W' balance: the metric that separates a PB from a bonk in the last 1000

Physiology17 May 20268 min readDr. Borja Alfaraz

A cyclist who rides 4:12 the first time they attempt an IP and collapses to 4:22 two weeks later did not change fitness. They changed pacing. The difference between the two times is not in the engine, it is in how they manage a finite anaerobic reservoir. That reservoir has a name: W'. And its depletion is called W' balance.

Where the model comes from

Monod and Scherrer's (1965) two-parameter model described the hyperbolic relationship between sustainable power and time to exhaustion:

t = W' / (P − CP) · valid for P > CP.

Here CP (critical power) is the horizontal asymptote of the curve: the power you could theoretically sustain indefinitely. And W' (W prime) is a constant in joules representing the finite anaerobic energy available above CP. Skiba (2012) turned that static model dynamic: below CP, W' recharges; above CP, it depletes. That dynamic is W' balance.

Skiba's equation in two lines

W'_bal(t) = W' − ∫₀^t (P(τ) − CP) · f(t−τ) dτ
τ_W' = 546 · e^{−0.01·(CP−P_avg)} + 316 (seconds)

In words: every second above CP subtracts (P − CP) joules from the reservoir. When you drop below CP, it recharges with a time constant τ that depends on how far below CP you are. Emptying is fast. Refilling is slow.

What it means in individual pursuit

In a 4 km IP the rider is at 108-115% of CP for the whole four minutes. They never drop below CP. W' balance can only fall: the only question is how fast.

An elite pursuiter has CP ≈ 400 W and W' ≈ 22,500 J. Riding at a constant 445 W spends 45 W × 240 s = 10,800 J. That leaves 11,700 J: they could have gone harder. Riding at 465 W spends 65 W × 240 s = 15,600 J. That leaves 6,900 J. Riding at 500 W spends 100 W × 240 s = 24,000 J. They run out of W' before lap 15. That is why at 3:15 they can no longer hold the speed. They collapse.

The classic mistake: going out too hard

The first 15 seconds of a pursuit are a pure sprint above 700 W. That effort spends 4,500-6,000 J on the start alone. If the rider doesn't budget it, they arrive at kilometre 3 with less W' than they expected. Practical rule: the start is not optional, it's a fixed cost of the event. The cruise budget is total W' minus start cost, not total W'.

Numerical example

Rider with CP = 400 W, W' = 22,500 J, 4 km IP.

Fig. 1 W' balance depletion during a well-executed 4 km IP. The start consumes 21% of the reservoir in the first 15 s. Finishes with 6 kJ reserve.

Phase	Duration	Avg. power	W' spent	W'bal at end
Start	15 s	720 W	4,800 J	17,700 J
Stabilisation	45 s	470 W	3,150 J	14,550 J
Cruise	150 s	445 W	6,750 J	7,800 J
Close	30 s	460 W	1,800 J	6,000 J

This profile finishes with 6,000 J reserve: the rider could have gone harder. A well-tuned pacing leaves 1,500 to 3,000 J of reserve at the line. Zero reserve = likely collapse on the last lap. Reserve > 5,000 J = you left time on the table.

Estimating your CP and W' without a lab

The standard protocol is a 3-min max test after 20-30 min warm-up. Average power over the last 30 s approximates CP with ±5% error. W' is obtained by:

W' ≈ (P_3min − CP) · 180 s

Another option is a double protocol: a 3-min test and a 12-min test 48 h apart. CP is calculated by least-squares fitting of the hyperbola. CP precision ±2%, W' precision ±8%. Sufficient for pacing.

Ride your pursuit with W'bal computed lap by lap

AthletePro simulates W' balance second by second with your real CP and W', and tells you what reserve you cross the line with. Adjust pacing until the reserve is exactly what you want.

Start free trial

References: Skiba P. et al. (2012), Med Sci Sports Exerc. Monod H. & Scherrer J. (1965), Ergonomics. Jones A. M. et al. (2019), Front. Physiol.. Corbett J. (2009), IJSPP. Coakley S. & Passfield L. (2018), Eur J Appl Physiol.