Thursday, September 24, 2009
I dig number crunching. Which is why I have fun throwing together stuff like yesterday's post on my running goals. Today's post is really part II to that post. It's another way of quantifying improvement. The data above are average heart rates and pace over mile segments at back cove from this summer. The top graph is pace as a function of HR. Pretty simple, my HR sets limits on how fast I can run, so the faster the HR the faster I can run. I fit a quadratic polynomial curve to the data. Some of the variation off the curve is due to things like coffee status, time of day, heat, humidity, wind direction and speed, etc. But I'm interested if the speed that I can run at a certain HR has increased over the summer. So in the bottom figure, I took the residuals from the curve in the top figure and plotted them against day of year (DOY), with Jan 1 =1 and today being 266. I then fit a linear regression to these data. It's pretty crystal clear that today I can run faster at a given HR than I could early in the summer (the first datum is from May 27). In fact, the curve suggests that I can run about 50s/mile faster at any given HR. That seems like too much. Indeed, it would mean that on May 27 my 5K speed was about 20:53. Certainly I coulda run faster than that! Although maybe it explains my bonking at Muddy Moose, Pineland 25K, and the Clam Festival. Another possibility is my little analysis doesn't work so well for predicting the extremes. So I redid the analysis using only HR>155, which is a fast tempo run. With this subset of data, I find that I'm running 32s/mile faster at the faster heart rates. So that's a 19:59 5K. Still think I coulda beat that on May 27. Maybe next year I'll run the Mother's day 5K just to see how well my HR retrodiction works.