CTL, ATL, and TSB, the three curves that predict your race performance

Every training platform shows three curves: CTL, ATL, and TSB. Coaches throw these acronyms around like everyone knows what they mean. But most athletes either ignore them (too abstract) or obsess over them (checking daily like a stock ticker). Neither approach works. This post explains what the curves actually measure, the one equation that powers all three, and how to use them to peak for race day.

The Banister model: one equation, three curves

In 1975, exercise physiologist Eric Banister proposed that athletic performance could be modeled as the difference between two competing processes: fitness (positive training effects) and fatigue (negative training effects). Both respond to the same training stimulus (TSS), but on different timescales.

The math is an exponentially weighted moving average (EWMA). For each day:

That's it. Same formula, two different time constants: 42 days for fitness (slow to build, slow to fade) and 7 days for fatigue (fast to spike, fast to clear). TSB is just the gap between them.

The genius of this model is its simplicity. One input (daily TSS), one equation, three outputs. It won't capture every nuance of human physiology, but it's been validated across 50 years of research and remains the backbone of every major training platform.

What the time constants mean

The number 42 (CTL) and 7 (ATL) aren't magic, they're time constants that control how fast each curve responds to new training. Here's the intuition:

• CTL (τ = 42 days): after a single training day, CTL moves only ~2.3% toward today's TSS. It takes weeks of consistent training to shift CTL meaningfully. This is why "fitness" in the Banister model represents deep physiological adaptation, it can't be built in a weekend.
• ATL (τ = 7 days): after a single training day, ATL moves ~13% toward today's TSS. One hard week and ATL spikes. One easy week and it plummets. This is why "fatigue" responds fast, it captures the short-term cost of recent training.
• TSB = CTL − ATL: when you train hard, ATL rises faster than CTL → TSB goes negative (you're tired). When you rest, ATL drops faster than CTL → TSB goes positive (you're fresh). This asymmetry is what makes tapering work.

A common misconception: some resources use 1/τ as the smoothing factor instead of 1 − e−1/τ. For CTL (τ=42), the difference is small (~1%). But for ATL (τ=7), the approximation overestimates the smoothing factor by ~7%, enough to make ATL respond too aggressively and produce inaccurate TSB readings. The exponential form is the mathematically correct version.

Watching the curves respond

The best way to build intuition is to see how CTL, ATL, and TSB respond to different training patterns. Select a scenario below and watch the curves:

Key observations from the scenarios above:

• Single hard day: ATL spikes immediately, CTL barely moves. TSB plunges negative and takes ~10 days to recover. One ride doesn't build fitness, but it definitely creates fatigue.
• Steady training: CTL gradually climbs toward the daily TSS level. After ~6 weeks, CTL and ATL converge and TSB stabilizes near zero. You've adapted to the load, time to increase it or add a build block.
• Overreach + recovery: during the hard block, TSB drops to -20 or below. During the rest week, ATL drops fast while CTL barely dips. TSB swings positive, you're fitter AND fresher than before the block started. This is supercompensation.
• Race taper: the build phase raises CTL high. The taper drops ATL fast. TSB crosses into positive territory. The sweet spot for race performance: TSB +5 to +25 with the highest possible CTL.

The TSB spectrum: where are you right now?

Your current TSB tells you what kind of training day is appropriate. Not every day should be hard, and not every easy day is wasted, it depends on where you sit on the spectrum.

The critical insight: TSB is not a performance score where higher is always better. A TSB of +40 means you've rested so much that CTL is falling, you're deconditioned, not "super fresh." The optimal zone for race performance is positive but modest: +5 to +25, with the highest CTL you can maintain.

Peaking for race day: the taper

The taper is the most counterintuitive part of training: to perform your best, you train less. The science is clear, a well- executed taper improves performance by 2-6% compared to training through a race. For competitive cyclists, that's enormous.

The mechanism is pure Banister math: cut training volume by 40-60%, and ATL drops 40-60% in 10 days while CTL drops only 3-5%. TSB swings from deeply negative to the +5 to +25 window. You arrive at the start line with nearly all your fitness and very little fatigue.

Experiment with the simulator below. Notice the trade-off: taper too short and you arrive still tired; taper too long and you start losing fitness.

Research-backed taper guidelines:

• Duration: 8-14 days for most endurance events. Shorter (5-7 days) for crits and short road races. Longer (14-21 days) only for grand tours or if deeply fatigued.
• Volume cut: 40-60% of your build-phase volume. This is the most important variable. Cutting volume sheds fatigue while keeping enough stimulus to maintain fitness.
• Keep intensity. This is critical. Don't replace intervals with more Zone 2 during the taper. Keep 2-3 short, sharp sessions (e.g., 4×4min at VO₂max) but reduce the number of sets and total duration.
• Target TSB +5 to +20 on race day. Use the chart to plan backward from your event. If your current TSB is -20 and race day is 10 days out, the math tells you exactly what volume to taper to.

Building fitness safely: the ramp rate

How fast can you raise CTL without breaking down? This is the ramp rate question, and it's where most athletes get into trouble. The temptation is always to do more, especially when motivation is high and the body feels good.

The research consistently shows that a CTL ramp rate of 3-7 points per week is sustainable for most athletes. Above 7, illness and injury rates climb sharply. Above 10, you're almost certainly headed for a forced break.

Set your current CTL and weekly TSS target below to see where your ramp rate falls.

An important subtlety: the ramp rate naturally slows as CTL rises. If your CTL is 30 and you train at 500 TSS/week, the ramp is steep. At CTL 80 with the same 500 TSS/week, the ramp is much smaller. This isn't a plateau, it's the math. To keep climbing at the same rate, you'd need progressively more TSS, which eventually exceeds your recovery capacity. This is why periodization matters: build for a while, rest, then build again at a higher baseline.

Common mistakes with the PMC

• Chasing CTL as a goal. CTL is a descriptor, not a target. A CTL of 100 built on junk miles is worse than a CTL of 70 built on polarized training. What matters is how you build the fitness, not just the number.
• Ignoring negative TSB for weeks. A build block should keep TSB between -10 and -30 for 2-3 weeks, then recover. If TSB stays below -20 for a month, you're no longer overreaching, you're overtraining.
• Panicking over a rest-week CTL dip. A rest week might drop CTL by 2-4 points. That's noise. The adaptation from the preceding build block hasn't been fully expressed yet. After the rest week, CTL often rebounds higher within 2 weeks.
• Using the PMC without accurate TSS. The curves are only as good as the TSS feeding them. If you ride without a power meter and rely on estimated TSS, the PMC will be directionally correct but quantitatively unreliable. A power meter makes this system trustworthy.
• Treating TSB as the only readiness metric. TSB captures training load but not sleep, HRV, life stress, or illness. A positive TSB doesn't guarantee readiness if you slept 4 hours. Use TSB as one input, not the only one.

The big picture

CTL, ATL, and TSB are the scoreboard of training, they summarize what's happening but don't prescribe what to do. The real skill is combining the PMC with daily readiness signals, understanding your race calendar, and making smart trade-offs between building and recovering.

A practical workflow:

• Monthly: check your CTL trend. Is it rising at 3-7 per week? Are rest weeks producing positive TSB?
• Weekly: check your TSB. Are you in the right zone for your training phase (building vs. resting vs. peaking)?
• Daily: check morning readiness (HRV, sleep, resting HR). The PMC says what's planned; your body says what's possible.
• Pre-race: plan backward. Target TSB +5 to +20 on race day. Use the taper simulator to set volume reduction.

Atomic Metrix calculates all three curves automatically from your ride data, using the exact exponential EWMA formula with no approximation errors. The PMC chart updates with every synced activity, so you always know where you stand.

References

• Banister et al. (1975), A Systems Model of Training for Athletic Performance, the original impulse-response model paper.
• Bosquet et al. (2007), Effects of Tapering on Performance: A Meta-Analysis,8-14 day taper, 40-60% volume reduction, 2-6% performance gain.
• Training and Racing with a Power Meter, Allen & Coggan, Chapter 7 on the Performance Manager.
• The Cyclist's Training Bible, Joe Friel, Chapters 6-8 on fatigue management and tapering.