Dual Factor Theory: The Fitness-Fatigue Model

A number of professions rely on exercise prescription to improve health and athletic performance. Among others, this includes those involving health and fitness training, rehabilitation from disease or injury, and sports performance.

Typically, coaches and health professionals approach the subject of exercise prescription empirically. Meaning, they predict the effects of training on an individual guided mostly by skill, experience, and ongoing monitoring. In contrast, the sports science community advocates a more evidence-based approach, in which exercise prescription is based exclusively on the current best available research.

However, while probably ideal, evidence-based exercise prescription is a challenging goal to accomplish. Controversies in the literature and data incompleteness add to the fact that people respond to training differently. As a result, in the effort to at least partially addressing these issues, exercise physiologists have developed mathematical models of training and performance.

Mathematical models have two main purposes. The first is to describe and predict the effects of training on performance in a more objective fashion. The second is to allow researchers to develop and test new theories, which might be useful in guiding training planning. In this regard, one of the most useful theories is the Dual Factor Theory, based on the Impulse-Response Model.

The Impulse-Response Model

The very first attempt at mathematically quantifying training and its relationship to performance was the Impulse-Response Model, proposed by Banister et al. in 1976. Essentially, the model describes how and how much an individual’s performance changes over time as a function of training.

In its original version, the Impulse-Response Model (IR Model) utilized four components to explain the effects of training on performance. However, that model was too complex and Banister simplified it focusing only on the input-output relationship between the quantity of training and the time of a criterion performance. Then, he used this simplified version to model the training and performance of a competitive swimmer.

The basic idea was that training sessions are short (hours) if compared to the time constants of the system (days). As such, it is legitimate to regard them as impulses. Meaning, each training session act as an impulse that generates an impulse response to performance after the session is over.

This approach was however too simplistic. Indeed, Banister noticed that his model did not adequately fit the data from the swimmer he had monitored.

Giovanni Baldi - Dual Factor Theory 3

Specifically, he noticed that performance decreased when the training load was increased. After repeatedly swimming long distances for several weeks, in fact, the swimmer could not perform very well. Banister attributed this phenomenon to fatigue and proceeded to modify his model to be a two-component system.

His new theory was that training sessions do not only generate positive effects on performance, but also negative effects. The positive training effects were ascribed to “fitness”, while the negative training effects to “fatigue”. Performance was calculated as the sum of the positive effects of fitness and the negative effects of fatigue. This latter version of the IR Model is better known as the Fitness-Fatigue Model, cornerstone of the Dual Factor Theory.

The Dual Factor Theory

The Fitness-Fatigue Model is at the basis of the Dual Factor Theory, which we can consider an improved version of the Single Factor Theory. Contrary to the Single Factor Theory (SFT), in fact, where the only variable is the response of the body to a single training stress, the Dual Factor Theory (DFT) proposes two independent outcomes to any stress event. These outcomes are fitness and fatigue.

Fitness is our physical capability to perform in sports and daily activities. It results from proper training and gradually improves over time if we continue to train effectively. However, fitness will decrease if we wait too long between training sessions or the workload is not enough to induce adaptations (detraining). Most importantly, fitness always has a positive effect on performance.

Fatigue, intended here as physical fatigue, is instead the momentary inability of a muscle to perform optimally. Fatigue also results from training but varies according to the workload performed in relation to workload capacity. In fact, the larger the workload, the more fatigue it will generate. The higher our work capacity, though, the less fatigue we will experience. Fatigue always has a negative effect on performance.

Performance is the sum of the positive effects of fitness and the negative effects of fatigue. Each training session increases the potential for improved performance yet, at the same time, causes fatigue that masks those improvements. However, after some recovery time, fatigue dissipates and the increase in performance becomes apparent.

It is important to point out that both fitness and fatigue depend on more factors than just training. Similarly, other external factors and stressors besides training affect performance. Therefore, it is impossible to completely isolate performance to the combination of fitness and fatigue. Nonetheless, their relationship remains one of the strongest determinants of performance.

Effects on Performance of a Single Training Session

According to the DFT, any training session will have both a fitness-building effect and a fatigue-inducing effect. Using the Fitness-Fatigue Model, this is how a single, isolated training session would affect performance.

Prior to the training session, both fitness and fatigue are zero while performance is at base levels. Then, the training impulse elicits a fitness response that increases performance, and a fatigue response that decreases performance. The fitness gain is supposed to be moderate in magnitude but long lasting. Conversely, the fatigue effect is greater in magnitude but shorter in duration (conventionally three times shorter for average training loads).

On the graph, fatigue initially outweighs fitness yielding a sudden drop in performance. This is what we experience when, after a hard training session, we cannot lift as much as we would when we are fresh. However, as the stressor (training) is removed, the body starts recovering. This process dissipates fatigue, and performance starts ramping up consequently.

Furthermore, because the negative effect of fatigue drops faster than the positive effect of fitness, fitness eventually outweighs fatigue. This means, at some point, fatigue no longer masks fitness and we are able to display our full physical potential. In other words, the virtual improvement in performance (fitness) coming from the training session becomes apparent. On the graph, supercompensation above baseline in the performance curve represents this state.

Over time, though, even the positive effect of fitness dissipates. This causes a progressive decrease in performance that gradually returns to baseline. We refer to this state as detraining. Now, although detraining is certainly something we want to avoid, keep in mind we are only looking at the effects of a single, isolated training session. Ideally, we would have a higher training frequency with multiple training sessions cumulatively adding up their effects over time.

Effects on Performance of Multiple Training Sessions

The case study of a single training session is good to understand the theory but less useful in practice. This because, if we want to keep making progress, we cannot expect to train every now and then. Reasonably, we would have a higher training frequency and go to the gym multiple times per week.

However, how do multiple training session interact with each other? And how do they affect performance overall? Luckily, the Fitness-Fatigue Model remains valid. Meaning, we can still calculate performance as the sum of fitness and fatigue. The only difference is that we also need to consider their residual effects coming from prior training loads.

For example, the graph below illustrates the effects of three consecutive training sessions. For simplicity, we will assume that each workout produces the same fitness and fatigue responses.

As you can see, the graph is not substantially different from the previous one. Just like in the single training session case, in fact, each workout elicits both a fitness response that increases performance and a fatigue response that decreases performance. However, because of the higher training frequency we are adopting, all these effects overlap.

This means that, when starting a new training session, we might still have residual fitness or fatigue coming from previous training sessions. Then, the new session will add new fitness to residual fitness and new fatigue to residual fatigue. Being the sum of the two, performance at some time is the sum of all positive effects of fitness and all negative effects of fatigue that are present at that time.

A very important thing to notice is the overall positive trend of performance on the graph. Essentially, this depends on two factors. The workload (volume) of each training session and the training frequency we decide to adopt.

Detraining, Overreaching, Overtraining

Part of the reason why the Fitness-Fatigue Model is valid is that it is capable of explaining various features of performance as a function of training. These features include the initial decrease in performance when training is increased and detraining effects when training is reduced.

In the graph above, performance has an overall positive trend. Yes, performance drops after each session because fatigue has a greater magnitude than fitness. However, the positive effects of fitness last longer. This determines a net gain in fitness and performance after each training cycle.

Ideally, performance would continue increasing with fitness over time, while fatigue would keep fluctuating without any net gain. However, things are not always going to be that simple. As we advance in training age, the push to drive progress often results in the accumulation of residual stress. Conversely, there will be times when we might have to markedly reduce training or cease it altogether. The Dual Factor Theory can capture and explain both statuses.

In the first case, an increase in training workloads and/or frequency causes the accumulation of residual fatigue. And when fatigue outweighs fitness, performance decreases inevitably.

At this point, there are two possible outcomes. The first outcome is that we insist training and accumulating fatigue to the point where performance starts regressing (overtraining). Instead, the second outcome is that we let fatigue dissipate through a period of lower stress. As you can see, this allows performance to come back to a level we would have never achieved otherwise. We call this state overreaching.

On the other hand, if we excessively reduce training volume and/or frequency, we will enter a state of detraining. In this case, not only fatigue but also fitness will dissipate. As a result, performance returns to baseline even though we are still training.


The Dual Factor Theory and the Fitness-Fatigue Model provide a window into the dynamics of adaptation to physical training.

Compared to other models, the Fitness-Fatigue Model stands out for its ability to capture several features of performance, such as detraining, overreaching, and overtraining. In particular, the Fitness-Fatigue Model overcomes one of the main flaws of the Supercompensation Model. That is, timing workouts to correspond to performance peaks.

This is possible because, in the Fitness-Fatigue Model, fitness and fatigue are completely separate identities. As a result, every time we train fitness improves right away. Only, the improvement in performance is not immediately visible because fatigue is hiding it. This means we don’t have to wait to be fully recovered before working out again. To maximize performance, we just need to keep fatigue at bay and let fitness display.

The same principle explains how we can make progress and advance in training age despite the accumulation of residual fatigue. As we know, every training session induces an increase in fitness. Therefore, as long as fatigue is capped, fitness and performance are free to increase every training cycle.

For all these reasons, the Dual Factor Theory is especially useful for guiding long-term training. Firstly, because it helps planning for tapering and peaking before competitions. Secondly, because it focuses on maximizing fitness while minimizing fatigue. This way, we can maintain higher levels of performance when training and consequently progress at a faster rate.


Calvert TW, Banister EW, Savage MV, Bach TM. A System Model of the Effects of Training on Physical Performance. IEEE Trans Syst Man Cybern SMC-6: 94-102, 1976. (Abstract)

Clarke DC, Skiba PF. Rationale and Resources for Teaching the Mathematical Modeling of Athletic Training and Performance. Adv Physiol Educ 37: 134-152, 2013. (Abstract)

Taha T, Thomas SG. Systems Modelling of the Relationship between Training and Performance. Sports Med 33: 1061-1073, 2003. (Abstract)

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