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Original Research

Scaling—Which Methods Best Predict Performance?

Comfort, Paul; Pearson, Stephen J.

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Journal of Strength and Conditioning Research: June 2014 - Volume 28 - Issue 6 - p 1565-1572
doi: 10.1519/JSC.0000000000000394
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The ability to generate force and power is of primary importance within many sports and are associated with indices of performance (18,43). The affect that body mass (BM) has on these performance variables is an important issue for researchers and trainers. For example, athletes with larger BM often exhibit a greater level of lean BM and are likely able to generate greater levels of absolute force or power (5,25,33,35,36,42). However, the ability to generate greater power with increased lean BM may not overcome the disadvantage of a greater absolute mass where the performance has to overcome the BM. More importantly, for sports performance, it is essential to determine if such indices are related to sports-specific performances; for example, sprinting requires high levels of acceleration and as such force generation to overcome the inertia of the BM. A number of studies have investigated the relationship between force and sprint performance, demonstrating that, in general, athletes with greater force capacity perform better during sprint performances (4,8,9,16,34,48), which may be explained by the fact that peak ground reaction forces and impulse are strong determinants of sprint performance (26,45–49).

To account for the effect of different BM between athletes, it is common practice to normalize the outcome variable by BM, which is also known as ratio scaling, although this approach assumes a linear relationship between BM and performance (28,29,34,41,44). Moreover, Hansen et al. (22) found that ratio scaling of peak power better predicted sprint performances compared with absolute measures and helped distinguish between levels of play.

Allometric scaling potentially offers a more effective method for normalizing athlete performance, by first raising BM using a power exponent of 0.67, based on the theory of geometric symmetry (28). This theory states that muscle force and power increases with BM to the power of 2:3. Allometric scaling has been used to normalize power and strength data in rugby league (2) and rugby union (14,15), ice hockey (24), weightlifting (7,17) and powerlifting (17). The appropriate use of allometric scaling is based on a number of assumptions; first, that a linear relationship exists between BM and performance; and second, that individuals are geometrically similar. Thus, it may well depend on the muscles being used for the performance as to whether the 2:3 ratio is appropriate. Some research has questioned the theory of geometric symmetry in athletes (5,37,38). For example, Nevill et al. (38) showed a greater proportion of muscle mass to BM was found in controls (0.38) than that predicted by geometric symmetry (0.33), and greater still for a combined group of athletes (0.44). Likewise, some athletes (e.g., rugby union players) have been found to differ from controls not only in BM and lean muscle mass but also in their relative distribution in the upper and lower extremities (6). Dooman and Vanderburgh (17) also found that different power exponents (BM−0.57, BM−0.60) were preferential for association with the bench press and squat performance, respectively. Given these findings, it would be informative to evaluate the use of both ratio and allometric scaling by comparing the proposed exponents (i.e., based on theoretical predictions) and exponents derived for a specific group of athletes and tests, which may aid coaching staff in determining the most appropriate methods of comparing performance data between athletes.

Examination of these factors could provide improved understanding of these relationships to improve athlete selection, assessment, and training for sport, and for standardizing the scaling of performance. This information would be particularly useful for comparing performances in team sports, such as rugby league and rugby union, where body stature tends to determine the players' position (14,18–21). The aim of this study, therefore, was to compare absolute, ratio and allometric scaling of strength, and power to examine their relationship with sprint speed, in male rugby league players. It was hypothesized that absolute measures would not demonstrate a strong relationship with performance, but that both ratio and allometric would be related to performance. It was further hypothesized that allometric scaling would demonstrate the strongest relationships with performance, although this was likely to be similar to ratio scaling as the derived power exponents for allometric scaling are derived from BM.


Experimental Approach to the Problem

Professional rugby league players (n = 15) performed 1 repetition maximum (1RM) back squat, squat jumps (without countermovement), and 20-m sprints (including 5, 10, 20 m, flying 5 m, and flying 10-m sprint performances) and 1RM power clean, on separate days. A within-subject repeated measures design was used to determine if absolute, ratio or allometrically scaled performances in 1RM back squat, 1RM power clean, or the kinetic (peak vertical ground reaction force, peak power) and kinematic (peak bar velocity) data collected during squat jumps were the best predictors of short sprint performances. The allometric scaling factor for all above performances was determined as the gradient from the linearized peak power during the squat jumps. Here, the scaling factor was the gradient derived from the log-log plot of peak power performance in the squat jump to BM (Figure 1), for back squat performance to BM, and for power clean performance to BM. These derived exponents were then applied to the various components as described above such that, for example, allometrically derived squat jump would become Power·kg0.94, for 1RM back squat kg·kg0.28, and for 1RM power clean kg·kg0.46.

Figure 1
Figure 1:
Example of derived exponent plot (linearized body mass vs. squat jump power).


At the end of preseason training after completing a 4-week power mesocycle preceded by a 4-week strength mesocycle, 15 male professional rugby league players (age, 26.27 ± 3.87 years; height, 183.33 ± 6.37 cm; BM, 96.86 ± 11.49 kg; body fat 13.95 ± 3.35%) were recruited for testing. For detailed analysis, the group was split according to their BM with those on either side of an arbitrary cutoff (mean of maximum and minimum BM) representing those of the lighter subgroup (LG) and heavier subgroup (HG). This resulted in a split of 8 in the LG and 7 in the HG (78.3–97.64 and 97.65–117 kg), conveniently representing the forwards and the backs, respectively.

Each subject had ≥3 years experience of resistance training and good squat technique as determined by a certified strength and conditioning specialist (CSCS). The study was approved by the Institutional Review Board of the University, and all subjects provided written informed consent.

A priori power calculations, from data previously collected on these athletes in our laboratory revealed that ≥7 subjects per group, and for the correlation analysis, would provide a statistical power ≥0.80 at an alpha level of p ≤ 0.05.


On arrival at the human performance laboratory, all athletes had their height, BM, body composition (Σ7 skinfolds) assessed by the primary investigator to eliminate intertester error (31), following the method described by Jackson et al. (27) along with their equation for calculating body fat percentage.

Strength Testing

One RM back squat testing was performed during subject's regular training and fitness testing schedule using a power rack (multi-rack, Power Lift; Jefferson, IA, USA), Olympic bars and Olympic weights (Werksan, NJ, USA). All subjects were familiar with the 1RM squatting protocol (3); however, testing was completed on 2 occasions, 7 days apart, to determine reliability of the 1RM performances and reduce learning effect. To maintain the appropriate squat depth, visual checks were made and verbal communications were given by the researcher. As a secondary precaution, a rubber band was placed across the squat rack at a height that touched the subject's posterior thigh when they reached the correct depth (90° of knee flexion), as measured during the warm-up using a goniometer. The highest load lifted across both testing sessions was used for calculation of loads for the squat jumps. Where testing was conducted across separate days, participants were assessed at the same time of the day and asked to standardize their individual fluid and dietary intake on each day of testing.

One RM power cleans were also performed twice, 3 days after each back squat testing session, using a standardized protocol (3), to determine the reliability. As with the 1RM back squats, the best performance was used for analysis.

Squat Jumps

Squat jump data were collected in a separate session, approximately 1 week after the final 1RM testing, using the FT700 Isotronic System ballistic measurement system (Fitness Technology, Adelaide, Australia). This incorporated the 400 series force plate (sampling at 600 Hz) to record the vertical ground reaction force and the BMS PT5 linear position transducer (LPT) fitted on the FT700 overhead tracking cradle to record vertical displacement and velocity of the bar; furthermore, this provided immediate feedback to identify if participants performed a countermovement.

To produce an accurate measure of vertical displacement without horizontal deviation, the LPT was positioned at a point directly above the force platform so that the subjects jumped from a position perpendicular to the LPT to minimize horizontal deviation (10–13). This foot position was marked on the force plate for each subject, to maintain accuracy and standardize jump position before each repetition and each set. Height at take off was zeroed with subjects stood on their toes (fully plantar flexed) and the LPT attached to the Olympic bar positioned across the trapezius. Subjects were familiar with squat jumps and explosive exercise, permitting the use of warm-up sets and initial calibration for familiarization with the equipment to ensure reliable jump performances (1).

Subject performed 3 repetitions of static squat jumps with a small bar (weight equal to the load of the pull of the LPT). Squat jumps began from a static self-selected height of approximately 135° knee flexion, with subjects required to pause for a count of 2 at the end of the descent phase to minimize the risk of a countermovement jump being performed. If the subjects performed a countermovement, identified from a decrease in displacement (≥1 cm) from the static position, the set was terminated and the subjects were asked to perform the set again after a 4-minute rest. The subjects received verbal instruction after completion of each repetition from the researchers to return to the correct position, underneath the LPT with the cable perpendicular to the floor in both the sagittal and frontal planes to standardize each jump (10,12). After the first set of 3 repetitions, the subjects rested for 4 minutes before performing an additional set of 3 squat jumps, to permit the calculation of reliability of this assessment. Peak power output was determined from the product of the vertical ground reaction force and vertical velocity at each time point. Velocity of the center of mass was determined from integration of the acceleration data (derived from Newton's second law), whereby the starting velocity was zero. The best performances were used for further analysis.


After a standardized warm-up, participants performed three 20-m sprints on an indoor track (Mondo, SportsFlex—10 mm; Mondo America, Inc., Conshohocken, PA, USA), wearing standard training shoes. Sprints were interspersed with a 1-minute rest period in accordance with McBride et al. (34). Time to 5, 10, and 20 m was assessed using infrared timing gates (Speed Trap 2, Wireless Timing System; Brower, Draper, UT, USA), with flying 5 m (10–5 m time) and flying 10 m (20–10 m time) calculated later. All subjects began with their front foot positioned 0.5 m behind the start line and were instructed to perform all sprints with a maximal effort. The best performance was used for further analysis.

Momentum Calculation

Momentum of the athletes was also calculated for the 0- to 5-, 5- to 10-, and 10- to 20-m sprint performances:

This was used to differentiate performances between forwards and backs in terms of the application of their resultant momentum and differential roles in the game of rugby league.

Statistical Analyses

Intraclass correlation coefficients (ICC) were calculated to determine the reliability between trials of both the 1RM back squat and the 1RM power clean. In addition, a further ICC was calculated to determine the reliability of the dependent variables during the squat jumps and sprint performances. All data were examined for normality (Shapiro-Wilk's), after which, a Pearson's correlations were used to examine the relationship between each performance variable (sprint time, squat jump) and force or power (normalized or absolute). Differences between groups were assessed through independent t-tests. A priori alpha level was set to 0.05. Normalization of the data was by either ratio scaling (division of measure by BM) or allometric scaling.


Intraclass correlation coefficients calculated from a subgroup of the population (n = 12) that were available for retesting determined a high reliability between trials for each of the dependent variables from the squat jump (r ≥ 0.92, p < 0.001) and for each sprint distance (r ≥ 0.96, p < 0.001). Back squat and power clean performances also demonstrated high reliability between trials (ICC: r = 0.97, p < 0.001; r = 0.95, p < 0.001, respectively). Mean and SD for the whole group and divided into forwards and backs are presented in Table 1.

Table 1
Table 1:
Absolute and scaled strength and power performances.*

Ratio and allometrically scaled power clean performance showed strong inverse and significant correlations (r = −0.625, −0.675; p = 0.001) with 0- to 5-m and (r = −0.6201, −0.638; p = 0.001) 20-m sprint times, and moderate inverse correlations (r = −0.558, −0.459; p = 0.001) with 10- and 10- to 20-m sprint times (r = −0.389, −0.537; p = 0.001). Ratio scaled back squat and allometrically scaled back squat performance also showed moderate inverse relationships with 10 m (r = −0.471, −0.495, p = 0.001), 0 - to 20-m sprint times (r = −0.471, −0.495, p = 0.001) and 5- to 10-m times (r = −0.544, −0.433, p = 0.001) (Table 2) (Figures 2 and 3).

Table 2
Table 2:
Relationships between squat and clean performances; kilogram lifted (absolute and ratio scaled) and sprint performances and jump height.*
Figure 2
Figure 2:
Independence of normalized (derived) power with body mass.
Figure 3
Figure 3:
Independence of normalized (ratio scaled) power with body mass.

Squat jump height was strongly correlated with absolute peak power (r = 0.665, p = 0.001), ratio scaled peak power (r = 0.753, p = 0.001), and allometrically scaled peak power (r = 0.753, p = 0.001) (Table 3). No significant correlations were found between squat jump performance and sprint performances.

Table 3
Table 3:
Relationships for peak power (Ppk) output during squat jumps and jump height.*

Forward demonstrated significantly greater (p < 0.001) momentum over 5 m (5,276.4 ± 363.6 vs. 4,409.1 ± 402.8 W), 5–10 m (7,526.6 ± 527.7 vs. 6,328.7 ± 559.8 W), and 10–20 m (8,578.3 ± 576.9 vs. 7,115.3 ± 801.1 W) compared with the back, respectively (Figure 4).

Figure 4
Figure 4:
Comparison of mean momentum between forwards and backs; *p = 0.001.


When the group was split into weight categories, it was observed that there were significant differences in BM between the subgroups, these 2 groups represented the backs and forwards, as would be expected. Thus, as expected, the HG generated significantly greater absolute levels of power during the squat jump compared with their lighter counterparts. When the power data were scaled, however, using either ratio or allometric methods the differences in power were not apparent. In contrast, squat results indicated no significant differences in absolute ability between the subgroups, although interestingly, when scaled, the mean values of the LG were significantly greater than those of the HG using either ratio or allometric methods. It has been suggested that scaling using ratio methods may in fact bias the results in favor of the lighter subjects (28). This was seen here in terms of the squat data, but not the power data. Thus, it would appear only where absolute differences are apparent between individuals of different BM, that the use of appropriate scaling is useful or indeed required.

In terms of the use of scaling, previous work has suggested that performances where rapid movements are seen or involved may not in fact benefit from scaled power or strength measures (32). It was noted that sprint times for the groups split by BM were not significantly different, in general agreement with the idea that where rapid movements are seen BM scaling may not be required (32).

In the present study, when the power data for unloaded jumping were used to determine a scaling factor for squat jumps, the scaling derived was 0.94, in general agreement with this idea of scaled values being unnecessary where higher velocity movements are used. However, despite this scaling factor approaching 1, when the data were compared in absolute terms, significant differences were seen in power, whereas when allometrically scaled the differences were not apparent. Therefore, it may be reasoned that here the data for higher velocity movements would still benefit from scaling to enable comparisons where BM is significantly different, in contrast to the previous observation by Markovic and Jaric (32). In addition, the scaling factors for both the back squat (0.28) and power clean (0.46) were somewhat lower than the exponent derived for squat jumps (0.94), and appear to reduce in line with the velocity of the associated movements.

In terms of comparisons between the scaling methods, both ratio and derived allometric scaling methods effectively removed any differences in power and strength between the subgroups, suggesting simple ratio scaling to be as useful for normalizing indices of performance as a derived allometric scaling exponent.

The findings of this study indicate that sprint performance (0–10 and 0–20 m) is significantly associated with the maximal squat and power clean performance, respectively, when normalized for BM. Performance in the power clean was also seen to correlate significantly with shorter sprint distances of 0–5 and 0–10 m. This could be partly because of the nature of the clean being more explosive in its performance, compared with the squat, and hence more similar to the requisite for acceleration in the short sprints. In addition, previous research has demonstrated that force production is a key determinant of sprint performance (26,45–49). It is likely the case that these early stages of the sprints were primarily related to the clean performance as the flying 10-m sprint showed no significance to either the clean or squat performance. Normalization here appears to negate the BM term; however, it is perhaps not a simple matter of using BM in either a linear (ratio) or power-(derived) related way. For example, it may well be that the scaling would be dependent on the task, that is lower or upper body. It could be argued that there are regional differences in the distribution of muscle mass to body fat ratios (6); in addition, it may also be that with increases in general BM the distribution between muscle and fat mass is not consistent. These factors will affect the use of scaling to normalize power across individuals of different BM and performances.

In terms of scaling method, it can be seen from Tables 2 and 3 that the sprint times for different distances were significantly correlated to both methods of scaled strength and power with no differences between the methods. Scaling squat jump power by either allometric scaling or linear scaling gave the highest correlation with jump height in contrast to absolute power vs. jump height. Where force-velocity multi-joint efforts have been recorded (39,40), the relationship is almost linear and thus maximal power would occur at half the maximum velocity or force generating capacity. Previous works by Nedeljkovic et al. (35,36) reported that normalized tests of muscle power can predict performance in rapid movement tasks such as running, this is in general agreement with the finding here.

It is worth noting that relationships do not infer cause and effect and that although scaled power clean and back squat performances show strong inverse correlations with short sprint performances, additional research exploring these relationships is recommended. Although research has shown that an increase in sprint performance appears to mirror increases in squat strength (9,23,30), it is suggested that further research investigate if increasing power clean performance in multisprint sport athletes' results in increases in sprint performance.

In addition, forwards demonstrated significantly greater (p < 0.001) mean momentum over 5 m (5,276.4 ± 363.6 vs. 4,409.1 ± 402.8 W), 5–10 m (7,526.6 ± 527.7 vs. 6,328.7 ± 559.8 W), and 10–20 m (8,578.3 ± 576.9 vs. 7,115.3 ± 801.1 W) compared with the backs, respectively. This greater momentum is a product of the significantly greater BM in the forwards, as the sprint performances were similar between positions. In practical terms, calculation of momentum in such athletes may be useful for coaches to be able to determine the effects of changes in BM and sprint performance on resultant momentum in sports where collisions between athletes are common. The greater the momentum of the individual the harder they are to tackle.

Practical Applications

The normalized power and force generating capacity for rugby league players can be seen to be significantly related to sprint and jump performance. Hence, for practical purposes, simple sprint times may provide adequate information regarding the power output of players. Scaling of power data effectively removes the potential confounding effects of BM between individuals. Both ratio and allometric scaling provide effective means for normalizing power data in this group. In addition, scaled power clean and squat performances demonstrate a strong inverse correlation with short sprint performance. It is suggested that strength and conditioning coaches' maximize both back squat strength and power clean performance, in a periodized manner, as this is likely to enhance short sprint performance. In addition, when comparisons between athletes are required, ratio scaling (dividing strength or power by BM) is simple and as effective as more complex allometric scaling.


No funding was received to support this study. The authors have no conflict of interest. The results of the present study do not constitute endorsement by the National Strength and Conditioning Association.


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ratio scaling; allometric scaling; power; strength; sprint performance

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