Submitted:
16 October 2026
Posted:
19 October 2026
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Abstract
Special exercises are routinely used to monitor strength qualities in weightlifting when recent maximal snatch and clean-and-jerk performances are unavailable. This study developed and internally assessed an exploratory model for estimating a training total from special-exercise strength measures while accounting for sex and body mass. Retrospective records from 27 senior high-performance weightlifters (14 men and 13 women) were analyzed. The training total was calculated from the most recent maximal snatch and clean-and-jerk records obtained within an approximately two-week precompetition window. Simple and partial correlations, hierarchical linear regression, collinearity diagnostics, residual analyses, and leave-one-out cross-validation were examined. Sex and body mass explained 94.3% of the variance. Adding front squat and strict military press increased explained variance to 97.9% and reduced the standard error of estimate from 16.58 to 10.52 kg. The internally assessed RMSE was 11.47 kg and MAE was 9.25 kg; however, front squat showed substantial collinearity. The model may provide a provisional monitoring reference under comparable conditions, but the small sample, predictor selection within the same dataset, collinearity, and absence of external validation preclude treating it as a confirmed predictive equation.
Keywords:
weightlifting
; strength monitoring
; front squat
; military press
; predictive modeling
; cross-validation
; athletic performance
1. Introduction
Competitive weightlifting is contested through two classical lifts: the snatch and the clean and jerk. The sum of the best valid load in both lifts constitutes the competition total and determines ranking within each body-mass category. This arithmetic identity means that a model including snatch and clean and jerk simultaneously does not predict an independent outcome; it reproduces its definition. The applied problem is different when recent maximal values for both classical lifts are unavailable or when training monitoring is conducted through partial and auxiliary exercises [1,2].
Within weightlifting preparation, special exercises allow coaches to develop and observe strength qualities linked to specific phases or positions of the competitive lifts. The front squat and back squat express maximal lower-body strength under different postural demands; snatch and clean pulls overload the initial pulling phase; and the strict military press assesses vertical pressing strength without deliberate contribution from the lower limbs. These exercises do not replace technical assessment of the snatch and clean and jerk, but they may provide complementary information for athlete monitoring [3,4].
Squat strength is strongly associated with weightlifting performance, as summarized by Joffe et al. [5]. Lucero et al. [6] reported relationships among front squat, back squat, snatch, clean and jerk, and total performance. Zecchin et al. [7] proposed that the joint association of front squat and overhead press with the competitive lifts may partly reflect a general strength component. In elite weightlifters, Zaras et al. [8] also related performance to maximal lower-body strength and other neuromuscular characteristics. These associations are physiologically and mechanically plausible, although a cross-sectional design cannot demonstrate that an isolated increase in an auxiliary lift causes a proportional improvement in the total.
Pulling and pressing derivatives represent different mechanical stimuli. Pulling derivatives can accommodate high loads in specific phases with lower technical complexity than the full lifts [4], whereas overhead pressing variants differ in lower-limb contribution, movement velocity, and attainable load [9]. Weightlifting exercises also target different portions of the force–velocity relationship [10]. Therefore, the magnitude of the association for each special exercise should be interpreted according to its actual execution rather than its name alone.
Body mass and recorded sex require explicit consideration when absolute loads are analyzed. Heavier weightlifters tend to lift more kilograms, but this relationship is neither perfectly linear nor equivalent between men and women [11,12]. Performance zones also vary by body-mass category and competitive level [13]. Consequently, bivariate correlations among exercises may be inflated because several measures share associations with body size and sex-related performance differences [14].
Predictive research in weightlifting remains limited. Ulupınar and İnce [15] used ridge regression to identify strength and power tests associated with performance in junior female weightlifters. Sandau and Kipp [16] compared ordinary and penalized regression in 29 elite male weightlifters and showed that penalization produced more plausible coefficients when predictors were highly correlated. These findings indicate that a high coefficient of determination alone is insufficient; out-of-fit error, collinearity, model stability, and the origin of predictor selection must also be considered.
Accordingly, the aim of this study was to develop and internally assess, on an exploratory basis, a model for estimating a training total from special-exercise strength measures in high-performance weightlifters after accounting for sex and body mass. We expected front squat and strict military press to add information beyond a sex-and-body-mass baseline model, while recognizing that the strong interdependence among strength measures could limit interpretation of individual regression coefficients. The resulting model is therefore presented as a monitoring reference requiring external validation rather than as a substitute for direct assessment of the competitive lifts.
2. Materials and Methods
2.1. Study Design
A quantitative, retrospective, cross-sectional, correlational, and predictive study was conducted. Training-monitoring records generated during routine sport preparation were analyzed; no experimental session was scheduled specifically for this research. The analyses were intended for descriptive and exploratory model-development purposes. Accordingly, regression slopes were not interpreted as causal effects or as expected changes following an intervention.
2.2. Participants
The analysis included all 27 senior high-performance weightlifters from the Valle del Cauca Weightlifting League with complete records within the predefined monitoring window: 14 men and 13 women. Mean age was 21.89 ± 3.99 years and mean body mass was 75.85 ± 12.72 kg. Among men, age was 21.71 ± 4.36 years and body mass was 84.07 ± 10.69 kg; among women, the corresponding values were 22.08 ± 3.73 years and 67.00 ± 7.95 kg.
Eligibility required senior-category status, active participation in the competitive calendar, and recent maximal records for body mass and all exercises analyzed. Incomplete records or records obtained during a different preparation phase were excluded. No data were missing among the 27 included cases. The dataset therefore represented a census of eligible available records from this highly selected sport population. No a priori sample-size calculation was performed because of the retrospective design and the specificity of the population; the ratio between cases and candidate predictors reinforced the exploratory nature of the model.
2.3. Ethical Considerations
Participation of athletes, coaches, and officials was voluntary. Athletes provided informed consent authorizing the research use of anonymized monitoring records. The study was conducted in accordance with Colombian regulations governing health research and personal-data protection [17,18] and with the ethical principles of the Declaration of Helsinki [19]. The research was approved by the Ethics Committee of the Institución Universitaria Escuela Nacional del Deporte (approval No. 320.02.15.11-05, 21 September 2026).
2.4. Outcome and Predictor Variables
The dependent variable was the training total, expressed in kilograms. It was calculated as the sum of the most recent maximal snatch and maximal clean-and-jerk records obtained within the same approximately two-week precompetition window. It did not correspond to an official competition total, nor were both marks necessarily obtained on the same day. This distinction prevents extrapolation of the equation to an outcome that was not directly measured.
Training total (kg) = snatch (kg) + clean and jerk (kg)
Candidate predictors were recorded sex (women = 0; men = 1), body mass, and five special exercises: front squat, back squat, snatch pull, clean pull, and strict military press. The front squat was considered an expression of maximal lower-body strength in a posture related to recovery from the clean; the back squat represented general maximal lower-body strength; and the pulls represented overloaded tasks associated with the initial phase of the classical lifts. The strict military press was performed from the front rack to full overhead elbow extension without deliberate leg drive. All loads corresponded to the heaviest technically accepted single repetition and were expressed in kilograms.
2.5. Procedures
Data were obtained from routine monitoring sessions of the Valle del Cauca Weightlifting League. These checks were generally performed weekly and alternated classical and special exercises according to the training plan. For each variable, the most recent maximal record obtained during the final preparation phase and within the same temporal window was selected. Body mass was recorded during monitoring rather than at official weigh-in; some athletes were still adjusting body mass toward their intended competitive category.
One-repetition maximum determination followed a progressive increase from submaximal loads to the heaviest successfully completed load with accepted technique, consistent with the testing logic described by Naclerio Ayllón et al. [20]. Warm-up procedures and load increments were individualized according to usual team practice. Because the records were retrospective, an identical sequence of increments, number of attempts, or recovery intervals could not be reconstructed for every athlete. This lack of complete standardization was treated as a measurement limitation.
2.6. Statistical Analysis
Mean, standard deviation, 95% confidence interval, minimum, and maximum were calculated. Distributional form was examined with the Shapiro–Wilk test. Because clean and jerk showed evidence of departure from normality, associations were examined using both Pearson and Spearman correlations. Partial correlations between each special exercise and the training total were also estimated while simultaneously controlling for sex and body mass. These tests used 23 degrees of freedom, corresponding to 27 observations and two control variables; approximate confidence intervals were derived using Fisher’s z transformation.
The primary regression analysis was hierarchical. Block 1 included sex and body mass; Block 2 added front squat and strict military press. Selection of these two exercises was exploratory and used the same dataset, considering observed associations, error, number of predictors, and collinearity. As a sensitivity analysis, five specifications were compared: a baseline model, a model with all five special exercises, a reduced special-exercise model, a reduced adjusted model, and a fully adjusted model. We report coefficients of determination, adjusted coefficients, change in explained variance, F change, standard error of estimate, unstandardized and standardized coefficients, confidence intervals, and variance inflation factors (VIFs).
Internal predictive error for each prespecified model was estimated using leave-one-out cross-validation (LOOCV). Root mean square error (RMSE) and mean absolute error (MAE) were calculated. Predictor selection was not repeated within each resampling partition; therefore, these indices were interpreted as potentially optimistic internal estimates rather than independent validation [21,22]. Assumptions of the retained model were examined using Shapiro–Wilk testing of residuals, the Breusch–Pagan test, Durbin–Watson statistic, Cook’s distance, leverage, and externally studentized residuals. A common linear relationship between body mass and the outcome was assumed; nonlinear terms and sex-by-body-mass interactions were not modeled because of sample size. All tests were two-sided with α = 0.05. No multiplicity correction was applied because the analyses were exploratory.
All analyses were performed in IBM SPSS Statistics (IBM Corp., Armonk, NY, USA).
3. Results
Mean training total was 268.67 ± 66.96 kg (range: 171–393 kg). Mean snatch was 120.22 ± 31.28 kg and mean clean and jerk was 148.44 ± 35.80 kg. Clean and jerk was the only variable showing evidence of departure from normality in the Shapiro–Wilk test (W = 0.919, p = 0.038); all other variables had p ≥ 0.066. Table 1 summarizes the descriptive statistics.
Simple correlations were high for all five special exercises. After adjustment for sex and body mass, strict military press showed the largest partial association (r = 0.709), followed by front squat (r = 0.605) and back squat (r = 0.587). Snatch pull retained a positive partial association (r = 0.454, p = 0.023), whereas clean pull did not reach the conventional significance threshold (r = 0.387, p = 0.056). Partial-correlation p values were based on 23 degrees of freedom (Table 2).
3.1. Hierarchical Regression
The baseline model including sex and body mass explained 94.3% of the variability in training total (R2 = 0.943; adjusted R2 = 0.939; standard error of estimate = 16.58 kg; p < 0.001). After front squat and strict military press were added, the model reached R2 = 0.979 and adjusted R2 = 0.975. The increase was ΔR2 = 0.036, with ΔF(2,22) = 18.78 and p < 0.001; the standard error of estimate decreased to 10.52 kg.
All four predictors in the retained model had coefficients different from zero at p < 0.05 (Table 3). Front squat showed a VIF of 14.78, indicating substantial collinearity. Therefore, the regression slopes describe the joint equation and should not be interpreted as an independent partition of each strength quality.
3.2. Model Comparison and Internal Error
The fully adjusted model reduced LOOCV RMSE from 11.47 to 11.30 kg relative to the reduced adjusted model, a difference of only 0.17 kg. However, it added three predictors and increased the maximum VIF from 14.78 to 63.40. The reduced adjusted model was therefore retained as the exploratory specification because of its lower complexity, although it did not eliminate collinearity (Table 4).
3.3. Equation and Diagnostics
Estimated training total (kg) = 13.247 + 28.920(sex) + 0.987(body mass) + 0.539(front squat) + 0.926 (strict military press)
In the equation, sex was coded as 0 for women and 1 for men; all remaining variables were expressed in kilograms. The sex coefficient does not represent an isolated biological difference, and the exercise coefficients should not be translated into causal expectations of improvement.
LOOCV of the retained model yielded an RMSE of 11.47 kg and an MAE of 9.25 kg. The RMSE corresponds to approximately 4.3% of the mean training total, but it should not be interpreted as a fixed error margin for an individual athlete. Residuals were compatible with normality (W = 0.984, p = 0.934), and the Breusch–Pagan test showed no evidence of heteroscedasticity (LM = 6.28, p = 0.179). Durbin–Watson was 1.75. Maximum Cook’s distance was 0.248, maximum leverage was 0.445, and externally studentized residuals ranged from −2.04 to 2.29. No observation warranted exclusion solely on the basis of these diagnostics.
4. Discussion
The principal finding was that front squat and strict military press retained information associated with the training total after sex and body mass were considered. Adding these measures increased R2 by 3.6 percentage points and reduced the standard error of estimate by 6.06 kg relative to the baseline model. Interpretation must nevertheless begin with the actual scope of the outcome: the model estimated a sum of recent training records rather than an official competition total, and it was developed and internally assessed using only 27 athletes from the same population.
Sex and body mass alone explained 94.3% of the variance in absolute-load training totals. This result illustrates how simple correlations can be inflated when multiple strength measures share associations with body size and sex-related performance profiles. Huebner and Perperoglou [11] and Huebner et al. [12] showed that the relationship between body mass and performance differs by sex and is not described identically across the full body-mass range. Chavda et al. [13] likewise documented meaningful differences across categories and competitive levels. For parsimony, the present analysis used a common linear body-mass term; with this sample, sex-specific curves or more complex interactions were not reasonably estimable.
The association of front squat was consistent with its postural proximity to recovery from the clean and with previous evidence. Lucero et al. [6] reported strong relationships between squat strength and weightlifting performance, while Zaras et al. [8] related maximal lower-body strength to snatch and clean-and-jerk performance in elite lifters. The partial correlation of 0.605 indicates that the relationship was not fully summarized by sex and body mass. However, the VIF of 14.78 prevents attribution of a stable independent contribution to front squat.
Strict military press showed the largest partial correlation. This exercise does not reproduce the jerk because it removes deliberate lower-limb drive; rather, it may index vertical pressing strength and trunk control under load. The present study did not measure scapular stability, electromyographic activity, or fixation kinematics. Soriano et al. [9] emphasized the distinct demands of overhead pressing derivatives, and Zecchin et al. [7] reported an association between overhead pressing strength and competitive weightlifting exercises. This agreement supports plausibility but does not establish mechanical equivalence or causal transfer.
The pulling derivatives displayed simple correlations above 0.93, but their partial associations were attenuated. Clean pull did not reach statistical significance after adjustment (p = 0.056). This finding does not imply a lack of training value. Pulling derivatives have specific overload and technical-development functions [4], and their external-load and fatigue responses may differ from those of the full lifts [3]. In this dataset, however, their statistical information was more redundant with other indicators of body size and strength.
Model comparison highlighted a trade-off between predictive error and interpretability. The seven-predictor model reduced RMSE by only 0.17 kg while increasing maximum VIF above 60. Sandau and Kipp [16] described an analogous issue in elite male weightlifters and demonstrated advantages of ridge regression for producing more plausible coefficients under strong predictor correlation. The present findings therefore support future comparison with penalized models; they do not retrospectively convert the reduced model into a confirmatory specification.
The proximity between the standard error of estimate and cross-validated error suggests that model fit did not deteriorate abruptly when observations were successively omitted. Nevertheless, predictor selection was performed using the complete dataset and was not repeated within each resampling partition. Methodological literature shows that cross-validating a model selected on the same data can underestimate prediction error [21,22]. For this reason, internal assessment is more precise terminology than validation, and the reported errors should be regarded as optimistic until an external sample is available.
The approximately two-week monitoring window partially reduced temporal mismatch among measurements. Strength and power qualities can vary across a training cycle [23], and Morris et al. [24] similarly used measurements close to recent performance marks when examining kinetic predictors in young weightlifters. In the present study, however, exercises were monitored on alternating days rather than within a single session. Changes in fatigue, body mass, or readiness across the window may therefore have introduced additional error.
The equation may function as a provisional reference in athletes and monitoring conditions similar to those studied, provided that the same exercise definitions are used and the estimated outcome is interpreted specifically as a training total. It should not replace direct assessment of the snatch, clean and jerk, technical observation, or competition performance. The study also did not test whether the equation is more informative for longitudinal within-athlete monitoring; that question requires repeated measurements and analyses of intra-individual change.
4.1. Practical Applications
- The equation may provide an exploratory reference when recent and comparable values are available for body mass, front squat, and strict military press.
- A discrepancy between observed and estimated training total should prompt review of the athlete’s preparation context; by itself, it does not diagnose fatigue, technical deficiency, or insufficient transfer.
- Front squat and strict military press are not the only relevant special exercises. Exclusion of other predictors reflected a statistical compromise among redundancy, error, and model complexity.
- External validation is required before the equation is applied to another league, body-mass category, competitive level, or phase of the season.
4.2. Limitations and Future Research
The study was limited by its small sample, non-probability sampling framework, and substantial collinearity. The outcome was a sum of recent maxima obtained across alternating monitoring sessions rather than an official competition result or two lifts necessarily performed in the same session. The retrospective protocol did not preserve an identical warm-up sequence, load increments, number of attempts, or rest intervals for every athlete. Body mass was not obtained at official weigh-in, and body composition, training experience, barbell velocity, and kinematic variables were unavailable.
Exploratory predictor selection and error estimation were performed using the same sample, and nonlinear relationships or sex interactions were not examined. Future studies should collect prospective data, repeat predictor selection within nested cross-validation, compare ordinary and penalized regression, quantify uncertainty around prediction error, and assess calibration in an external sample. Longitudinal repeated-measures designs would also allow between-athlete associations to be distinguished from intra-individual changes.
5. Conclusions
Sex and body mass explained a very large proportion of variability in the training total. After both variables were considered, front squat and strict military press increased explained variance and reduced estimation error. The reduced adjusted model produced an internally assessed RMSE of 11.47 kg, but it retained substantial collinearity and was selected using the same dataset on which its performance was evaluated.
Accordingly, the equation should be regarded as an exploratory monitoring tool for comparable conditions rather than as a confirmed, causal, or generalizable predictive equation. Use beyond the present sample requires standardized measurements and external validation, while longitudinal usefulness should be tested using repeated observations.
Author Contributions
Conceptualization, L.F.G.A. and M.D.F.C.; methodology, L.F.G.A., M.D.F.C. and R.C.J.; formal analysis, L.F.G.A. and R.C.J.; investigation, L.F.G.A.; resources, L.F.G.A.; data curation, L.F.G.A.; writing—original draft preparation, L.F.G.A.; writing—review and editing, M.D.F.C. and R.C.J.; supervision, M.D.F.C.; project administration, L.F.G.A. All authors have read and agreed to the published version of the manuscript.
Funding
This research received no external funding.
Institutional Review Board Statement
The study was conducted in accordance with the Declaration of Helsinki and approved by the Ethics Committee of the Institución Universitaria Escuela Nacional del Deporte (approval No. 320.02.15.11-05, 21 September 2026).
Informed Consent Statement
Informed consent was obtained from all subjects involved in the study for the research use of anonymized training-monitoring records.
Data Availability Statement
Individual-level data are not publicly available because the small sample of high-performance athletes creates a risk of re-identification. Reasonable requests for access to anonymized data may be considered by the corresponding author, subject to the scope of participant consent and applicable institutional approval.
Acknowledgments
The authors thank the athletes, coaches, officials, and technical staff of the Valle del Cauca Weightlifting League who made the monitoring records available for this study. During the preparation of this manuscript, the authors used ChatGPT (OpenAI) for language editing, text reorganization, and formal adaptation to journal requirements. The tool was not used to generate data or conduct the original statistical analyses. The authors reviewed and edited the output and take full responsibility for the content of this publication.
Conflicts of Interest
The authors declare no conflicts of interest.
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Table 1.
Descriptive statistics and Shapiro–Wilk normality tests.
| Variable | Mean ± SD (kg) | 95% CI | Min–Max | W | p |
|---|---|---|---|---|---|
| Snatch | 120.22 ± 31.28 | 107.85–132.60 | 77–180 | 0.935 | 0.091 |
| Clean and jerk | 148.44 ± 35.80 | 134.28–162.61 | 94–213 | 0.919 | 0.038 |
| Training total | 268.67 ± 66.96 | 242.18–295.16 | 171–393 | 0.929 | 0.066 |
| Front squat | 171.48 ± 40.62 | 155.41–187.55 | 105–240 | 0.931 | 0.071 |
| Back squat | 200.41 ± 44.92 | 182.64–218.18 | 120–280 | 0.964 | 0.456 |
| Snatch pull | 156.67 ± 43.77 | 139.35–173.98 | 90–240 | 0.955 | 0.283 |
| Clean pull | 184.26 ± 46.94 | 165.69–202.83 | 105–265 | 0.941 | 0.131 |
| Strict military press | 79.07 ± 22.75 | 70.08–88.07 | 42–123 | 0.953 | 0.250 |
Note: SD = standard deviation; CI = confidence interval; W = Shapiro–Wilk statistic.
Table 2.
Associations of special exercises with the training total.
| Exercise | Pearson r | Spearman ρ | Partial r | 95% CI | p |
|---|---|---|---|---|---|
| Front squat | 0.972 | 0.946 | 0.605 | 0.276 to 0.807 | 0.001 |
| Back squat | 0.958 | 0.943 | 0.587 | 0.250 to 0.797 | 0.002 |
| Snatch pull | 0.947 | 0.936 | 0.454 | 0.072 to 0.720 | 0.023 |
| Clean pull | 0.931 | 0.907 | 0.387 | −0.010 to 0.678 | 0.056 |
| Strict military press | 0.949 | 0.953 | 0.709 | 0.436 to 0.863 | <0.001 |
Note: n = 27. Partial correlations were simultaneously adjusted for sex and body mass; df = 23. Confidence intervals are approximate and based on Fisher’s z transformation. Tests were two-sided.
Table 3.
Final hierarchical regression model for estimating training total.
| Predictor | B | SE | β | t | p | 95% CI for B | VIF |
|---|---|---|---|---|---|---|---|
| Constant | 13.247 | 16.700 | — | 0.793 | 0.436 | −21.387 to 47.881 | — |
| Sex (men = 1) | 28.920 | 9.801 | 0.220 | 2.951 | 0.007 | 8.595 to 49.245 | 5.85 |
| Body mass | 0.987 | 0.377 | 0.187 | 2.617 | 0.016 | 0.205 to 1.768 | 5.40 |
| Front squat | 0.539 | 0.195 | 0.327 | 2.758 | 0.011 | 0.134 to 0.944 | 14.78 |
| Strict military press | 0.926 | 0.233 | 0.314 | 3.970 | <0.001 | 0.442 to 1.409 | 6.61 |
Note: Dependent variable = training total. B = unstandardized coefficient; SE = standard error; β = standardized coefficient; CI = confidence interval; VIF = variance inflation factor. Final model: R2 = 0.979; adjusted R2 = 0.975; standard error of estimate = 10.52 kg.
Table 4.
Performance of candidate model specifications.
| Model | Predictors | Adj. R2 | SEE | RMSE-LOOCV | MAE-LOOCV | Max. VIF |
|---|---|---|---|---|---|---|
| Baseline | Sex + body mass | 0.939 | 16.58 | 17.73 | 13.84 | 1.88 |
| Full special-exercise | Five special exercises | 0.969 | 11.76 | 13.23 | 10.51 | 41.53 |
| Reduced special-exercise | Front squat + strict military press | 0.966 | 12.36 | 13.33 | 10.88 | 5.91 |
| Reduced adjusted | Baseline + front squat + strict military press | 0.975 | 10.52 | 11.47 | 9.25 | 14.78 |
| Full adjusted | Baseline + five special exercises | 0.977 | 10.15 | 11.30 | 8.99 | 63.40 |
Note: SEE = standard error of estimate (kg); RMSE-LOOCV = root mean square error from leave-one-out cross-validation (kg); MAE-LOOCV = mean absolute error from leave-one-out cross-validation (kg); VIF = variance inflation factor. Predictor selection was not nested within cross-validation.
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