Decoding Fatigue: Can We Measure It Live in Team Sports? – Part 3

Introduction

In the previous installment, we explored the Critical Velocity (CV) model and the \(D'\) balance model, two widely used approaches for modeling fatigue and anaerobic energy reserves. These models attempt to estimate an athlete’s capacity to sustain effort by tracking the depletion and replenishment of anaerobic energy during high-intensity activity.

The CV model provides a structured way to map out performance limits by defining two key parameters:

• Critical Velocity (CV): The theoretical velocity an athlete can sustain indefinitely, closely related to the anaerobic threshold or 2nd ventilatory threshold.
• \(D'\) (D prime): A finite anaerobic reserve that is depleted when the athlete exceeds CV and replenished when velocity drops below CV.

By applying \(D'_{balance}\) models, we estimated live fatigue levels in running-based team sports using GPS data, specifically through the Maximum Mean Velocity Profile (MMVP) derived from multiple training session and matches (i.e., last 6 weeks of rolling data). This provided insight into how an athlete’s anaerobic reserves were managed over time and helped illustrate fluctuations in performance during real-game and real-training situations.

While this method offers a quantitative approach to fatigue monitoring, it comes with several limitations:

• Unreliability of \(D'\) Estimates – \(D'\) is highly variable, both within and between athletes. This variability can stem from differences in muscle recruitment, metabolic efficiency, and prior fatigue, making real-world application of \(D'_{balance}\) less reliable than the model assumes.
• Reliance on Manifested Performance – The MMVP-derived parameters (CV and \(D'\)) are based on historical match and training data, which may not reflect an athlete’s true physiological capacity. If an athlete never fully pushes their limits in a game or training, their fatigue model may be biased downward.
• Uniform Depletion & Recovery Assumption – The \(D'_{balance}\) equation assumes that all athletes deplete and replenish anaerobic reserves at the same rate, ignoring individual physiological differences (e.g., muscle fiber composition, metabolic efficiency).
• GPS Limitations – The model uses velocity data alone, meaning it does not account for external loads, inclines, or biomechanical variations that affect energy expenditure.
• Computational Complexity – Implementing real-time \(D'_{balance}\) tracking in a team sport environment is computationally demanding, making live, in-game applications difficult.

Given these constraints, we need a simpler, more intuitive approach—one that acknowledges the limitations of the Small World model (i.e., mathematical model and its assumptions) and the challenges of real-time fatigue assessment, while remaining practical for coaches and practitioners and still providing valuable insights into athlete fatigue and performance capacity.

In this installment, we explore a more accessible alternative: Zignoli’s Workout Reserve Model (Zignoli 2023). This model offers a coach-friendly, data-efficient way to estimate an athlete’s performance limit without the complexities of CV and \(D'_{balance}\) tracking.

How does it work? What makes it more intuitive and practical than the traditional Critical Velocity models? Let’s dive in.

Manifested Effort Level (MEL)

Although Zignoli (2023) originally named his approach the Workout Reserve Model, I will refer to it as Manifested Effort Level (MEL) to make it even more intuitive. This term better reflects what it represents—the current level of manifested performance compared to the historical best, as observed in actual match or training data.

Figure 1 illustrates the Maximum Mean Velocity Profile (MMVP) for six AFL matches, which we introduced in the previous installment.

While a 3-parameter Critical Velocity model could be fitted to these data—using either 0.95 percentile quantile regression or by identifying the maximum velocity for each rolling window—the MEL approach deliberately avoids any type of modeling.

Instead, the focus is on keeping the method as intuitive and direct as possible, relying solely on raw performance data without additional curve fitting or extrapolation.

Figure 1: Maximum Mean Velocity Profile for six AFL matches

To determine the maximum profile, we simply identify the highest recorded velocity across multiple matches (or training sessions) for each rolling time-duration window. This is illustrated in Figure 2.

The black line in Figure 2 represents what we can call the rolling 6-week MMVP, serving as a reference for the athlete’s historical performance profile. This profile captures the peak sustained velocities over various durations based on past data.

We will use this historical MMVP as a benchmark to compare against current or live performance, providing a practical way to assess whether an athlete is performing at, above, or below their previously manifested effort levels.

Figure 2: Estimated maximal/best MMVP from multiple sessions/matches by simply finding the highest velocity for each time duration window

Table 1 presents a selection of key time-duration windows extracted from Figure 2.

While Figure 2 includes a much finer resolution, using 5-second step increments for a more detailed profile, Table 1 focuses on a few major rolling window time-frames for easier interpretation. This allows for a clearer overview of the most relevant performance benchmarks without overwhelming detail.

Table 1: Few time frames extracted from Figure 2

Table 1 once again highlights how match performance is often below an athlete’s true capacity. This raises important questions about the validity of position-specific conditioning programs that are based solely on match-derived performance data. However, this is a topic for another article.

Now that we have established our historical (rolling 6-week) MMVP, collected from matches in this example, we assume that this represents 100% of the athlete’s manifested performance or effort level (MEL).

The next step is to compare live match (or session) data to this MMVP to assess how current performance aligns with past benchmarks.

Let’s return to our single AFL match dataset (first quarter), as depicted in Figure 3.

Figure 3: The first quarter GPS data (instantenous velocity) collected during single AFL match for a single player.

The next step is to repeat the MMVP analysis, but this time applying it to live match data, just as we did with the historical dataset.

For this example, we will compute rolling averages over different time windows for the first quarter of the match. Figure 4 illustrates a selection of these rolling averages, providing a snapshot of how the athlete’s velocity fluctuates over various durations during live play.

Figure 4: Rolling velocity of different duration windows (5, 10, 15, 30, 60, 120) for the first quarter of the sample AFL match. Values are first squared, then averaged, then square root is taken. This is done to give more weight to the higher velocities due to the intermittent nature of the activity.

Let’s take the 30-second rolling velocity as an example.

We will compare it to the historical best manifested 30-second mean velocity from the rolling 6-week MMVP to calculate the 30-second Manifested Effort Level (MEL).

This comparison is visualized in Figure 5, illustrating how the athlete’s current 30-second performance aligns with their historical best.

Figure 5: Rolling 30-sec mean velocity compared to the historical best manifested 30-second mean velocity (from MMVP)

As shown in Figure 5, the 30-second MEL reaches 100%, meaning that the athlete’s current 30-second rolling velocity (i.e., performance) has matched their historical best from the rolling 6-week MMVP.

But does this necessarily indicate fatigue, especially if MEL exceeds 100%?

It’s difficult to say for certain, but it can definitely serve as a red flag. If an athlete surpasses 100% MEL, they are pushing beyond any previously recorded effort for that specific rolling window. This suggests a particularly demanding effort, which could have implications for fatigue accumulation and pacing strategy.

However, MEL should be seen as a tool, not an absolute truth. Unlike the \(D'\) balance model, MEL is model-free—it does not rely on assumptions about anaerobic energy depletion or replenishment. Instead, it provides a direct, intuitive comparison of current vs. historical performance.

Extending MEL to All Rolling Windows

So far, we have calculated MEL for the 30-second rolling velocity window, but the same approach can be applied to all other rolling windows. This will give us a continuous MEL value for each time duration.

The next step is crucial: