How is training measured? Part 1: Math


When you train, you want to know two variables: how much you train (the variable you control) and your adaptations, or your improvements in fitness, that result from that training.

It’s pretty easy and straightforward to measure your fitness. There are tons of tests you can do.

But quantifying how much you train, or your “training load” is not as easy as it seems.

Your training load is the product of intensity and duration. Duration is an obvious calculation no matter how abstract the concept of time is (if you exercise in space – don’t even try).

Intensity is measured either externally, in watts, running pace, calories, etc., or internally.

Your internal training load is what you really want to know. It’s the actual physiological demand on your body. In other words, while 200 watts or 9 miles per hour is the same external intensity, everyone’s internal response to that load will vary.

But here’s the problem with measuring internal training demands: it’s really really difficult to accurately measure an internal physiological process without expensive equipment and a team of lab coats. Even then, your oxygen consumption only represents exercise intensity when you’re doing submaximal, steady-state “aerobic” activity.

So that leaves us with the next-best physiological metric of your body’s response to exercise, that anybody can measure: heart rate.

Heart rate is an excellent way to measure your training intensity and your fitness. But not every heartbeat represents a linear increase in exercise intensity, so using heart rate to accurately define exercise intensity over many many training bouts requires some math. And not just simple arithmetic; it requires the type of math that only computers can do.

The most popular heart rate-based mathematical method for quantifying internal training load, and the one used by all those other guys in the quantified fitness world, is the ‘‘training impulse’’ method. TRIMP, as it’s known, was created in the early 90’s and re-born in a few similar forms in the several years afterwards. It’s calculated by multiplying training session duration by its average intensity (percentage of heart rate reserve) and by a sex-specific coefficient. This method allows for the quantification of internal training load in a single term balancing exercise duration and intensity.

The heart rate-based mathematical models are popular because they’re based on objective easily quantified data, and they’ve been validated in some scientific literature.

But they’re also based on some huge assumptions, which you definitely need to consider. Here are the three main assumptions, in order of how critically you should evaluate them:

1. The first assumption is that physical training and the adaptations to that training are described in a dose-response manner. The dose-response will be discussed in a future blog post, but it basically means that for every dose of exercise, an individual will show a given response, up to a certain point. This is true, but everyone’s dose-response curve is different.

2. The second assumption is that with training, you will lose fatigue much faster than you will lose fitness. In other words, you will recover from Monday’s workout by Wednesday, but whatever training gains you made on Monday won’t be lost till next week. This makes sense physiologically, but fatigue is much more than just a metabolic process. Your brain and your musculoskeletal system need an unknown amount of time to recover. Just because I think you should be recovered after 48 hours based on the energy cost of your workout doesn’t mean you actually are.

3. The third and most important assumption is that these models apply to endurance events with year-round training. The mathematical predictions cannot quantify non-endurance types of events like pickup basketball, or mountain biking, or any other type of exercise in which your effort level is constantly fluctuating. Nor are they really meant to predict your fitness and fatigue if you’re only training for your half-marathon for 4 months. How many people actually train only for endurance events, year-round?

So why use these internal training volume calculations? On a population level, these predictions look amazing. The noise of inter-individual variation dies down, and tends to normalize into nice attractive numbers.

But (and this is a big but!), on the individual level – you, that variation still exists. And it may be a big variation.

And remember, your heart rate predicts your physiological training intensity. When your heart rate is then used to predict training volume, it increases the estimation error. The more you predict a prediction, the further away you get from what is actually physiologically happening inside your body.

So what does all this mean? It’s complicated. But know this: when a computer breaks down highly complex physiological processes into its components, then re-builds them in the form of a prediction, many people’s actual responses are lost in the statistical noise.

That’s why probably half the people that use Training Stress Score or any other TRIMP-based training volume calculators find it doesn’t apply to them.

Every athlete is an individual, and will respond differently to training. So how you quantify your training load is up to you: either go with what you should be feeling, or go with what you actually are feeling. That method is in part 2.

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