Not all training goes into what you're training for..
We usually think all the effort expended in training goes into what is being optimised for: strength, muscle mass, endurance. There is a factor in the equation of outcomes that is very frequently overlooked. It can be termed fatigue or friction, which F to choose is up to you.
Adaptation = Stimulus − Fatigue
A = S - F
Where:
Adaptation A(t) = overall gain over time
Stimulus S(t) = effort expended
Fatigue F(t) = accumulated debt from energy depletion, wear and tear, tiredness over time
All three are functions of time and adaptation is a net fuction of accumulated stimulus and fatigue. A more precise representation using summations and rate of changes: integrals and differentials in mathematical terms is such that for a given time (t):A(t) = ∫0t S(τ) dτ − ∫0t F(τ) dτ
This means that the current metric you are optimising for, for example how strong you are, is a sum of all the actions taken over time t: adding the resulting stimulus per session τ and subtracting the accumulated fatigue, gotten by adding up the friction per session τ The workout that brought about strong legs is the same one that made the legs tired. Same coin, different sides, even though they are actually different qualities:
Stimulus S(t): the training signal applied at time t. Load, volume, intensity. This is what you control.
Fatigue F(t): accumulated biological debt at time t. A state variable, not a rate. It builds from stimulus and decays with rest.
Adaptation A(t): accumulated fitness quality at time t. Also a state variable with its own dynamics.
The differential form, what’s happening right now is:
dA dt = S(t) − F(t)
There will be a net increase in adaptation when stimulus exceeds fatigue. To get the outcomes over an extended period, integrating both sides yields:
Both F and A are driven by S, but they are separate responses to the same input, not one thing subtracted from the other. Fatigue is fast and loud. It accumulates quickly and is immediately felt. Adaptation is slow and quiet. It builds underneath the fatigue, only visible when fatigue clears. This births three states in practice:
| State | Condition | What is happening |
|---|---|---|
| Productive | S(t) > F(t) | Adaptation is growing |
| Overtraining | F(t) > S(t) | Fatigue consuming more than stimulus builds |
| Plateau | S(t) = F(t) | Effort without net gain |
Training hard and becoming overly tired produces less results because more effort goes into compensating for fatigue. This is why deload weeks matter. Reducing the stimulus allows fatigue to decay faster than adaptation fades, narrowing the gap to let what you have already built surface. A deload is not lost time. It is the clearing of debt that was hiding the result.
Viewed over time, beneficial and detrimental effects stem from the same stimulus; they are interdependent, and whether an effect is judged “bad” depends on your perspective.