📈 Sports Science Modeling

Performance Management Chart (PMC)

The definitive mathematical framework for tracking aerobic fitness, systemic fatigue, and dialing in peak race freshness.

1. The Three Pillars of the PMC

CTL 42-Day Constant

"Fitness" (Chronic Training Load)

An exponentially weighted rolling 42-day average of daily training stress. CTL models the long-term aerobic structural adaptations of your heart, capillary density, and mitochondrial density. It takes months to build and weeks to lose.

ATL 7-Day Constant

"Fatigue" (Acute Training Load)

An exponentially weighted rolling 7-day average of daily training stress. ATL captures recent exhaustion, muscle damage, and glycogen depletion. Because its time constant is 6 times faster than CTL, fatigue spikes and subsides very quickly.

TSB CTL - ATL

"Form / Freshness"

The difference between your long-term Fitness and your acute Fatigue. Positive TSB values mean you are fresh and race-ready. Negative values indicate you are actively accumulating fatigue to drive training adaptation.

2. Visual Peaking & Taper Progression

How a periodized 12-week build cycle orchestrates CTL, ATL, and TSB into peak performance on race day:

Weeks 1 – 6

Base Building

• Steady aerobic volume.
• CTL climbs from 40 → 65.
• TSB hovers between -10 and -20.
• Goal: Establish mitochondrial baseline.

Weeks 7 – 10

Intensity Overload

• High-intensity interval blocks.
• CTL climbs to peak ~85.
• ATL spikes to ~110; TSB dips to -25.
• Goal: Stimulate VO2max and threshold.

Weeks 11 – 12

The Exponential Taper

• Cut volume 40–50%; maintain intensity.
• ATL rapidly drops from 110 → 40.
• CTL held high (~78–80).
• Goal: Supercompensation.

🏆

Race Morning

TSB +18

Maximum Fitness + Zero Fatigue!

3. Real-World Calculation Walkthrough

Let's trace how a single workout mathematically shifts your numbers using the actual exponential equations:

Athlete: Clara (FTP 250W)

Starting State: CTL = 65.0 | ATL = 70.0 | TSB = -5.0

Today's Ride: 3h30m Endurance Ride → 120 TSS

                        // 1. Calculating New CTL (Fitness):

                        CTLnew = (CTLprev × 0.9765) + (TSStoday × 0.0235)

                        CTLnew = (65.0 × 0.9765) + (120 × 0.0235) = 63.47 + 2.82 = 66.3 (+1.3)
                    
                        // 2. Calculating New ATL (Fatigue):

                        ATLnew = (ATLprev × 0.8669) + (TSStoday × 0.1331)

                        ATLnew = (70.0 × 0.8669) + (120 × 0.1331) = 60.68 + 15.97 = 76.7 (+6.7)
                    
                        // 3. Calculating New Form (TSB):

                        TSBnew = CTLnew - ATLnew = 66.3 - 76.7 = -10.4

Scientific Takeaway: Notice that Clara's Acute Fatigue jumped by +6.7 points, while her Chronic Fitness only moved +1.3 points. Fatigue responds 5.7 times faster to a single session than fitness. This is why consecutive rest days can quickly restore Form while keeping accumulated fitness intact!

4. Interpreting Your Form (TSB) Score

TSB Score	Status	Recommended Action & Physiological State
> +25	Detraining / Transition	Active fitness loss. Useful for annual post-season breaks, but too high for competitive racing.
+10 to +25	Optimal Race Freshness	Peak performance zone. Legs feel light, neuromuscular recruitment is maximal, glycogen is full.
-10 to +10	Neutral Maintenance	Balanced state. Great for recreational weekend rides or transition weeks between training blocks.
-10 to -30	Optimal Building (Overload)	The adaptation sweet spot. You are progressively challenging your cardiovascular system safely.
< -30	Overreaching Danger	High risk of injury, illness, and autonomic depression. Reduce intensity and insert recovery days.

5. Weekly Ramp Rate Safety Limits

Ramp Rate measures how quickly your CTL is increasing per 7-day period:

+3 to +6 CTL / week Conservative / Master Athletes

+5 to +8 CTL / week Optimal Progressive Overload

> +10 CTL / week Excessive / High Injury Risk