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# Interlimb Asymmetry: Calculations, Interpreting Data and Adding Direction

Updated: Jan 17

We are delighted to welcome Dr Chris Bishop for this guest post on calculating interlimb asymmetries. Chris is a Senior Lecturer at the London Sports Institute at Middlesex University, as well as the Programme Leader for the MSc in Strength and Conditioning. He is also the Chair of the Board for the UKSCA.

There have been multiple publications recently in the area of interlimb asymmetries. In this article, he summarises the literature in this area and the practical implications for those collecting such information. Further information on these publications can be found on the project page on ResearchGate.

## Introduction to the Asymmetry Calculation

Recent years has seen an increase in the number of articles investigating the prevalence of inter-limb asymmetry in both healthy and injured athletic populations. Whilst no universally accepted definition exists to date, Keeley et al. [17] define inter-limb asymmetry as the difference in performance or function of one limb relative to the other. This represents an important distinction to intra-limb asymmetry which addresses imbalances within the same limb (e.g., hamstrings to quadriceps ratio). The remainder of this article will focus on inter-limb asymmetry.

Previous articles have identified that multiple formulas exist for calculating between-limb differences [5,7]. This poses challenges to practitioners given that there often is not any obvious reason why one formula should be chosen over another. Bishop et al. [5] highlighted the existence of this “calculation conundrum” and encouraged practitioners to consider which method may be right for them.

A more recent article, in response to this, highlighted that different formulas might need to be considered for the quantification of inter-limb asymmetries during bilateral and unilateral tasks [7]. For example, during a countermovement jump (CMJ), if practitioners wish to quantify between-limb differences in a given metric (e.g., peak force), it is likely that the imbalance must be expressed relative to the total output given that both limbs are interacting together. The key point here being that if each limb is not acting independently, the quantification of imbalances should not be treated as separate entities.

“If each limb is not acting independently, the quantification of imbalances should not be treated as separate entities.”

In contrast, during a single leg CMJ (SLCMJ) there is no contribution from the other limb; thus, quantifying any existing side-to-side differences can be done without considering the opposing limb’s involvement (noting that it has none). This is best represented by Table 1 (below), which uses a hypothetical scenario of two separate peak force values (800 and 700 Newtons [N]). In this example, the reader should assume that the 800 N value corresponds to the dominant (D), right, stronger, preferred and uninjured limb. Naturally, there is no guarantee that test data will consistently present itself in such a way and this article will discuss these complications later on.

## Differentiating between Asymmetry Test Methods

Before deciding which formula to use, first we must consider the notion of how standard percentage differences are calculated. For this, we must comprehend how fractions of 100 are computed, noting that traditional mathematics only teaches this one way (i.e., in relation to the maximum value) and that difference then gets expressed as a percentage of 100. Thus, with standard percentage differences quantifying imbalances relative to the maximum value, Table 1 highlights three formulas which calculate our hypothetical peak force asymmetry value in such a way: Bilateral Strength Asymmetry, Symmetry Index and the Standard Percentage Difference method.

The Bilateral Strength Asymmetry and Standard Percentage Difference equations are set up to always calculate the percentage difference the same way, noting that the equations themselves do not change, just the raw data that goes into them. In addition, the reader should note that these formulas do not consider the total value generated by both limbs; therefore, these can be considered when calculating inter-limb asymmetry from unilateral test methods.

Table 1 also shows that the majority of formulas have previously chosen to define inter-limb differences in terms of ‘dominance’. Thus, the reader could look at Table 1 and think that the Limb Symmetry Index 2 formula could be used to calculate asymmetry from unilateral test protocols. However, when defining limbs via dominance, there is no guarantee that the dominant (D) limb will always get the larger score, especially in healthy athletes which has been shown in previous research [9,14].

To prove this point, if we swap the peak force values around in that second equation from Table 1 so that the D limb now scores 700 N instead of 800 N, the asymmetry value becomes -14.3%. The negative sign tries to tell us that the non-dominant (ND) limb scored higher; however, it has compromised the magnitude of asymmetry, which was previously determined from our standard percentage difference. In addition, given the absolute difference between limbs has not changed (i.e., 100 N), it seems strange that the percentage difference should be altered. Thus, it seems apparent that not all equations are robust enough to withstand every scenario that may be presented to practitioners. Therefore, when calculating asymmetry from unilateral tests, the formulas proposed by Impellizzeri et al [16] or Bishop et al. [7] are the suggested options because they adhere to fundamental mathematical principles and abide by the standard percentage difference rule.

When calculating asymmetries from bilateral test methods, the formulas proposed by Kobayashi et al. [18] or Shorter et al. [28] calculate between-limb differences relative to the total value, remembering that this is suggested because both limbs are interacting together. Whilst other formulas also do this in Table 1 (e.g., Bell et al. [3], Wong et al. [30] and Robinson et al. [25]), there is no evidence to suggest that the asymmetry outcome should be altered anywhere in the formula by either dividing by 0.5, multiplying by 2 or dividing by 2 respectively. Thus, the proposed formulas for calculating inter-limb differences during bilateral tests are either the Symmetry Index or Bilateral Asymmetry Index 1.

Now that proposed formulas have been suggested for the quantification of asymmetries, it is important to realise that practitioners are merely left with a percentage value, known as the magnitude of asymmetry. Previous literature has tried to suggest that magnitudes of 10-15% may increase the risk of an athlete getting injured [2,19,24,26]. However, with an abundance of evidence to show that asymmetries are task-specific [4,6,8,9,15,20,21,23], this notion appears rather superficial given that any magnitude could only be applied relative to the chosen test, metric or population in question. Thus, when left with the magnitude of asymmetry, it poses the question of how to interpret the data.

## Interpreting the Magnitude of Asymmetry

Exell et al. [13] highlighted the need to consider intra-limb variability in conjunction with the inter-limb difference value. In short, it was inferred that an asymmetry may only be considered real if greater than the variability in the test. From a testing perspective, we can measure variability in the form of the coefficient of variation (CV) which is determined by looking at the standard deviation relative to the mean, and then expressed as a percentage by multiplying by 100 [29]. Previous literature has suggested that values < 10% [11] or 5% [1] can be considered as acceptable variability. Despite any disagreement on a proposed threshold, it is accepted that the lower the CV value, the more reliable the test or metric [29].

Where asymmetry is concerned, practitioners need to be able to differentiate between what is greater or smaller than the error in the test. Thus, reporting any existing side-to-side differences in conjunction with test variability (i.e., the CV) may help to differentiate between the ‘signal and the noise’. Furthermore, both values are reported in percentages providing practitioners with an easy comparison between the two.

Figure 1 shows hypothetical individual asymmetry values for peak force during a CMJ. In this example, the CV has been mapped onto the graph as a red dotted line at 4%, highlighting that peak force is a reliable metric to consider during the CMJ. When each individual’s asymmetry score is plotted (blue bars), this provides a clear visual representation of who is exhibiting a between-limb difference in peak force greater than the variability in the test. It is important to note that this does not mean that any athlete exhibiting a real asymmetry must undergo a targeted intervention to reduce the existing deficit, as this data only represents a single time point. Previous research has highlighted the variable nature of asymmetry [4,6,8,9,12,20,21]; thus, it is probable that when athletes are tested again, their inter-limb asymmetry value may change. Equally, assuming test protocols are robust, the CV value should not vary much with minimal change and low values being a sign of a consistent and usable metric.

A final point of consideration when viewing Figure 1, is that all asymmetry values are positive, which is a by-product of always using the maximum score as the reference value in the equation (as per standard percentage difference calculations). Recent literature has highlighted the importance of the ‘direction of asymmetry’ [22], which refers to the consistency of asymmetry favouring one side (i.e., right vs. left or D vs. ND). However, as previously mentioned, some equations provide the direction of asymmetry (by creating a negative value) but also compromise the magnitude if the ND limb scores larger. Thus, practitioners need a way to calculate the direction of asymmetry, without altering the magnitude. This can be done by adding on an ‘IF function’ to the end of the relevant equation in Microsoft Excel:

*IF(D<ND,1,-1)

Simply put, this tells the asymmetry value to become negative if the ND limb is the larger value without changing the magnitude, and is represented in Figure 2. Therefore, when defining limbs via dominance and aiming to monitor the direction of asymmetry, the following equations are suggested for bilateral and unilateral tests:

1. Bilateral tests: ((D–ND)/Total*100)*IF(D<ND,1,-1)

2. Unilateral tests: ((D–ND)/D*100)*IF(D<ND,1,-1)

The direction of asymmetry may actually be a stronger consideration for practitioners when monitoring inter-limb asymmetry in healthy athletes. For example, when an athlete is injured, an obvious between-limb deficit will exist; thus, the magnitude of asymmetry is likely to be interpreted in relation to the injured limb. In contrast, if healthy athletes have had a consistent period of training/competing without injury, and practitioners are fully aware of that athlete’s training/injury history, there is arguably less reason for a between-limb difference to be present. In short, using the magnitude alone may be missing a piece of the puzzle when reporting an athlete’s between-limb deficits.

This notion is supported by Bishop et al. [6] who used a test-retest design to monitor both the direction and magnitude of asymmetry in 28 healthy recreational athletes. The Kappa coefficient was used as a statistical method to quantify how consistently asymmetry favoured the same limb between test sessions in the unilateral isometric squat, SLCMJ and single leg drop jump (SLDJ). Kappa values ranged from fair to substantial (0.29 to 0.64) in the isometric squat, substantial in the SLCMJ (0.64 to 0.66) and fair to moderate (0.36 to 0.56) in the SLDJ.

These findings are further supported in previous work by Bishop et al. [4], who again used the Kappa coefficient to report the consistency in the direction of asymmetry for comparable metrics across tests. When peak force was compared across the unilateral isometric squat, SLCMJ and single leg broad jump, Kappa values ranged from slight to fair (-0.34 to 0.05). Thus, when the available evidence is considered, it appears the direction of asymmetry may be just as variable as the magnitude, especially in healthy athletes. This has led to recent suggestions that the interpretation of inter-limb asymmetry should be done on an individual basis, rather than using the group mean value as a guide.

For a more detailed guide on how to use the Kappa coefficient to assess the direction of asymmetry, watch the video below:

## Conclusion

As the evidence suggests, calculating inter-limb asymmetries is perhaps more complex than we might think. The selection of an appropriate equation may depend on the nature of the test selected (e.g., bilateral or unilateral); however, it is essential that practitioners always keep in mind the needs of the athlete when selecting the most appropriate test. Owing to asymmetry being a variable concept, there is a need to be able to distinguish between ‘the signal and the noise’, which is why practitioners may wish to consider the CV to be useful when interpreting asymmetry scores. Finally, the use of an IF function in Microsoft Excel can enable the direction of asymmetry to be monitored without altering the magnitude, and should be considered as an additional tool in understanding the both the relevance and consistency of asymmetry in healthy athlete populations.

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