Fitness Score

With an idea of how work output is calculated and how we estimate a model for looking at average work output over time, we are now ready to talk about fitness scores. At a high level fitness scores provide a snapshot of your general level of metabolic conditioning. Let’s imagine that you’ve just completed entering in a months worth of workouts, assuming you’re on a 3 days on, 1 day off schedule for your training that adds up to about 22 workouts (we like round numbers so call it 20).

Next, let’s suppose you were to add up all the work done (in terms of ft-lbs) across those 20 workouts. If the time domains of those workouts were pretty evenly spread out over 0 to 20ish minutes (e.g. you did a workout that was around 1 minute, 2 minutes, etc.), that total work value would give you an idea of your “total work capacity” in the 1 to 20 minute time domain. This is essentially what we call your fitness score.

However, a couple of issues come up with estimating fitness score in the way just described. First, while the distribution of times we hit over the course of 20 workouts will generally tend to cover the 0 to 20 minute time domain, rarely will they be as evenly distributed as described above. Thus if we happened to be even moderately biased in short, medium or long time domains (as shown in the figure below), that would throw off the fitness score calculation. Second, as we saw from before, there can be a TON of variation in work output between workouts, even those that take about the same amount of time to complete (recall our example of Cindy vs Mary). This makes it difficult to meaningfully compare fitness scores over time. In order to alleviate this issue we use the estimated work output values from the work capacity curve over the 0 to 20 minute time domain to get a more reliable estimate of fitness score.

Returning to the example shown in the figure above, each of these is actually generated from the same underlying work capacity curve, and should produce the same (or similar since we added some noise) fitness scores. If we simply add up the work output values we see that there is considerable variation in the fitness score estimates (see table below), however using the area beneath the work capacity curve (basically summing up the work estimates at each point along the curve, corresponding to the shaded region in the plot below) the estimates are very close. The reason we see a discrepancy in the values is that the number of points being summed over is different using the work capacity curve as compared to the raw data.

Sum Raw Work Output            Sum Based on Work Capacity Curve
592,874 ft-lbs                              46,442,732 ft-lbs
791,343                                         47,356,813
1,032,530                                     46,735,558
830,705                                        48,777,134

It’s important to note that we’re not saying that looking at the sum of work output values over a week or month is not a useful metric, but it doesn’t lend itself as nicely to tracking progress over time. In our next post we’ll look at tracking fitness score over time and what the trends can tell us about our training.

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Comment from James FitzGerald at Optimum Performance Training

We were fortunate enough to receive an interesting and insightful set of comments from James FitzGerald of Optimum Performance Training (OPT) about our post on the Work Capacity Curve. If you don’t know who James is and what OPT is about you should check them out, they’ve done some amazing work in the health and fitness area and training athletes of every caliber and walk of life. Below is our response to his comments.

First off, thank you for your comments! I’ll try to answer it as best I can (italicized comments are from James).

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.

So based on our estimates (or what we’ve been able to find in the literature or from other references) work for 1 push-up, in terms of movement of center of mass (COM) is approximately the same as the work for 1 handstand push-up (HSPU). Similarly for 1 vs. 2 leg squat. The values you mentioned represent the total work per round for each movement. (5 HSPU vs 10 Pushups — results in 1500 vs 3200).

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…) –

This is absolutely true, the work calculations we provide do not directly capture this information. Someone may be perfectly capable of doing push-ups, but unable to perform a HSPU. In this case, strictly based on work estimates and no other information, these movements would be deemed “equivalent” in terms of their overall level of difficulty or what they say about a person’s overall ability to do work.

Of course this really isn’t the case. What we would expect (reflected in our analysis of athletes data) is that a person who is capable of performing (more) HSPU’s should, in principle, be able to perform more regular push-ups (or movements involving similar major muscle groups) than a person who is not able to do (or can only do a few) HSPUs. There is definitely a skill/technique component with HSPU’s, so this may not always be the case. However, on average we would expect that the person capable of performing (more) HSPU’s to be able to perform more work faster when HSPU’s or any related movements are involved. So in terms of comparative analysis these things will still play out.

Things like movement difficulty can be directly captured by looking across a population of similar individuals (in terms of height, weight, age, gender) and evaluating the effect of a particular movement on work output/time.

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 agree, to an extent. Our aim with these types of movements is to obtain a general estimate of work. For example, with the Olympic lifts we can approximate the length of the bar path based on an athlete’s height and use this to estimate work. There is a fair amount of research published on this, and we use this information in our work estimates. That being said, technique is going to play an enormous role. Just because someone is 5’9’’ and weighs 210 lbs doesn’t mean they can move a bar as efficiently or as explosively as Ilya Ilin. Additionally, if you were to take a look at the distribution of limb lengths amongst the population of people who were 5’9’’, Ilya’s would likely be very different. Thus, as before, a person who is able to move more efficiently will be able, in general to do more work faster. So for population based analyses we are able to make statements about how these movements affect an athlete’s performance on a given workout.

As far as some of the other movements you mentioned (and other similar ones), we generally rely on average distance travelled, or pace of the run/row, etc. So, for example, the skill associated with something like double unders is certainly going to play an important role in calculating work output. Someone who is very efficient at this movement may only jump about 2 inches at each skip, by comparison someone who isn’t as efficient may be jumping upwards of a foot (and missing a bunch reps as well). In our calculations of something like this we take the “average” (loosely speaking here) and assume that most people will jump about 6 inches per skip. As above efficiency in movement plays itself out in a person’s ability to complete more work (e.g. more double unders) faster as compared to their peers.

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…

I think that this will vary on an individual-by-individual and workout-by-workout basis (21/32 rounds is just ridiculous by the way :)). I can honestly say the most painful variant Cindy I’ve ever done was back at Sections in 2010, it was with a 20 lbs weight vest (I think)… I can’t remember the exact number of rounds I did but I think it was somewhere around 17 (I’ll try to find my results). At the time my Cindy PR was around 24 rounds. The amount of work for the weighted Cindy is about 225,000 ft-lbs and unweighted is about 300,000 ft-lbs and I have to say I’d take unweighted over weighted any day. My point is that though there is probably a correlation between amount of work done and how painful a workout is, I don’t think that this is necessarily the case across the board.

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…

I’d be very interested in reading up about this, if you happen to have any recommendations/ references it’d be greatly appreciated! In terms of modeling the work output over these time durations, yes there is absolutely a great deal variation and noise, both from our estimates of work, as well as the various complexities affecting an athlete’s performance on a given workout on a given day. What we do see is that as an athlete enters more workouts, general and systematic trends begin to appear. It’s these trends that we’re interested in studying and providing feedback on.

I hope these generally answer your questions. We’re always looking for better ways of capturing and analyzing athletes performances and we would love to get your thoughts about any ideas you might have about how to do this. Thank you again!

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!!