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)


Site Overview Part 1

Greetings everyone from the team at Science Behind Sweat!! This post has been a long time coming and will hopefully provide you with an adequate update of various features on the site. Recently we’ve made a lot of changes to improve functionality and give people better information on the drivers of their fitness. In particular, we’ve modified work output calculations, developed new analytics (soon to be widely released!), and have added and will be adding a host of other updates and features. Today I’d like to talk about the specifics of our work output calculations so people can better interpret what they’re seeing when they look at their Work Capacity chart and Fitness Scores. Ultimately, we want you to have a full understanding of all of our features and how they feed into our analytics but for now we begin by laying the foundation.  So let’s start with calculating work output.

Work output

One of the key goals of CrossFit is to maximize an athlete’s ability to do work over broad time and model domains. From a practical standpoint, this could mean anything from shoveling snow off your driveway to battling renegade ninja’s or carrying Uncle Lou to bed after he’s had one too one too many wine spritzers.

How do we take these varying daily activities or exercises like squats, dead-lifts, pull-ups, bosu-ball squats (= terrible idea) and meaningfully quantify them?  To do this we have to calculate or at least estimate the amount of work it takes to perform all the movements in each activity or exercise in terms of foot-pounds (ft-lbs) of force.  Once all work estimates are calculated for each movement, we can then figure out the total work done.

As an example, let’s take your average statistician (aka, myself).

Build: Height: 6’1”, Weight: 215 lbs.

Workout: Cindy.  This is a 20-minute AMRAP (as many rounds as possible); 1 round = 5 pull-ups, 10 push-ups, 15 squats.  I have to do as many rounds as I can in 20 minutes.

Work Estimate (per movement):

1 pull-up = 570 ft-lbs x 5 = 2850 ft-lbs

1 push-up = 320 ft-lbs x 10 = 3200 ft-lbs

1 squat = 400 ft-lbs x 15 = 6000 ft-lbs

1 round of Cindy = 12,050 ft-lbs

With my PR (personal record) for Cindy being 27 rounds the total work done is 325,350 ft-lbs or 12,050 ft-lbs x 27.

This feeds into our analytics in two important ways…

1) We can break down activities into key movements and calculate work estimates for a variety of different workouts while also tracking the amount of time it takes to complete a workout.

2) We can plot work output vs. time to get an idea of your ability to do work over broad time and model domains.

In our next post, we’ll talk about the work capacity chart which will draw on some concepts that we discussed in this blog.  Please don’t hesitate to provide feedback, post comments on Facebook, or send us an email with any questions.

Remember we are here to help you train smarter!!

Entering non-standard types of workouts.

I have gotten questions from a lot of you about entering non-standard types of workouts. Below is quick rundown on how I do it. Also, if you have any suggestions — I am happy to hear them.


1. Death by (pullups, situps, burpess…. pick your poison) : How I enter:

a) Pick custom workout

b) Select timed

c) Enter the minute you were able to get to for the “time taken”

d) Enter total reps in the reps column next to the movement selected.

*** I also make a note in the notes section that it was a Death by… workout


2. Tabata : We are working on a better way of doing this and once again would welcome any suggestions.

Here is how I do it:

a) If it is just 1 movement I enter it as a 4 min AMRAP with that movement and enter total reps done either in reps per round and keep the rounds at 1 or say that I did 1 rep per round and enter the total reps in 4 minutes under rounds.

b) If it’s more than one movement: I enter it as a timed workout. Enter total time take in the time box and just enter the total number of reps done for each movement.

** I, once again, make sure to note that it was a Tabata workout. 

*** The chart below explains why only keeping track of your lowest score is not an accurate measure of your performance.

Person 1 did 81 reps versus 43 reps for person B. The rate of decay (how fast you tire in this case) is also very different. Thus we need to have the entire picture to make any kind of interpretation.