Banister's Fitness-Fatigue Model — CTL, ATL, TSB Explained

Quickstart

Want to know if you are fresh, flat, or grinding on a given day? The Banister fitness-fatigue model gives you a number, not a guess. Three numbers, in fact.

CTL: your chronic training load. Think of it as fitness.
ATL: your acute training load. Think of it as fatigue.
TSB: CTL minus ATL. Think of it as readiness, or form. Plus means fresh. Minus means tired.

A TSB above +5 puts you in the peaking zone. This is race-day turf. Don’t spend it on junk volume.

A TSB between −10 and +5 is where most training happens.

A TSB between −10 and −20 is a planned grind block. You can hold it for a few weeks, not forever.

A TSB below −20 means you are deep in the hole. A deload now beats one forced on you later.

That is the short version. The rest of this page covers the math, how to read your own curve, and why the model holds up so well.

The impulse-response idea

In 1975, Eric Banister had a simple idea. Training is a jolt to your body. Your body answers on two clocks. A fast bad answer, which is fatigue. And a slow good answer, which is fitness. What you can do on any day is the gap between the two.

This view did two things. It split the slow payoff of training from the fast cost. And it let scientists model both with simple decay curves. The math is older than the sport science. It is the same first-order curve engineers use for a charging battery, a thermostat finding its setpoint, or a pot of water cooling to room temperature.

The jolt is your daily training load. Banister called it TRIMP. TrainingPeaks calls it TSS. You can just call it “load.” It is one number for how hard a session was.

The answer comes out as two smoothed averages:

A slow one set to 42 days, for CTL. This is fitness.
A fast one set to 7 days, for ATL. This is fatigue.

A hard week spikes ATL fast and nudges CTL up slowly. A taper week drops ATL fast and lets CTL drift down slowly. The gap between them, CTL minus ATL, is TSB.

The math

Here is the smoothed-average formula for daily load L(t) with a time setting τ:

X(t) = X(t-1) × e^(-1/τ) + L(t) × (1 − e^(-1/τ))

Set τ to 42 days for CTL and 7 days for ATL. Each day you take yesterday’s value, let it fade a little, and add a slice of today’s load.

The curves come out smooth. One brutal session won’t whip CTL around, but it does move ATL. A full rest week won’t drop CTL to zero, but it does drop ATL to near zero.

TSB is CTL minus ATL each day. It is read on your own scale. A TSB of −15 for a 200-CTL cyclist is the same state as a TSB of −15 for a 60-CTL lifter. Each is measured against their own past.

Reading your own curve

The shape of your curve over 90 days tells a story. Here are five common shapes:

1. The classic peaking taper

CTL —————─────────────╲
                       ╲__
ATL —╱╲────────────────╲_____
         (big block)
TSB ────────── → ──── rising → +8

You ran a hard block. CTL climbed and ATL stayed high the whole time. Then you tapered. Load drops, ATL falls fast, CTL drifts down slowly, and TSB rises into the peaking zone. Race day sits at the TSB peak.

2. The slow grind (overreaching)

CTL ─╱╱╱╱╱╱╱╱╱╱
ATL ─╱╱╱╱╱╱╱╱╱╱
TSB ──────────── hovering at −10 to −15

You have trained hard for weeks with no taper. CTL is climbing, but ATL is right there with it. TSB stays negative. You can hold this for about 3 weeks in a typical block. After that, the curve starts to lie. You keep loading, but CTL stops rising, because your body can no longer soak up the work.

3. Detraining

CTL ─╲
ATL ──╲─────
TSB ──── → positive, then drifting down

You stopped training. ATL fell off in a week. CTL is drifting down over months. TSB went positive, but you are not fit. You are just rested. This is one of the model’s big lessons. A TSB above zero does not mean you are strong. It means you are fresh for your current CTL. If CTL is low, a high TSB is not a peak. It is detraining.

4. Maintenance

CTL ────────────
ATL ──╱╲──╱╲──╱╲──
TSB ──── oscillating around 0

Steady, moderate load. CTL flat. ATL waves through the week (heavy Monday, easy Saturday, and so on). TSB swings around zero. Dull, but healthy.

5. Return from injury

CTL ╲____╱╱╱
ATL ──____╱╱╱
TSB ──── deep positive → normalizing → near 0

You took two months off. CTL fell off a cliff. You came back with care, so ATL is rising slowly. TSB is deep positive, since there is no fatigue yet. Over weeks, CTL climbs and TSB settles toward zero as real training resumes.

Four of these shapes are healthy. One, shape 2 (the slow grind), is the warning sign. If you spot shape 2 for the second month in a row, you are sliding into overreach, and the numbers will start to fool you.

What counts as load?

This is where the model meets real training. Banister’s first version used heart rate (TRIMP). TrainingPeaks and Intervals.icu made it watts-based (TSS) for cycling. Most fitness apps stick to one sport.

Kinoku’s Form Band runs the model across three:

Gym tonnage: volume per session, tuned by RPE when you log it. A heavy 5x3 squat counts for more than a light 5x10 curl.
Run TSS: a training stress score from your heart rate or pace.
Brisk-step load: minutes above your brisk step pace, turned into a steady load.

One curve holds your whole training stress. That is the big edge over running-only tools that ignore gym days.

Using the curve: a simple routine

Most people check Form Band once or twice a week, not daily. Here is a routine that works:

Monday morning: look at last week. Did CTL climb? Did you get the load you planned? If TSB sits below −10, a lighter Monday may help.
Mid-block: in week 3 of a 4-week overreach, a deep negative TSB is normal. That is the plan. No need to worry.
Pre-event: plan a taper 10 to 14 days out. Aim for a TSB of +5 to +15 on race day.
Post-event: let ATL crash. Rebuild CTL only as fast as you recover.

Why the model works

The decay math is not exactly how the body works. You do not have one fitness clock or one fatigue clock. But the model proves useful in practice. It catches the direction of the two numbers well enough to guide real choices.

Newer models (Busso’s two-part version, Hellard’s per-person time settings) add a bit of accuracy at the edges. For most people who train on their own, the plain Banister model is already far more than they had before. Trading it for a fancier one rarely pays off.

The weak spots are known. Skip logging a session and your load drops, so CTL acts as if you rested. Garbage in, garbage out. Log a hard session as easy (or the other way around) and the TRIMP or TSS is wrong, so everything below it is wrong too. Honest logging is the price of using the model well.

Track this in Kinoku

The Form Band feature runs this model on your device across your gym, run, and brisk-step load. The Elite Analytics Recovery tab shows the 90-day curve, marked with peaking, overreaching, and maintenance zones. Tap any day to see the inputs behind that day’s CTL, ATL, and TSB. When you wonder why today’s TSB sits where it does, the math is right there.

Every step runs on your device. Your training record never leaves your phone. It is the same model TrainingPeaks made famous, but private and offline.