How to measure fitness?

Measuring fitness is a lot like gerrymandering — it’s all how you look at the data. Gerrymandering is the act of manipulating voting boundaries to influence elections. Could we do the same with the sport of fitness?

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SOURCE

CrossFit has given us The CrossFit Games. The goal of the ‘Games’ is to crown the fittest humans alive. The 2013 Games was the year Jason Khalipa was supposed to beat Rich Froning for the crown. But Khalipa fell short.

What if we changed the way we measured fitness? Could Khalipa have beaten Froning if we looked at the data another way?

How CrossFit crowns the fittest

  • A bunch of athletes come together in an agreed upon location.
  • They compete over a few days.
  • The athletes at the bottom of the scoring are cut from the competition at the end of each day. The rest of the athletes get to continue competing.
  • Points are awarded based on finishing place of each event.
  • The person with the most points at the end wins.

Dave Castro, the Director of the CrossFit Games, abides by the philosophy it pays to be a winner when it comes to awarding points. The points awarded are shown below.

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Top finishers are separated by 5-point increments. Bottom finishers are separated by 1-point increments. It really does pay to be a winner, especially now that the winner of the Games is award $300,000.

At the end of the 2013 CrossFit Games, the top 5 athletes were

  1. Rich Froning
  2. Jason Khalipa
  3. Ben Smith
  4. Scott Panchik
  5. Garret Fisher

Now let’s take a look at how we could do things differently.

Measuring fitness another way

If an athlete won every event, then they are obviously the fittest. Likewise with the least-fit. If someone gets last in every event, then they are obviously the least-fit. The data might look like this:

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Simulated data from a CrossFit competition.

The two columns on the far right are the average finish place “rank” and the standard deviation of the rank. We can use the average rank and the rank standard deviation to visualize the data. See below.

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A theoretical fitness plot. Each dot is an athlete. The vertical axes is the athletes’ average rank across all events. The horizontal axes is the athletes’ standard deviation of their ranks. The theoretical limits if fitness would be at (0,1) for the fittest and (0,5) for the least-fit. It’s like golf in that the lowest score wins.

Above is a “Fitness Plot” where each point represents an athlete. The two points on the far left are the extreme cases. The bottom left point is best case scenario for the fittest person possible. The top left point is the best case scenario for the least-fit person possible. The points on the right are what expect from people between the fittest and least-fit. We can use this plot to measure the distance to the bottom-left point . We will call this is “fittest-point”.

The 2013 CrossFit Games

We first start by using each athlete’s rank, average rank, and rank standard deviation. We use the average rank and rank standard deviation to make a fitness plot for the 2013 Games.

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Our reference for the fittest and least fit changes. Now we would expect the fittest person to have 100 points with each event rather than 1 point. This is not like golf, where the lowest score wins. Here, the person with the highest score wins.

Rich Froning is obviously closest to the fittest-point with Garret Fisher, Scott Panchik, Ben Smith, and Jason Khalipa close behind. The plot below shows their exact distance to the fittest-point.

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Here we see Froning as the fittest but a different 2nd and 3rd place. Scott Panchik would have had a podium finish.

Now we can see that the results have changed. With this new system, the outcome would be

  1. Rich Froning
  2. Garret Fisher
  3. Scott Panchik
  4. Jason Khalipa
  5. Ben Smith

So Froning would still sits atop the podium, but Khalipa would slip further down the rankings.

One criticism of this method is that we consider the average rank and the rank standard deviation equally. This is a tad bit ridiculous if you think about it. Just ask yourself who is fitter?

  • An athlete that finished 4th in every event
  • An athlete that placed 4th overall because of how the final score was calculated

In some ways this is why Castro gives more points to the top finishers and cuts those at the bottom. But this skews the data. Let’s look at the fitness plot using points, rather than ranks.

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Our reference for the fittest and least fit changes. Now we would expect the fittest person to have 100 points with each event rather than 1 point. This is not like golf, where the lowest score wins. Here, the person with the highest score wins.

The vertical axes is now the average points earned per event and the horizontal axes is the standard deviation of the points. Four athletes clearly have the highest average points:

  1. Garret Fisher
  2. Scott Panchik
  3. Ben Smith
  4. Rich Froning

Now the horizontal axes gives us some insight into their performances. A higher standard deviation (horizontal axes) means that their performance was not as consistent.

Now Rich Froning appears to be one of farthest, but still closer than Khalipa. We can look at the distance plot again.

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The top 5 are now:

  1. Garret Fisher
  2. Scott Panchik
  3. Ben Smith
  4. Rich Froning
  5. Albert-Dominic Larouche

So, Froning is still in the top 5, he wouldn’t sit atop the podium but he would still beat Khalipa. In fact, Khalipa has moved all the way down to 25th.

What about income?

The 1st place prize in 2007 was $500. The first place prize in 2019 was $300,000. Awarding $300,000 based on total final points and finding ways to awards those points is part of what makes The CrossFit Games a game, otherwise it’s an experiment — a test of fitness. With the prize money increasing we have to wonder if The CrossFit Games are incentivized to truly find the fittest or to provide entertainment, especially when only two men sat atop the podium for 8 of the last 9 years. If we are after entertainment, then I demand that The CrossFit Games include dynamic tests, such as wrestling and jiu jitsu. Because, what’s the point of collecting all of that fitness if you can’t use it for something practical?

What I’m trying to say is:

all of physics is just the study of momentum exchange, and the human body is just a momentum exchanger. The CrossFit Games gives static tests (i.e. move the weight from here to there) to measure a athletes’ ability to exchange momentum.

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But who would win in a fight, Khalipa or Froning?

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