Saturday, 22 March 2014

Arches: a new conceptual model for running

I don't like pyramid models. Although a well-built pyramid certainly looks nice, they rarely provide a good model for a healthy system. Think Ponzi schemes: a strict hierarchy where only the topmost members benefit. Pyramids are a great analogy for dictatorships, kingdoms, or the catholic church. None of these things are something you'd aspire to mimic for a system that benefits most through cooperation.

Before I get to running, consider one other bad pyramid model: food. For some reason pyramids are used in nutrition. The food pyramid clearly makes no sense. How is it that vegetables are supporting fish and oils, and not the other way around? Why are eggs and sweets near the top? What if you are vegetarian? Do you want to place the most important food items on top, or the least? Why are calorie-rich foods scattered so randomly? For any practical purposes the food pyramid is confusing. More to the point it's just a bad model for something so intricate.

And so it is with running. Running pyramids are popular because here at least we agree the pinnacle of practice is to prepare for race pacing speed, and the base is used to support everything else. Right?  Consider the following image I borrowed from a Running Times piece:

If you look closer, the order is a little arbitrary, no? For instance, strength fits between speed and aerobic. Running a fast 2km interval, which is mostly aerobic, also needs strength. Strength supports the ability to run hard intervals, but it's above the latter. Notice we have speed work underneath "peak" performance. In terms of volume should perhaps speed be on top, and race pace under that (since as an endurance running you'd run more miles at race pace than sprint)? Maybe we need to modify the stacking order. Maybe we need to have some other shapes in there too. Here's a pyramid from running-wizard that attempts to tweak the -ironically enough- shaky foundations of the pyramid model:

Somehow "work" and "recovery", vague terms to begin with, are no longer an integral part of the structure, and once again the stacking order is rather arbitrary (coordination and health at opposite ends?). Conceptually, or qualitatively, pyramids are impractical for explaining the mechanics of training. Can they do any better quantitatively?

Pyramids are meant to represent training 'volume', which usually means miles run per week. Let's assume we have a well-conditioned runner who's weekly volume is 100 miles. Supposedly the pyramid volume represents running volume. Mental math is hard, but if pyramids are 3-dimensional objects their total volume V is length*width*height/3. Or if they are 2D the area is
A = length*height/2.

Let's stick with the 3D model, and for the sake of ease let's say the pyramid has a square base and equal height to its width so l=w=h and the volume is now l3/3.

The total volume of a pyramid is 100 miles. Roughly speaking, it's typical for such a runner for about 15 of those miles to be spent running fast. If we divide the pyramid volume to be 15% of total, you'll discover the top 15% of volume occupies the top 53% of the pyramid's height!

(Note that if the pyramid is 2D, the top 15% of area represents 38% of the total height rather than 53%). Even for a well-meaning training program, these details prevent the pyramid model from ever being intuitive.

That I've seen pyramids used so ineffectively in training made me wonder if pyramids are the right choice to begin with. That's when I thought to try something else: stone arches.

Arches are a beautiful piece of architecture, and they require tools and materials no more sophisticated than what built the Giza Pyramids. The difference is conceptual. You realize that stones, when precisely carved, can be mutually self-supporting and even load-bearing. Both of these points are important in training: the elements should support each other and the resulting total structure should support an external load. In the case of running this "load" is a competitive race (or race season).

Arches can also be scaled. Here is the training re-visualized for early and advanced runners:
Beginner or intermediate truing regime
Advanced training regime
Although speed work and other fast elements are at the top of the arch, this is almost arbitrary; in terms of creating a self-supporting structure they are no more or less important than the easy pace blocks. You may re-arrange the order of the arch colours into anything and the total structure shape remains unchanged. This model permits us to acknowledge how sprints can be as important to supporting a large volume of easy mileage as vice versa. And although the base blocks do experience more total force, all the elements are necessary for the structure to take its full shape. The absolute hierarchy of the pyramid is broken and remoulded into an interlocked structure.

Speaking of training blocks, unlike the pyramid, individual arch blocks are of equal volume (or area). The amount of total work to be done in each volume category can be tallied with ease, no calculator necessary.

As one grows as a runner the total volume of training expand from one year to the next. You can see imagine that from moving to beginner to advanced runners more elements are distinguishable in their various forms (sprints, hill work, tempo, etc), hence the colouring scheme may grow with the volume. Your training history should look like the annular growth rings along the cross-section of a tree. As you mature as a runner you do slightly more of everything.

One can picture the entire arch system supporting a competition. The stronger the arch system the greater the load it can bare. If the arch system is weak or faulty, it will fail under the "external" load of a race: in other words it means you got injured or bonked in the middle of your race. In a sense the races are an integral part of the structure in that training alone never truly tests the composite strength of the entire structure. Note that smaller arches will usually bare smaller loads, but not always (hence to match the observation that he with the greatest training volume does not always win).

I have finished explaining the basic elements of this model. The only point left to emphasize is that I'm not after any kind of 'revolution' in training itself, but rather the way it is represented. Here I argue the pyramid scheme is a problematic one and there are likely much better models to visualize your running habits. Here I'm suggesting one possible alternative to the pyramid. There are no doubt others.


  1. This is bang on. I think you can add to the metaphor the idea that the cement between the bricks could represent things like strength, balance, technique, etc, to drive home the point that one does not come before or after another, but that all must work together to form a solid structure. Love this!

    1. Thanks! Although to keep the analogy faithful as possible an archway doesn't need any cement/grout/mortar to support itself.

      That said, a little extra binder never hurt any construction :)

  2. Hello!

    I have a quick question for you, could you email me when you have a chance? Thanks! –Heather