TIS
Extra model · builds on Module 4

Workout Reserve model

Introduction

The Workout Reserve (WR) model quantifies, in real time, an athlete's capacity to sustain exercise intensity across multiple time domains. Unlike the W' balance of the critical power model, which tracks a single reserve, the WR model tracks ten. It uses Exponentially Weighted Means (EWMs) with different time constants to capture performance capacity from sprint to endurance durations.

Critical power (CP) is the horizontal asymptote of the power–duration curve, and W' is the finite amount of work that can be performed above CP (both are introduced in Module 3: see Critical power and W′M3). The Wbal model tracks how much of W' is left during exercise, as a single balance; Workout Reserve replaces that single balance with ten EWMs, one per time constant.

The model was developed by Athletica to track fatigue and recovery during exercise.

Workout Reserve on Garmin watch

Workout Reserve shows the margin between your real-time performance and your personal best.

The exponentially weighted mean (EWM) framework

At the core of the Workout Reserve model are multiple Exponentially Weighted Means (EWMs), each with a different time constant (τ). These EWMs track power output at different time scales simultaneously:

Time constants (τ): 12s, 30s, 60s, 120s, 180s, 300s, 600s, 1200s, 1800s, 3600s

Each EWM evolves according to a first-order differential equation, the moving-average form of the equation in One equation, many systemsM4:

dEWMτdt=P(t)−EWMττ\frac{dEWM_\tau}{dt} = \frac{P(t) - EWM_\tau}{\tau}

Where:

  • EWMτEWM_\tau = Exponentially weighted mean for time constant τ
  • P(t)P(t) = instantaneous power output at time t
  • τ\tau = time constant in seconds

Discrete implementation

For real-time calculation with discrete data points (typically 1-second intervals), the continuous differential equation is discretized using forward Euler integration:

EWMτ[i+1]=EWMτ[i]+(P[i]−EWMτ[i])⋅ΔtτEWM_\tau[i+1] = EWM_\tau[i] + \frac{(P[i] - EWM_\tau[i]) \cdot \Delta t}{\tau}

Where Δt\Delta t is the sampling interval (typically 1 second).

Historical maxima (EWMMAX)

For each time constant τ, the model requires a historical maximum value (EWMMAXτEWMMAX_\tau). These values represent the athlete's best sustained power output over each time duration and are typically derived from:

  • Historical peak power data from training and racing
  • Structured testing protocols (e.g., maximal efforts at various durations)
  • Best-power-for-duration analysis from the athlete's power profile

Constraint: the EWMMAX values must be monotonically decreasing with increasing τ, because shorter efforts can be sustained at higher power outputs.

EWMMAX12s≥EWMMAX30s≥EWMMAX60s≥...≥EWMMAX3600sEWMMAX_{12s} \geq EWMMAX_{30s} \geq EWMMAX_{60s} \geq ... \geq EWMMAX_{3600s}

Calculating Workout Reserve

At each time point during exercise, the model:

  1. Calculates all EWMs for each time constant
  2. Computes ratios between current EWM and historical maximum:
ratioτ=EWMτEWMMAXτratio_\tau = \frac{EWM_\tau}{EWMMAX_\tau}
  1. Identifies the limiting time domain by finding the maximum ratio:
ratiomax=max⁡(ratio12s,ratio30s,...,ratio3600s)ratio_{max} = \max(ratio_{12s}, ratio_{30s}, ..., ratio_{3600s})
  1. Applies an activation function (proprietary to Athletica):
WR=f(1−ratiomax)WR = f(1 - ratio_{max})

The Workout Reserve value ranges from 0 to 100%, where:

  • 100% = fully fresh, maximum capacity available
  • 0% = complete depletion, task failure imminent

In the simulation on this page, WR can also go below 0. A negative value means that at least one EWM has risen above its historical maximum: the session asks for more than the athlete's best for that time scale. The chart flags this as unsustainable.

The limiting tau (the time constant with the maximum ratio) indicates which energy system or duration capacity is currently most stressed.

Interactive simulation

Use the simulation below to see how different workout structures change Workout Reserve:

Athlete Power Profile

HIIT Session Parameters

Session Statistics

✅ SUSTAINABLE: session completed successfully!
18 min
Total Time
9 min
Work Time
275 W
Avg Power
16%
Min WR
37%
Avg WR
43%
Final WR

Workout Reserve Over Time

Power Profile

Note: This implementation uses a placeholder activation function. The proprietary "secret-sauce" activation function from Athletica is not included. Contact andrea@athletica.ai for the actual implementation.

Learn more: Visit the Athletica Workout Reserve project page for detailed documentation and research.

Interpretation

  • Workout Reserve trajectory: Shows real-time capacity across the workout
  • Power profile: The prescribed workout structure

Applications

The Workout Reserve model enables:

  1. Real-time pacing guidance: Athletes can monitor their reserve capacity during exercise
  2. Workout prescription: Coaches can design sessions that target specific depletion levels
  3. Fatigue monitoring: Track recovery status across multiple time domains
  4. Training load quantification: ten reserves instead of the single W' balance of the critical power model

A possible further use, not shown on this page, is estimating the power an athlete can sustain for the rest of a workout.

Technical notes