CTL, ATL and TSB: definition, formula, example

CTL, ATL and TSB are three curves drawn from the same daily training load. CTL (chronic training load) is usually called fitness, ATL (acute training load) fatigue, and TSB (training stress balance) form. They come from the impulse-response model Eric Banister published in 1975: every session raises both your fitness and your fatigue, fatigue fades within days, fitness over weeks, and performance sits somewhere in the gap between the two. The CTL, ATL and TSB names were popularised later by cycling software, but the maths is Banister’s.

How they are calculated

Start with one load number per day, for example the sum of the TRIMP of that day’s sessions (0 on a rest day). Fitness and fatigue are exponentially weighted averages of that series, with different time constants:

With τ = 42 days, the effect of a session on CTL halves in about 29 days; on ATL, it halves in under 5 days. Some tools use the moving-average shortcut 2 / (N + 1) for the daily weight. That is not the same model: with N = 42 it gives 0.047, twice 0.0235, which effectively halves both time constants and makes the curves react much faster (Clarke and Skiba, 2013, walk through the derivation).

Tools also differ on which day TSB uses. OpenAthlete subtracts the values of the same day, after that day’s load is counted; others use yesterday’s values, so that TSB describes how fresh you are when you start today’s session. On the same data the two can differ by a few points, so don’t compare numbers across apps.

A worked example

A runner has averaged 60 TRIMP a day for months: CTL and ATL both sit at 60, TSB at 0. They start a hard week at 90 a day. After the first day:

• CTL = 60 + 0.0235 × (90 − 60) = 60.7
• ATL = 60 + 0.133 × (90 − 60) = 64.0
• TSB = 60.7 − 64.0 = −3.3

After seven days at 90, CTL has crept up to 64.6 while ATL has jumped to 79.0: TSB is −14.4. The runner is a little fitter and clearly tired. They then drop to 40 a day for a week. ATL falls quickly to 54.3, CTL only slips to 60.8, and TSB turns positive at +6.5. That asymmetry, fatigue leaving faster than fitness, is the whole principle of a taper.

How to use them in training

CTL tells you how much training you have been absorbing over the last month or two. A steady rise of a few points a week during a build is the usual picture; a sharp jump is worth questioning, a long plateau too if you expected progress. ATL moves with each week and mainly explains why you feel heavy. TSB is the one people watch before a race: most athletes race well somewhere between slightly negative and clearly positive, but the right value is personal and you only learn it by noting your TSB before races that went well and badly.

The curves get more useful when they extend into the future. If your planned sessions carry a load estimate, the model can project CTL, ATL and TSB to race day and show whether the last two weeks really bring you in fresh. OpenAthlete does this: it computes the curves from your activities and projects them over the sessions in your calendar. It flags a TSB below −20 or above +25; those thresholds are conventions to describe the curve, not validated limits. See the training load page for the details and the code.

Limits

The model is only as good as the daily load you feed it. Heart-rate TRIMP underrates sprints, strength work and downhill running, so the curves miss part of what a trail runner or a triathlete does in the gym. Missing data hurts too: a week of runs without a heart rate strap looks like a week off.

The time constants are conventions. Banister fitted them per athlete, and fitted values vary widely; 42 and 7 days are reasonable defaults, not your physiology. Hellard and colleagues (2006) showed how unstable the fitted parameters are even with good data from elite swimmers. And nothing in the model knows about sleep, illness or stress outside sport. A negative TSB does not diagnose overreaching, and a high one does not mean you are ready. Read the curves with session RPE, HRV and how you feel.