Workout Reserve Model

Introduction

The Workout Reserve (WR) model is an advanced approach to quantifying an athlete's real-time capacity to sustain exercise intensity across multiple time domains. Unlike traditional single-parameter models (such as Critical Power with W'), the WR model leverages Exponentially Weighted Means (EWMs) across different time constants to capture performance capacity from sprint to endurance durations.

The model was developed by Athletica and represents a sophisticated method for tracking fatigue and recovery dynamics during exercise.

Workout Reserve on Garmin watch

Workout Reserve exists to provide you with the info of 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:

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

Important constraint: The EWMMAX values must be monotonically decreasing with increasing τ, reflecting the physiological reality that 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

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 interactive simulation below to explore how different workout structures affect Workout Reserve dynamics:

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 Evolution

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

  • WR Reserve trajectory: Shows real-time capacity across the workout
  • Limiting tau: Identifies which time domain is most limiting (sprint vs. endurance)
  • Power profile: The prescribed workout structure
💡Experiment

Try these scenarios:

  1. High-intensity intervals (450W × 3min): Notice which tau becomes limiting
  2. Short sprints (600W × 30s): Observe the sprint domains (12-60s) become limiting
  3. Threshold work (350W × 10min): See how longer taus (1200-3600s) dominate
  4. Adjust recovery power: Compare passive (0W) vs. active (100-150W) recovery

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. Performance prediction: Estimate sustainable power for remaining workout duration
  5. Training load quantification: More nuanced than single-parameter models

Technical Notes

📝Implementation Details

Activation Function: The current simulation uses a placeholder activation function (simple linear scaling). The proprietary Athletica activation function provides nonlinear scaling optimized through empirical validation.

Initial Conditions: All EWMs initialize at zero at the start of exercise. In practice, they could be initialized based on recent training history.

Computational Efficiency: Despite tracking 10 EWMs simultaneously, the computational cost remains minimal, making real-time implementation feasible on cycling computers and smartwatches.

📚References & Contact

The Workout Reserve model is proprietary technology developed by Athletica (www.athletica.ai).

Scientific Publication: Zignoli, A., & Whitehurst, P. (2025). "Real-time assessment of exercising maximal mean power and speed in endurance sports: a Garmin connect IQ App." Sports Engineering, 28, 45. DOI: 10.1007/s12283-025-00528-1

Published: 22 October 2025

Abstract: This manuscript presents an algorithm for the calculation of the ratio between the real-time maximal mean speed (or power) output and the individual's historical maximum. The algorithm has been developed using the Garmin Connect IQ SDK, and it runs on compatible devices, such as cycling and running computers. For outdoor running activities, a Kalman Filter (KF) was developed to estimate road gradients and compute 'gradient-adjusted speed,' ensuring accurate performance evaluation in varied terrains.

Garmin Connect IQ App: A Garmin Connect IQ application implementing the Workout Reserve model is available for compatible Garmin devices, enabling real-time monitoring during workouts with computational times of ~2 ms during cycling and ~12 ms during running.

Project Page: Visit the Athletica Workout Reserve project page for detailed documentation, research papers, and implementation guides.

For implementation details, licensing, or the proprietary activation function, contact: andrea@athletica.ai

The model builds on concepts from exponential filtering, work-balance modeling, and multi-component physiological systems analysis.