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Derivatives: Intensity vs Stability in Training

Sun Jan 25 2026

Most people fail from high volatility, not low effort.

We have been taught that better results require more intensity. More load. More sweat. More pain per session. It sounds true until you notice what it does to consistency. With squats, I started with something boring and stable: five sets of ten, adding five kilos each set. The work was predictable. I could show up, track it, repeat it. At some point I switched to something that felt more serious: timed sets, one-minute intervals, first set to failure, middle sets with reduced reps, last set to failure again. It was intense, but it was unstable. I lost connection with the process. It was harder to follow, harder to recover from, and harder to reproduce. I reverted to consistent reps with progressive overload. I will use differentials, a mathematical concept, to explain why.

You may not like math but spare me two minutes; a derivative is a measure of change. If you started running faster, your speed is the derivative of distance over time. It tells you how fast your output is changing. Training is the same, the useful part of derivatives is the question they ask: if I change the input a little, how much does the output move.

In calculus, when you differentiate xn, you get n xn-1. The power drops by one, and the expression gains a multiplier. In training terms, power is synonymous to intensity as multiplier is to stability. Differentiating essentially reduces intensity while improving stability. Big intensity spikes can look impressive, but can tempo be maintained? Small, controlled changes are less dramatic, but they multiply consistency. A practical example is running; sprints are high intensity, but they are not sustainable as a default mode. Working out is longer-term, and longer-term want smooth curves, not constant spikes.

The trap is that high-power moves feel like progress, especially early. Going to failure, shortening rest, maxing out load, stacking multiple changes at once. It creates a psychological signal of seriousness, but it often increases volatility faster than it increases capability. You gain a peak you cannot repeat, output becomes noisy, and recovery becomes unpredictable. The movement was borrowed from adrenaline and willpower.

Stability is a second-derivative skill.

Most people manage the first derivative (initial drive) without knowing it. They try to make the stimulus increase over time. More weight, more reps, more work. That is direction. The needed change to improve is about smoothness: how well the plan changes week to week without compromising consistency. The body can adapt to hard work, but it struggles to adapt to chaotic change. Volatility shows up as sessions you cannot repeat, inconsistent output, technique that degrades, recovery that becomes unpredictable, and friction before the set even starts. Intensity draws spikes. Differentials build slopes.

This is the practical takeaway, and it should make you kinder to yourself. The path to mastery is inevitable but you tolerate that phase better when you stop trying to learn everything at once. Your job is to return to differentials on purpose: change one variable at a time, respect improvement rates, and keep the tempo manageable enough that you can show up tomorrow with the same identity and nervous system. If you want a simple rule, use this: do not chase intensity that you cannot repeat.

More stability can look like less fire, but it is where compounding lives. The paradox is that the fastest growth often comes from slowing down the changes. If you want a higher peak, you do not start by climbing harder. You start by making the slope stable.

To grow faster, you often must slow down the changes.