Zones & Thresholds Methodology · · 5 min read

CTL, ATL, and TSB: The Mathematical Foundation of Training Load

CTL, ATL, and TSB are the three numbers that tell you whether to push harder or back off. Here's the math behind them and what they mean for your Ironman preparation.

AO
AthleteOS Data Science
TL;DR — The Answer

CTL (Chronic Training Load) is a 42-day exponential moving average of your daily Training Stress Score, representing your aerobic fitness base. ATL (Acute Training Load) is a 7-day EMA representing current fatigue. TSB — your Form — is simply CTL minus ATL: positive means fresh, negative means fatigued. For Ironman athletes, a pre-race TSB of +10 to +25 while maintaining CTL above 80 TSS/day is the target sweet spot.

Every serious endurance coach tracks three numbers above all others: CTL, ATL, and TSB. Together they form the Performance Manager Chart (PMC) — the closest thing to an objective, mathematical description of whether you’re getting fitter or digging yourself into a hole.

These metrics were originally derived from Banister’s 1975 impulse-response model of athletic performance, later quantified for power-meter training by Andrew Coggan and Hunter Allen. The math is straightforward; the interpretation is a career’s worth of art.

The Core Formula: TSS

Before CTL and ATL mean anything, you need Training Stress Score (TSS), the single currency of all three metrics.

TSS = (duration_sec × NP × IF) / (FTP × 3600) × 100

Where:

A perfect hour at exactly your FTP produces 100 TSS. A 3-hour Zone 2 ride at 65% FTP produces roughly 90–110 TSS depending on variability. A 40-minute VO2max interval session at 115% FTP can score 80–90 TSS despite its shorter duration.

For running and swimming without power data, TRIMP (Training Impulse) is used as the TSS equivalent, calculated from heart rate.

CTL: Your Aerobic Fitness Number

CTL (Chronic Training Load) is a 42-day exponential weighted moving average of your daily TSS. The formula:

CTL_today = CTL_yesterday × e^(-1/42) + TSS_today × (1 - e^(-1/42))

The 42-day constant (τ₁) was derived empirically by Banister et al. and validated across thousands of athletes. In practical terms, CTL is often called your “fitness” — the cumulative aerobic base you’ve built over the past six weeks.

Athlete LevelTypical Peak CTLExample Athlete
Beginner (first 70.3)30–50 TSS/day8–10 hrs/week training
Intermediate Ironman60–80 TSS/day12–14 hrs/week
Advanced Ironman age-grouper80–110 TSS/day15–18 hrs/week
Ironman World Championship qualifier110–140 TSS/day18–25 hrs/week
Professional triathlete140–180 TSS/day25–35 hrs/week

CTL builds slowly. With a weekly TSS of 700 (a big 14-hour week), your CTL increases by roughly 5–7 points per week if starting from a lower base. To build from CTL 60 to CTL 100 takes approximately 6–10 weeks of sustained loading — provided you respect the ramp rate.

Maximum sustainable CTL ramp rate: 3–7 TSS/day per week. Exceeding 7 TSS/day per week consistently is statistically associated with overuse injury and non-functional overreaching.

ATL: Your Current Fatigue

ATL (Acute Training Load) uses a 7-day exponential moving average (τ₂ = 7 days) of daily TSS:

ATL_today = ATL_yesterday × e^(-1/7) + TSS_today × (1 - e^(-1/7))

ATL responds quickly — a single hard day shifts it noticeably. It represents accumulated fatigue from your recent training window. Coaches often track the CTL:ATL ratio as a proxy for the monotony of training load.

TSB: Your Form Score

TSB (Training Stress Balance) — also called Form — is the simplest calculation in the PMC:

TSB = CTL − ATL

A positive TSB means your fitness (CTL) exceeds current fatigue (ATL): you’re fresh, possibly undertrained. A negative TSB means fatigue is suppressing your current performance — you’re in a productive loading phase.

Reading Your TSB Number

TSB RangeStateAthlete Experience
+25 to +15Peak / FreshRace ready; maximum expression of fitness
+15 to +5TransitionWell-recovered, slight training deficit
+5 to -10MaintenanceBalanced; sustainable training phase
-10 to -25Productive LoadingNormal hard training; some fatigue present
-25 to -40Heavy LoadingBuild phase; performance suppressed 5–10%
Below -40Danger ZoneHigh injury and illness risk; reduce immediately

The optimal pre-race TSB for Ironman is typically +10 to +25. This requires a taper of 10–18 days depending on your CTL and individual recovery rate. Athletes with CTL above 100 typically need longer tapers (14–18 days) than those peaking at CTL 60–70 (10–12 days).

The PMC in Practice: A 24-Week Ironman Build

Here’s what a typical Ironman build looks like on the PMC:

The Limitation: TSS Is Not Universal

The PMC’s weakness is that 1 TSS of running stress is not equivalent to 1 TSS of cycling stress. Athletes training across multiple disciplines must use sport-specific FTP equivalents (Critical Swim Speed, Running FTP/CP) and calibrate their TSS multipliers accordingly.

AthleteOS handles this automatically by tracking tri-specific TSS across swim, bike, and run disciplines — normalizing each sport’s load against your current fitness benchmarks and aggregating to a unified daily TSS.

Key Takeaways for Ironman Athletes

  1. CTL is your long-term investment. Every week matters. Don’t sacrifice the base phase.
  2. Don’t let TSB go below -40 for more than 3 consecutive days. Recovery is training.
  3. Start your taper when CTL peaks, not when you feel tired. The timer is objective; your feelings are not.
  4. Pre-race TSB target: +10 to +25. Higher than +25 means you’ve tapered too aggressively and CTL is declining rapidly.
#CTL#ATL#TSB#training-load#Ironman#periodization#PMC

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