How Many Matches? – W’ & Anaerobic Capacity

Since taking the plunge and investing in my Stages Power Meter, I have spent a substantial amount of time working on taking all this new data and understanding it so that I can use it to improve.

A big part of this ‘new data’ and a term thet keeps cropping up is something called W’ or Anaerobic Capacity. This post basically follows my research into W’ and my pathway to understanding it and what to do with that knowledge. I have decided to publish it in the hope that it will also help other cyclists out there.

Burning Matches?
The amount of W’ or Anaerobic Capacity as is sometimes called can get complicated, so when describing it, many people refer to W’ and it’s balance as how many matches a cyclist has because it makes for an easy way to visualize the concept:

Basically it goes like this: You have this reserve of energy stored up that gets used when you perform an effort above your Critical Power threshold (similar to functional threshold power (ftp) or the maximum power you can sustain over a long period of time). This reserve takes a long time to replenish and only does so during lower intensity efforts or rest. Thus in a race or hard training ride, you only have a certain amount of ‘matches’ that you can burn before having nothing left.

Monod and Scherrer
This reserve of W’ energy (or your W’ balance) can be represented in graph form and was first modeled by Monod and Scherrer back in 1965:

Monod and Scherrer CP Model

The graph above plots the peak power outputs in a range of durations and produces the very typical curve shown. So what it tells us is that as time increases the maximum amount of power you can output decreases until you get to a point where in theory you can sustain a given power indefinitely. In reality it will drop off again as you will need nutrition and sleep etc!

This point where it levels out is your CP (Critical Power or Anaerobic Work Capacity) and so if we draw a horizontal line here along the time axis, the amount of energy in the graph above this level (coloured in light green) is your reserve of W’ (W’bal).

So How Many Matches?

So how much of this W’ energy do you store? – Well, I came across this very interesting article on that explains just how much W’ we have using the figures taken from experiments carried out by Skiba et al in 2012:
After experimenting with subjects performing intervals above their Critical Power threshold, they were able to establish that the size W’ in their test subjects varied from around 14 to 28 Kilojoules (kj), with an average of 21 Kj.

Doing the Maths:

  • A Kilojoule is equals a thousand joules
  • A joule is equal to watts x seconds (J= W x s)

Therefore in the article it states that if you are putting out 333W for 3 seconds you’ve used 999 joules (which is basically 1 Kj).

So the article suggests that if we use the average according to Skiba, it means that we only have about 21 of these efforts in us, which if added together it means just about a minute at this intensity.

I think you will agree this is not very much and I don’t know about you, but to me does seem less than what I can actually achieve.

For example I have one particularly hard sprint training session that I do that involves me doing 12×20 second maximal sprints where I put out a lot more than 350W. Thus according to the figures above, I should only be able to do about two of these efforts before my W’ is exhausted?

So to me this means that either I have a much larger W’ than average, my maths is wrong, or perhaps I am forgetting something:


Recovery!! – If I am not mistaken, I think this discrepancy is at least partly explained by the recovery time in-between the intervals, where even though my W’ replenishes slowly, it is enough for me to repeat the interval many times and this is exactly why we do interval training. Breaking down hard efforts into smaller bite sized chunks that we can repeat many times.

W' on golden cheetah workout

If you take a look at the main image above of the data taken from a tough interval workout and analyzed on Golden Cheetah, the graph demonstrates the drop of my W’ reserve (red line) as I performed the hard intervals way above threshold (yellow line is power output) and just how slowly this reserve replenishes during the easy recovery periods.

Matches => Rechargeable Batteries

rechargable-batteryThis recovery and replenish aspect of W’ is why instead of matches, I like to think of it like a rechargeable battery that you are carrying. Every time you perform an effort above your FTP, you use this battery, but drop below it and you slowly charge it up again.

Maths Still Incorrect?
So what if there is no recovery time? If I take my 5 or even 3 minute peak power data for example and ‘do the maths’ again using the equation above, the total amount of Kilojoules I use is way more than the average or even maximum amount stated given by Skiba.

I could be wrong here and they do not mention it in the article on, but my explanation is that we are only supposed to use the energy above your Critical Power threshold (CP) in the equation when talking about your W’ balance?

So the amount in joules of W’ reserve used in any effort above your CP would be ((W-CP) x s). Divide the result by 1000 to get the amount in Kilojoules (Kj).

If I do this with my data, then the equation begins to work again and makes more sense.

W’Prime & Golden Cheetah

When trying to understand W’ better and then how to analyze and use it within your training and races, I found this instructional video to be extremely helpful:

Also note that the creator of this video who has worked on implementing W’ into Golden Cheetah, Mark Liversedge also has an excellent blog post where he goes over in great detail the science behind W’ as well as W’bal its implementation and optimisation. This along with the video above has really helped me to understand it and I feel is well worth reading over.

Building a Better/Bigger Battery

Phew, I think I have got it no.. hope you have as well! So now that we have all this information, the question is how can we use it in our daily training and racing?

Small Battery
I think it firstly it is very important to understand and remind ourselves that our W’bal or store of anaerobic energy is not very big at all and that it is important to conserve as much of it for the critical moments in a race. I don’t know how often I see strong but inexperienced cyclists make countless but obviously fruitless attacks in a race and use up much of the W’without any chance of it resulting in a victory.

Your strategy should always be to conserve W’ energy as much as possible until you make decisive moves.

Unless you are specifically training on reducing your recovery time, when riding intervals in training where you want to really work on your W’, it is important to fully recover between efforts so that replenish your W’bal. This ensures that your next interval will also be a quality effort.

Work on Raising your threshold (CP or FTP) – Skiba et al also showed that if you have a higher VO2max would recover and recharge their W’ battery quicker than those with a lower CP. They thought that this was down to the bigger gap between their CP and recovery power. So essentially those with a higher threshold have a bigger reserve or more time spent in recovery or recharge mode.

Skiba,et al: “Modeling the Expenditure and Reconstitution of Work Capacity Above Critical Power” Medicine & Science in Sport and Exercise, 2012