Saturday, April 27, 2013

Scoring an exercise session

I joined Fitocracy some time ago.  It is a nice social site for posting your workouts and getting points.  But of course, the points don't matter, except to motivate you.

Having said that, the Fitocracy algorithm strongly favors weight lifting: Lifting 100 pounds five times is "equivalent" to running a mile.  Yeah, right!

Therefore, I decided to create my OWN point system (again, the points don't matter), which rewards the sort of exercise *I* do (jogging).

Here is the way I figure it (qualitatively).  You get more points for:

  1. Running farther,
  2. Running faster,
  3. Running with extra weight (including your own weight).
The last item is based on the reality that heavier runners expend more energy.  For example, let's say you are a svelte 130 pound marathon runner, who averages around 5:30/mile for short runs.  What would she be able to do with, say, 60 pounds of extra weight?  Could she halve her pace (11:00/mile) for a 5K with that extra weight?  Hmm?  HMMMMM?

Long story short (and I think this will need tweaking), I'll take this form for the algorithm:

Points = (scaling1)*(C1 + miles) + (scaling2)*(C2- pace) 

I'll arbitrarily say that a 1-mile run at a moderate pace for me is worth 5 points.  I'll also set scaling2=C1=1.0 (yeah, I know, the units don't match; ignore it).  A moderate pace for me is 13:00/mile (C2).  Do the arithmetic to see that scaling1=2.5:

points = 2.5*(1 + miles) + 13 - pace.

Now, we add a factor for the weight.  Since BMI is a better measurement of your overweight-ness, I have settled on this formula:

Points = 2.5*(1 + miles) + 0.4*BMI - pace.

There is only one more factor that I have to add in: you can only get points if you go at least 1/2 mile.

Using this scoring system, here are some examples of an 11-point 5K run for different BMI values:
  • 25:00, BMI=22
  • 30:00, BMI=26
  • 32:30, BMI=28
  • 35:00, BMI=30
  • 37:30, BMI=32
The world record 5K is 12:37 by Kenenisa Bekele of Ethiopia.  Let's say this particular human specimen has a BMI of 18.  Kenenisa would have received 13.4 points for this run.  Patrick Mahu's world's best marathon of 2:03:35 would have earned him (assuming a BMI of 16) 64 points!

My point system favors more frequent, shorter exercises, which is what I need right now.  That is, it is better for me to do five 2-mile runs in a week than three 5K's (about 40 points versus 33 points).

My sort-term goal is 25 points per week.  I hope to increase this to 40 points per week over the coming weeks.

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