With this article I would like to quickly raise some points that can and probably should be taken into consideration before looking at changes in athletes’ performance with percentages. The discussion of limitations of percentage-based approaches has been addressed in other areas including clinical medicine, neuropsychology and business marketing. With this said, it is greatly applicable to sports performance and particularly physical preparation given that practitioners are constantly assessing changes in athletes.
There are five key limitations related to analysing changes using percentages that I would like to raise and illustrate with some practical examples. However, first it is important to understand what a percentage is. Two common definitions of a percentage are: “a rate, number, or amount in each hundred”and “a proportion or share in relation to a whole”. Now, it is common to use percentages in everyday life, for example a shop advertising X% off certain products. But equally and more relevantly, percentages are very commonly used in the strength and conditioning practice to assess change, prescribe load, monitor load, etc., common examples being percentages of 1RM, or inter-individual percentages of distance covered in a match or training session. With this in mind, using percentages has almost become instinctive to grasp some understanding or conceptualize the magnitude or meaning of changes that have taken place. However, this approach can distort one’s perception of reality and it is important to understand some of the contextual limitations and underlying assumptions of using this ‘metric’ to inform practice.
Limitation number 1 – “The whole”
One of the key assumptions percentages make is that of a static reference (i.e. the whole). For example, percentages of one-repetition maximum (1RM) are commonly used to prescribe loads, track progress and inform suitable training intensities. The case is similar when assessing other physical qualities such as top speed. However, percentages assume that the whole (e.g. 1RM or peak m/s) is static, when clearly neuromuscular capabilities fluctuate substantially in relation to a range of factors (both internal and external) and contextual constraints. A very simple illustration of this may be achieved by simply asking a player to perform an exercise or drill (e.g. deadlift or 20m sprint) at X percentage of the whole (e.g. 85% 1RM) on the day after a fatiguing match versus following a 72hr active rest period. These inconsistencies risk that the athlete is subjected to an inadequate load and increase injury risk on a given day because in reality, “the whole” is not static, it’s continually changing.
Limitation number 2 – Muting of negative changes
Percentages can be misleading and misinform the decision-making process. In medicine this example is commonly described: which is scarier, undergoing a possibly fatal surgery that has a 95% survival rate or undergoing a possibly fatal surgery that causes 1 death in 20 patients? Clearly, the first seems a bit less worrying, but the “chances” of death are exactly the same in this example. Using a percentage-based approach can lead to similar mistakes in the sports performance realm. For example, in review of a season, a coach may be happy to see that 70% of the squad reported no injuries throughout the season. However, what if the squad was a basketball team of 20 players, and 6 out of those 20 experienced non-contact season-ending ankle injuries? Those are two very distinct performance reviews in my eyes! Real numbers provide greater clarity, whereas expressing percentages can mute the impact of negative changes.
Limitation number 3 – Positivist bias
A major concern in terms of prescription of training intensities or loads is that percentages are positively biased (i.e. asymmetric). What do I mean by this? Simple as it sounds, percentages naturally favour larger numbers, and in the training world this can actually be the reverse of reality. For example, let’s say we are looking at a rookie footballer and a first squad footballer with 3 years of experience at the D1 level. The rookie is bench pressing 100 kg for 5 reps, whereas the experienced player is pressing 150 kg for the same reps. The players want to add 25% to their bench press loads over a given time period. That is an additional 25kg for the rookie (125kg lift), and an additional 37.5 kg for the experienced player (187.5kg lift). Now, if you have any experience in the gym whatsoever, you will know that the stronger you get the slower the rate of returns. Therefore, using a percentage-based approach in this regard is incongruent with reality (i.e. it will be harder for the experienced player to achieve that 25% gain than it would for the rookie).
Limitation number 4 - Ambiguity
Percentages lack identity and therefore are ambiguous. 0 is the addition constant and 1 is the multiplication constant of any number (i.e. A + 0 = A and A x 1 = A), the same is not true for 100 (i.e. %), so why 100? On the other hand, if percentages were intended to describe probabilities, and probabilities are a number between 0 and 1, what does a percentage add to the mix? This is made even more confusing by the fact that percentages do not correspond to units of measurements as 0 and 1 do. This inevitably means that percentages do not see fit in certain contexts. For example, a 20% change in endurance capacity is achievable by manipulating environmental conditions, a 20% body weight loss can take up to a year of hard work depending on a whole host of factors and a 20% improvement in a 100m sprint can a) never happen or b) take an entire professional career to achieve. So, percentages really do not always achieve what they set out to achieve in summarising relative changes.
Limitation number 5 – The percentage change confusion
Finally, percentages can be inherently confusing and misleading in the sense that it takes a person to decide what value is being used as the reference value (i.e. the whole). This is similar to the first limitation I mentioned, but it is also different. I’ll explain. It is particularly misleading when using percentages to assess asymmetry or differences between two systems; and this confusion is not present when we use absolutes to analyse such differences. For instance, we commonly employ percentages to assess limb asymmetries in physical preparation; it is popular to assess hamstring strength asymmetries or deficits at an inter-limb level. But, then the question remains, the difference is a percentage of what? And why? We may have an athlete that is coming back from a hamstring injury on his dominant leg. In his first session back, the dominant hamstring has a strength value of 300 N and the non-dominant of 350 N. After a given period of training, the dominant hamstring re-gains strength and achieves a strength of 400 N and the non-dominant also gains some strength and reads 360 N. I will summarise the values below to illustrate how confusing assessing such differences with a percentage-based approach can be.
Pre-training hamstring strength values:
Dominant leg: 300 N.
Non-dominant leg: 350 N.
Absolute difference: 50 N.
Percentage difference (using dominant as reference): 50N / 300N x 100 = 16.67%
Percentage difference (using non-dominant as reference): 50N / 350N x 100 = 14.29%
Post training hamstring strength values:
Dominant leg: 400 N.
Non-dominant leg: 360 N.
Absolute difference: 40 N.
Percentage difference (using dominant as reference): 40N / 400N x 100 = 10%
Percentage difference (using non-dominant as reference): 40N / 360N x 100 = 11.11%
Case almost closed. If we’re looking at inter-limb differences with percentages, we may end up interpreting the wrong thing. In this example, using the dominant leg (pre-training) as the reference point yielded a superior percentage difference than having used the non-dominant leg as a reference (i.e. 16.67% vs. 14.29% respectively). The opposite is true post-training (i.e. 10% vs 11.11% respectively). It is common practice to use the maximum value between the two limbs as the reference value (i.e. the whole). However, in a situation where the direction of the deficit changes, such as that of the above hypothetical training intervention, looking at differences as a percentage of the inter-limb maximum value is telling us two different stories because the 100% changed in magnitude and direction. Ultimately, making the interpretation a heck of a lot more confusing than simply saying:
“The difference in strength between left and right hamstrings was 50N in favour of the non-dominant leg and now it is 40N in favour of the dominant leg.”
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