Crossfit & Running: How many “miles” am I getting out of class?

Disclaimer: I am in no way affiliated with Crossfit™ or FIveThirtyEight™ and this column does not represent their opinions.

As an avid crossfitter for the past 2 and a half years whose yearly goals always revolved around a new squat personal record or improved snatch technique, I was adamant that I’d never commit myself to training for a marathon.  Too much cardio…Too hard on the body..You can’t possibly expect me to spend 2 hours running outside in the depths of Chicago’s winter.  Yet here I now stand, signed up for the Nashville marathon in late April, eager to go put in 13 miles in 20 degree weather up the coast of Lake Michigan.

While I’ve always preferred setting my eyes on weightlifting targets, cardiovascular improvements, and running in particular, have come easier.  Being taller and longer-limbed has some advantages.  So while thinking about my goals for 2018, I decided to stop fighting my dispositions and focus on maximizing my strength of aerobic capacity. New year, new me, right?

The typical marathon program (depending on current fitness levels and goals) lasts 3-4 months and builds from roughly 30 miles per week up to 60 before tapering going into the big race.  Like many fellow crossfitters who have trained for marathons have done in the past, I decided to substitute the short training runs for crossfit classes and add a mid-distance run midweek and a long-distance run on the weekend.  Goal #1 is to finish.  Goal #2 is to be able to run the whole distance.  And goal #3, if all goes to plan, is to finish under 4 hours.  

I know crossfit must be assisting my training.  A year ago, I ran a half marathon in under 2 hours without adding long runs to my 5.5 classes/week training routine.  But how much is it specifically adding?

As someone who likes to read (arguably too much) into data, I thought this would be a fun personal project to try to estimate over the course of my marathon training.

A lot of research has already been done to predict marathon times based on training run paces and weekly mileage.  I started by using FiveThirtyEight ™ ‘s calculator to back out expected training run distributions for various weekly mileage counts, assuming a 4 hour marathon time:

This chart illustrates the paces you would need to hold on training runs to expect to achieve a 4 hour marathon, controlling for weekly mileage (model fits are listed at the end of the article).  The gist is that if you’re running fewer miles per week, you need to be hitting those runs quicker to expect the same performance in the race as somebody with greater weekly mileage.

The point I am particularly interested in is the distance where a runner’s pace starts to increase at an increasing rate.  This point serves as a good model for “the wall”, a distance where an athlete’s body starts to break down and their pace starts to slow be it because of dehydration, fatigue, or injury. Athletes who are running fewer miles per week should expect to hit this point in their training sooner than more consistent runners.  For any calculus fans, I’m sure you’ll recognize this point as an “inflection point”.  I calculated these inflection points and charted them as a function of weekly mileage:

This chart illustrates the behavior described above.  The more miles you run per week, the further you stave off running into “the wall”.  According to FiveThirtyEight ™’s model, this behavior appears parabolic in nature.

Now all that’s left to do is look at the distribution of my own training runs, determine where my expected inflection point is, and back out my expected weekly mileage.  To improve the model fit and allow for clear comparison to the FiveThirtyEight ™ model, I’ve assumed a 4 hour marathon time for myself:

This chart displays the training runs I’ve already completed and includes the point indicating a 4 hour marathon as well.  To run a 4 hour marathon, you must hold an average pace of 9:10 minutes per mile. My last training run was a half marathon at an average pace of 8:38.  This doesn’t leave a lot of leeway for my pace to degrade over the next 13.1 miles, but luckily there are still 3 months to prepare.

Using the model fit for my marathon training, I calculated that my inflection point occurs at 17.6 miles.  Plugging this into the model fit for “The Wall”, this corresponds to a weekly mileage of 47 miles per week.  Finally, removing the 18 miles per week I’ve been averaging and assuming I attend 5 crossfit classes per week, 1 crossfit class breaks down to 5.8 “miles” of running!

Both the estimate of weekly mileage and the estimate of “miles” per class were higher than I anticipated prior to performing the analysis.  These indicate that without the additional running training, I’ve still been logging nearly 30 “miles” of running per week.  This isn’t to say that crossfit can be considered a pure substitute for actually putting in the miles, though.  Ultimately, these miles are necessary in preparing the joints, ligaments, and aerobic systems for 4 hours of steady effort.  The intention of this analysis was, therefore, to gain a bit of insight into how to structure my training going forward and to illustrate a method of normalizing among various forms of fitness.

Limitations to Analysis

The first source of error I want to address is that this is a model based on another model.  Every time we make assumptions from data, we’re adding another element of error.  I don’t have the data that FiveThirtyEight ™ used to build their model and, therefore, can’t assess their error. Consequently, I can’t assess the precision of the final estimate.  

Secondly, every athlete’s endurance dispositions are going to vary.  While I’ve primarily done crossfit the past 2 and a half years, I came into it with 15 years of playing sports, along with 8 years of fairly dedicated weight/cardiovascular training.  The point is that if you’re only running 15 miles per week, but have accrued a solid foundation of endurance, your inflection point is likely further out than that predicted by FiveThirtyEight ™’s model.

Finally, I’m currently assuming I can run a 4 hour marathon.  Based on my current training runs, I’d almost have to maintain my current half marathon pace to achieve this feat. Finishing above 4 hours would have the effect reducing the inflection point, reducing the estimated weekly mileage, and therefore, reducing the “miles” per class.

Further

I’m still very early on in my training.  I’ve never run further than a half marathon, so I’m very eager to see how my body will hold up as I start to push into the 18-22 mile range.  My plan is to update this model with more data at the end of each month in an effort to reduce error and improve the final estimate.

Hope this read has been fun and informative and feel free to reach out with any comments or questions!

*Model Regressions:

Based on FiveThirtyEight ™’s model:

  • 15m/week: 6.66 + .205x – .0122x^2 + .000306x^3
  • 30m/week: 6.99 + .182x – .0094x^2 + .000215x^3
  • 45m/week: 7.16 + .217x – .0115x^2 + .000235x^3
  • 60m/week: 7.55 + .188x – .0787x^2 + .000117x^3

The Wall:

  • 15.4 – .207x + .00534x^2

My Marathon Training:

  • 5.03 + .664x – .0393x^2 + .000761x^3

References:

  • https://projects.fivethirtyeight.com/marathon-calculator/