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Using that theoretical construct of fitness to plan training

The previous blog post was a pretty esoteric bit about how to visualize fitness as an object in n-dimensional space. And while that’s all well and good, how do we actually use it?

Basic Review of the n-Dimensional Concept of Fitness

First off – If you are really confused about what I’m talking about, go read the previous article were I explain in a little more depth the n-dimensional concept of fitness (

The basic idea is that we think about fitness (race performance in our case) being a function of several different physiological traits (speed, strength, endurance, neuromuscular coordination, capacity to buffer blood pH, etc.). If we were to graph each one of these out as a different dimension to a volume (like how a 3-dimensional object has height, width, and depth), then we can create an n-dimensional volume that represents how fit we are. The larger any of those dimensions are, the bigger the total volume inside that shape, and the more fit we are going to be. That is, the bigger the volume, the faster we are.

Some Basic Truths About Training

1) The Law of Diminishing Returns is a thing.

2) We don’t have enough time to maximize our fitness along every single dimension of that n-dimensional volume.

3) Even if we did have enough time to maximally train everything, we probably wouldn’t be able to recover from that volume of work fast enough to keep working hard enough to get fitter.

4) Most of us are now where near the theoretical maximum we could be at in any given dimension.

5) Our theoretical top end on any particular aspect of fitness (i.e. each dimension of that volume) is probably not equal to any other aspect of fitness. And where those top ends lay vary from person to person.

The Law of Diminishing Returns

The basic concept of the law of diminishing returns is that the more fit you are, the harder it is to improve. It’s something we all know and recognize when it comes to endurance athletics, but it takes on a new meaning when we think of fitness as an n-dimensional space. Yes, if we’ve approached our theoretical maximal fitness level then we won’t have an easy time getting faster. But most of us are nowhere near that point.

Most of us are used to the idea of the law of diminishing returns in thinking about our overall race fitness. But it may be more useful to think about it in terms of each aspect of fitness. If we break our “fitness” down into a bunch of different variables (speed, strength, muscular endurance, metabolic endurance, etc.), then we can think about how the law of diminishing returns suddenly becomes a little more useful again for planning our workouts. If we have spent a lot of time and effort working on improving our speed and strength, but not our endurance, we probably (hopefully) are further out on the speed and strength axes than we are on the endurance axis. Therefore, it stands to reason that getting faster or stronger is going to take a lot more work than improving our endurance.

For the sake of simplicity, let’s say that any particular axis ranges from 0-100. The closer to 100 a particular variable is, the more fit we are in that aspect (i.e. someone with a strength of 75 is going to be stronger than someone with a strength of 60). As we get further along any particular axis (strength, speed, endurance, etc.), it becomes harder and harder to continue improving that variable. We have to work harder and longer (requiring more recovery) after each workout to keep improving those high value variables. But we could easily stress a different variable with a lower score and see a bigger improvement with less effort. And that’s the whole goal right? We want to improve as much as possible for every bit of training we put in.

There are a couple of caveats here:

1) Everyone has different theoretical maximums for every variable we want to include in our concept of n-dimensional fitness, and those vary from person to person.

2) Most of us have probably not optimized our fitness for endurance athletics (i.e. we haven’t reached the theoretical maximum volume of that n-dimensional area).

3) Most of us will never reach our own maximized optimum fitness for endurance athletics.

4) We’re thinking primarily in theory here, not with actual data gathered from results. Today we’re talking just about the concept.

There isn’t enough time to maximize every single component of fitness

Once we accept that we don’t have the time to train every single thing that goes into our fitness (or ability to recover from that much training), we can acknowledge the need to prioritize our training. We need to use a budget when spending those precious training hours and our training volume. By budgeting our training in terms of hours and/or volume, every workout suddenly has a specific purpose. Yes, we can stimulate more than one physiological system in a workout. But everything in a workout has a purpose.

We have to actually recover from workouts that improve fitness

Anytime we workout hard enough to stimulate physiological development (i.e. get fitter), it’s going to take us some amount of time to recover from the workout. The harder the workout, the more recovery we’re going to need.

The recovery process is actually pretty complex when you get into the physiology. There’s a spike in cortisol (the stress hormone) that triggers the body to set in motion all the processes that are involved. There’s some swelling as blood and lymph fluid gets pumped into the damaged tissues. The heart rate elevates to get more nutrients to the area. The abused muscle cells soak up nutrients to refuel. Repair proteins are engaged to fix the physical damage. Etc. The greater the extent of the physical trauma suffered by our tissues, the greater these responses, and the longer it takes for them to get back to normal.

Most of us are nowhere near the top end of any of our various aspects of fitness

This is something we all know. There’s always room for improvement, right? Even elite level athletes can always get better. And those are folks who literally do nothing except eat, sleep, and train! For us mere mortals it’s almost impossible to actually be able to train any one (let alone multiple) aspects of fitness to the utmost. So we try to maximize our training to get as much total gain as we can out of the work we can put in.

Different aspects of fitness have varying theoretical top ends

The amount in variation we can see in any given parameter varies from one parameter to the next. What this means is that the amount of improvement we can potentially get from one parameter (e.g. maximal strength output) is different that another parameter (e.g. the range of motion at our hip). What this means is that while we may think about these different parameters as ranging somewhere between 0-100, an improvement on 10 points on one parameter isn’t the same as for another.

Where each one of us caps out in terms of any given parameter varies from person to person. We all know that Person A is going to be stronger than Person B if they both were to somehow maximize their strength. But Person B may have a greater potential maximum in terms of cardiovascular capacity, flexibility, speed, or any other aspect of fitness we could be interested in. But because we all have different maximum top ends, it means that the point of diminishing returns is going to come at different points for different people for different aspects of fitness.

The concept to take home

Some improvements come faster for us than others. This means that those improvements are low hanging fruits, and we’ll probably see more improvement in terms of our overall athletic performance if we focus more of our energy on those. This doesn’t mean that we ignore the easy long miles that build aerobic capacity because we can get “in shape” faster by doing 400 meter repeats every day. Those easy miles are what improve our potential top end when it comes to running fast. What it does mean is that over the short term a little speed work may improve our finish time for shorter races. The variables that we can most easily see gains in will vary from person to person. Some folks get more out of upping their total volume, some folks get more out of getting some speed work in, while other may see more improvement by incorporating some yoga into their weekly routine.

Some aspects of fitness may improve faster for you than others, but that doesn’t necessarily mean that those are the limiting factors for you over the longer term. I’d be willing to bet the majority of amateur road runners would probably run a faster 5k a month from now if they focused on speed work over that time span than by focusing on increasing their overall volume. But that overall volume is important if they want to be better a year from now than they are today.

What this demonstrates is that the variables that are the low-hanging fruit change over time. As you get more fit in one way (i.e. higher top speed), other variables get (relatively) less strong so you’re able to get more improvement out of those than you are out of the one that used to be the easiest to improve. This is basically a demonstration of the law of diminishing returns. The more fit you get on one axis of that n-dimensional volume, the harder it is to keep improving. The amount of work you have to put in to keep improving on that axis keeps increasing exponentially to continue seeing improvement.

Most of us will improve by simply becoming more fit (i.e. just getting more volume into that n-dimensional shape), no matter what axis we’re working on. And this is because most of us aren’t already at maximum fitness (or even close to it) because we don’t have Eluid Kipchoge’s training history and we haven’t had the time to really maximize any particular variable.

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