# Site Overview Part 2 – The Work Capacity Curve

The work capacity curve

In our last post we discussed how work output is estimated. Today we will discuss the work capacity chart. Recall that looking at work output vs. time provides the first key step of our analysis for determining your ability to do work over broad time and model domains. But with the large amount of variability among workouts, it can be challenging to gauge what your expected work output should be for specific time and/or modal domains.

This got us thinking…why not use a model that is physically representative of work output intensity over time to estimate expected work? There are a couple of criteria for this model:

1. It should stay true to the athlete’s data
2. Given that the level of exertion in a 20-minute workout is going to be less than in a 5-minute workout, the rate at which work output increases over time should begin to slow or plateau. To see exactly what we mean, take a look at the familiar work capacity graph below.

The blue line shows a strictly increasing trend in work output… chances are, unless you’re Chuck Norris or on bath salts this model is going to overestimate your physical capabilities. The red line shows our model which we believe is a more accurate reflection of what happens in practice, i.e. as you move into longer time domains the rate of work output begins to slow.

Expected work output range

Variation in work output is not surprising given that different movements will cause your muscles to fatigue at different rates. For example, handstand push-ups will lead to more rapid muscle fatigue and subsequent failure than bodyweight squats, the result of which is lower rep count and therefore less overall work.  To illustrate let’s compare Mary and Cindy, again using your friendly neighborhood statistician (aka, myself) at 6’1” and 215 lbs.

Mary = 20-minute AMRAP (as many rounds as possible); 1 round = 5 handstand push-ups, 10 alternating single-leg squats, 15 pull-ups

Work Estimate (per movement):

1 hand stand push-up =  300 ft-lbs x 5 =  1,500 ft-lbs

1 alternating single-leg squat (aka pistols) =  400 ft-lbs x 10 = 4,000 ft-lbs

1 pull-up =  575 ft-lbs x 15 = 8,635 ft-lbs

1 round of Mary =  14,135 ft-lbs

My PR for Mary is around 15 or 16 rounds making the total work for Mary fall between 212,025 and 226,160 ft-lbs.

By comparison, Cindy = 20-minute AMRAP; 1 round = 5 pull-ups, 10 push-ups, 15 squats.  If you remember from my last post, the total work estimate for Cindy was 325,350 ft-lbs.

From this example we can see that even though the two workouts take the same amount of time, the total work output is considerably different. Intuitively this makes sense since handstand push-ups, pistols and the volume of pull-ups will tend to result in increased muscle fatigue, lower rep count, and therefore less work.

For this reason, it’s helpful to determine a reasonable range of work output over time, which corresponds to the blue shaded region on the work capacity chart.  The blue region captures the expected variability of your workout data (yellow points) above and below the work capacity curve (this is called a “prediction interval”).  Points falling inside the shaded region are within your expected average range for work output.  Points falling above are outperforming your average and points falling below are underperforming.

In the near future we’ll have an additional feature added to the analytics page providing summaries and analyses of workouts falling within, above, and below the shaded region.  This wraps up our summary of the work capacity curve, in our next post we’ll talk about the fitness score.

Keep training smart!!!

(Mmmm… bacon flowers)

## 6 thoughts on “Site Overview Part 2 – The Work Capacity Curve”

1. not sure how in regards to “work” how 1 push up is a score of 3200 and i HSPU is a score of 1500, as well a 2 legged squat scoring 6000 and a pistol on one leg scoring 4000.
to me in just “knowing what it feels like” – there are levers and loading that is NOT included in your explanation of how to determine “work” done in these movements – if its COM and distance covered – this makes sense in measuring those things that can be measured like chin up and thruster (possibly…) – but in running, rowing, double unders, muscle ups, KBS, TGU, power snatch, squat snatch, power clean (or power clean slight squat, power clean full squat, power clean no squat) the movements cannot be simplified into weight over distance as everyone is different and EACH REP is different – therefore the movements if picked cannot be used to estimate “relative” work
i just simply remember what it took to complete 21 rounds of Mary as my PR, and weeks prior did 32 rds of Cindy – and honestly (of course based on training this can make a difference and I am open to that) – Mary kicked the shit out of me – so if power was SIGNIFICANTLY lower, don’t you think there would be the feeling of less work done over that time of 20 min…

the chart on lowered work output over time has been around since the 50’s when the milers needed an upgrade in their prescription and the German movement of intervals took precedent – therefore requiring some insight into why someone who sprints for 2 min cannot keep this pace for 20 min – but to argue work within that time frame over time for a chaotic, unknowable system is truly admirable, but very tough to do…

2. deepak8612 says:

James – Thanks for your comment. We decided that you made a lot of good points and everyone would like to read the answers. So, we went ahead and made the reply a new post. Cheers… lets chat again sometime soon.

• yup, saw that
good discussion, i’ll stay more in tune and up to date to where you are coming from before i formulate another thought…