# Training load = volume * intensity

When monitoring athletes, the most used (and usable) metrics are the training volume, intensity and load of workouts and across workouts over time:

• Volume indicates how much the athlete has worked out.
• Intensity measures the level of effort the athlete put in during the workouts.
• Load represents how much stress is placed on the body by the combination of volume and intensity of the workouts.

There is a direct relationship between these three metrics:

$$training\_load = volume * intensity$$

This relationship is true for a lot of different implementations of training load metrics. To name a few:

• $$TRIMP = sRPE * duration$$
• $$\verb|Lucia's TRIMP| = HR_{zone} \cdot constant * duration$$
• $$TSS = \dfrac{t * NP * IF}{FTP * 3600} * 100$$

(Explanation of these different implementations is beyond the scope of this post.)

## Volume

At the core of this relationship between metrics is the independence of volume and intensity: Volume should be a pure quantity of training that is not influenced by intensity.

This means that typically for endurance sports, the only valid unit of volume is duration. Distance, although regularly used as a measure of volume, is not completely independent from intensity: When you change the intensity (speed) of a run, the distance also changes. Following that rationale, distance should be considered a training load metric (and a very useful one in for example running).

For other sports like strength training, the unit of volume can be for example the number of repetitions.

## Intensity

For endurance sports, the intensity of a workout can be measure in terms of for example power, speed, heart rate or RPE. For other sports like weight lifting, intensity could be defined as the mass of the object that is lifted.

As a sidenote: I am explicitly using the term “speed” here and not “velocity”. Although velocity is used regularly in the field (TODO: Reference minimal power model paper, a podcast from Olav and a “velocity made good” reference), I think that is incorrect: Velocity is a vector quantity that specifies both the rate of displacement and the direction. Speed only specifies the rate of displacement, without the direction. As long as the direction is not reported (which is the case when we talk about intensity in terms of scalar values in km/h or min/km), we should use the term speed.

Although this point may seem like minor semantics, I think this point is important to make in this context as a measure of training load, it is specifically “speed” that we are interested in. In other contexts in this domain, talking about velocity does make sense. An example of this is when you are optimizing the course of an athlete on a race track. In that case you could reduce the path towards the finish to a 1-dimensional space and talk about velocity in terms of the “rate of displacement towards the goal”. This is for example how “velocity made good” (VMG) in sailing is used. Please note that in this case the velocity is a 1-dimensional ($$|v|$$) vector which looks a lot like the scalar speed ($$v$$). I might write a follow-up post on this specific topic.

The choice of intensity metric (and of volume for that matter) obviously determines the unit of the calculated load:

• Using power in Watt as an intensity metric will lead to a calculated training load that is equivalent to the mechanical work in Joules.
• Using speed in km/h as an intensity metric will lead to a calculated training load that is equivalent to the distance in km.
• Using heart rate in bpm as an intensity metric will lead to a calculated training load that is equivalent to a somewhat artificial $$bpm*minutes$$.
• Using heart rate in bpm as an intensity metric will lead to a calculated training load that is equivalent to a somewhat artificial $$bpm*minutes$$.

When volume is defined as the number of repetitions, the unit of the calculated load is then the total mass lifted in kg.

Please note that external intensity metrics like speed and power lead to external measures of training load. Similarly, an internal measure of intensity leads to an internal measure of training load.

## Summary

In summary, when monitoring the training of an athlete (or yourself), be aware of the difference between load, volume and intensity and choose the right units for the sport and purpose.

As a rule of thumb:

• When a power meter is available, use power as intensity and duration as volume. Training load is then the mechanical work.
• When no power is available, use speed as intensity and duration as volume. Training load is then the distance. This works really well in for example running and swimming.
• For cycling without a power meter, subjective or internal intensity metrics like (s)RPE or heart rate are more useful than speed because external load and speed are so poorly correlated in this sport (due to the quadratic relationship between speed and aerodynamic drag).