZR extracted the data, performed the initial RIR estimations, performed the statistical analysis,
and drafted the manuscript. JP, JR, and MZ provided the first peer-review of the RIR estimations
and edited the manuscript. MR and IJ provided the second peer-review of the RIR estimations
and edited the manuscript. JS assisted with the statistical analysis, and edited the manuscript.
Conflict of Interest
Zac Robinson, Joshua Pelland, Jacob Remmert, and Michael Zourdos are all coaches and
writers in the fitness industry. Martin Refalo, Ivan Jukic, and James Steele declare that they have
no conflicts of interest relevant to the content of this review.
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