Modeling Human Performance

There are a number of approaches to modeling how training changes performance and these models have some obvious value in optimizing a training routine, especially for tapering. Despite its simplicity, the TSB model has become the most widely used. The TSB model doesn't have the complexity to predict absolute performance, but can provide numbers that can be compared between athletes. As a result, there is a body of knowledge around how training stress should be built up and good targets for training stress for various levels of athlete. However, these models describe what you did rather than how you responded, they predict performance poorly, and none has been validated for judging whether you are ready to train on a given day (see Flaws in the models and Training Readiness).

TL/DR

Here's the key points that are good to understand.

• Choose a method for calculating TRIMP (AKA TSS). The best options are power or heart rate, normalized to 100 for an hour at Critical Power.
• Use the simpler TSB model, which is widely supported in various software packages such as Runalyze.
• Remember that the constants of 42 and 7 days are not what they seem. Your workouts are not averaged over 42 or 7 days. Each workout's contribution decays exponentially: with the formula TrainingPeaks uses, it halves about every 29 days for CTL and about every 4.5 days for ATL, and about a third of it remains after 42 or 7 days respectively.
• Use CTL to measure overall training load, to compare recent training with past periods, and to check that training isn't ramping up too quickly. It's counterintuitive, but this is how the model is generally used in practice.
• Don't use TSB or ATL to decide whether you are ready for today's session (see Training Readiness).

Training Stress

All the models are based on quantifying the stress of a workout using a "training impulse" (TRIMP for TRaining IMPulse) or TSS (for Training Stress Score). There are many ways of calculating TRIMP, and any method can be used with any model if the TRIMP is consistent. However, different methods give different answers and cannot be used interchangeably (see TRIMP).

The Models

The models assume that given a given TRIMP has both a positive and a negative effect. The positive effect is called "fitness" or Chronic Training Load (CTL), and the negative effect is called "fatigue" or Acute Training Load (ATL), and they are combined to provide a value of "performance" or Training Stress Balance. This article looks at three models:

• Banister. The initial work on modeling human performance was made by Eric Banister in 1975 and has been tested in a number of studies, including one on runners.
• Busso. The work of Banister was refined by Thierry Busso to modify the Banister model to at least partly account for how Training Monotony impacts recovery.
• TSB. The Training Stress Balance model is a simplification of the Banister model by Andrew Coggan which looks at just the relative changes in performance.

The TSB model will be examined first, as it's the simplest to understand.

The TSB Model

Training Stress Balance (TSB) uses the terms Chronic Training Load (CTL) for "fitness", Acute Training Load (ATL) for "fatigue" and Training Stress Balance (TSB) for "performance". As with all the models, both CTL and ATL are based on TRIMP, with the effect of a given workout reducing with passing time, but the effect lasts longer on CTL than on ATL. Because of the longer timeframe for CTL than ATL, the effect is spread out more, so the peak for a single workout is lower. Typically, CTL uses a 42-day time constant and ATL uses a 7-day time constant. (These numbers are misleading, as the impact of a workout lasts forever, approaching but not reaching zero. With the formula TrainingPeaks uses, the impact of a workout halves about every 4.5 days for ATL and about every 29 days for CTL.)

TSB for a Single Workout

The image above shows the effect of a single workout on the Training Stress Balance. You can see the workout creates a peak in both ATL and CTL. The peak is greater ATL, but reduces more quickly than in CTL. The Training Stress Balance is CTL-ATL, and you can see it initially go negative indicating a reduced ability to perform, then rises to be positive as CTL becomes greater than ATL. This green TSB line is the same as that seen in Supercompensation.

TSB for Multiple Workouts

The effect of a continuous series of identical workouts on TSB is shown in the image above. The ATL rises sharply and reaches a steady-state, with CTL rising more slowly to a greater level. The TSB (CTL-ATL) goes negative, slowly returning to zero.

TSB Constants

Because the TSB model is simpler than the other two, it only requires the time constants for ATL and CTL. The typical starting point is 7 days for ATL and 42 days for CTL.

Calculation Details

Understanding these details is not required for using the TSB, but you may find them interesting.

The TSB Formulas

TrainingPeaks describes CTL as an exponentially weighted average of daily training stress, calculated like this:

CTLtoday = CTLyesterday + (TRIMPtoday – CTLyesterday) × (1/Nf)
ATLtoday = ATLyesterday + (TRIMPtoday – ATLyesterday) × (1/Na)

Where N_f and N_a are the time constants, normally 42 and 7 days. This is the same as an exponential moving average with a weighting of λ = 1/N:

CTLtoday = TRIMP × λf + (1 – λf) × CTLyesterday

As you can see this is an iterative approach, calculating the value for the oldest workout, then iterating through each subsequent workout. After N days, (1 – 1/N)^N, or about 36%, of a workout's contribution remains. The half-life is ln(0.5)/ln(1 – 1/N), which is about 28.8 days for N = 42 and 4.5 days for N = 7.

Some descriptions instead use the standard weighting for an N-day exponential moving average, λ = 2/(N+1). That gives much shorter half-lives of about 14.6 and 2.4 days, and earlier versions of this page used it. Check which weighting your software uses before interpreting the numbers.

Limitations of the TSB model

The main limitation of the TSB model can be seen in the graph above, which shows that training reduces performance and never improves it. The TSB model only indicates an improved performance when training is reduced, as shown below.

The TSB model when training is reduced from a stable level of 100 TRIMP per day to zero, showing the rapid drop in fatigue (ATL) and the slower drop in fitness (CTL), resulting in an improved performance (TSB).

TSB is often used as "form" to judge readiness or to predict race-day performance, but it has not been validated in peer-reviewed research for either purpose (see Training Readiness).

CTL for Fatigue?

Looking at the body of knowledge that's been built up around the TSB model, it becomes clear that it's CTL rather than ATL that's used to measure fatigue and overall training load. There are web sites with recommended CTL levels for different events and different training levels. I've seen very little writing about managing ATL, and it's mostly use to calculate TSB, which in turn is used to estimate short term recovery for tapering. In my experience, the most useful thing CTL shows is how recent training compares with historical periods.

The Banister Model

The Banister model is a little more complex mathematically than TSB, using an exponential decay to model the effects of training stress. Unlike the TSB model, the Banister model will show that a steady state of training will improve performance. Of the available models, Banister's is the most experimentally validated, although it fits past data far better than it predicts future performance (see Flaws in the models).

The Banister Formula

The formula below looks rather complex, but is actually fairly simple to implement.

Here it is as some simple pseudo-code for those that want to implement it.

fitness = 0;
TRIMP[] = getDailyTRIMP(); //array of TRIMP for each day
for(i=0, i < count(TRIMP); i++)
{
    fitness = fitness * exp(-1/r1) + TRIMP[i];
    fatigue = fatigue * exp(-1/r2) + TRIMP[i];
    performance = fitness * k1 - fatigue * k2;
}

This model uses four constants.

• k1 is a positive weighting constant for fitness.
• k2 is a positive weighting constant for fatigue, with
• A larger k1 than k2 indicates an individual takes longer to recover, whereas a larger k2 than k1 indicates a faster recovery.
• r1 is the time decay for fitness in days (how long does it take for fitness to return to baseline).
• r2 is the time decay for fatigue in days (how long does it take for fatigue to return to baseline).
• Because fitness lasts longer than fatigue, r1 is larger (longer) than r2.
• The original paper used values of k1=1.0, k2=1.8-2.0, r1=49-50, r2=11.

The Busso Model

Thierry Busso created a refinement of the Banister model to try to take account of how an increase in Training Monotony also increased fatigue. This modification of Banister changes k2 from being a constant to being an exponential decay of the training stress.

The value of k2 uses a similar exponential decay:

Flaws in the models

There are a number of practical flaws in these models.

• The main flaw with the Banister and Busso models is that the values for the constants used are specific to each individual, and possibly to the particular training regime. The verification of the Banister and Busso models reverse engineered the constants so that the model accurately predicted the performance changes. In elite swimmers, the fitted decay constants averaged 38 days for fitness and 19 days for fatigue, with wide uncertainty (17–59 and 6–32 days), and some parameters were so correlated that the authors described interpreting them as worthless. A commentary on the model advised against using general constants, because fitted values depend on starting values, fitting technique and the training-load measure used.
• The models fit past data well but predict poorly. In 11 swimmers followed for 61 weeks, the best models predicted performance with a mean error of 2.0–2.7%, which the authors judged not satisfactory for individual training planning. A 2025 analysis found that adding the fatigue component did not improve prediction in two datasets, and questioned its biological relevance. Machine-learning models have generalized better than fitness–fatigue models in small groups of athletes.
• The values of the constants and the resulting predictions also depend on the performance metric being used.
• Another flaw is that the models assume a single value for that represents the adaptation to performance. In practice, different types of adaptation occur at different rates.
• The TSB and Banister models ignore Overtraining & Training Monotony and predict that any possible workload produces improved fitness.
• The TSB model assumes that training does not produce an improved performance. Instead the TSB model only detects a change in training level, with reduced training improving performance and increased training reduces performance.
• I suspect one of the biggest problems is that training impulse doesn't truly capture all aspects of training stress, and also ignores non-training stresses such as poor sleep or emotional stress, even though the consensus definition of overreaching includes both.

Comparison of the Models

• The TSB model is simpler than the other two models as it only has the two decay parameters.
• The Banister model has more experimental verification than the other models.
• The Busso model is the most complex, but is the only one that allows for Training Monotony.

See also

• TRIMP
• Training Readiness
• Supercompensation