Interesting (to me) Run Observations

Disclaimer

This post is all about a certain analytical aspect of running.  So, if your eyes glaze over the moment you hear the word "regression", this post is not for you.  However, if your of the sort, the geeky sort, who likes to "know how stuff works", this post is for you!

Background

I think it is well understood that running speed is directly and linearly related to effort through a large range of heart rates.  Surprisingly, there is a actually not a lot of clinical research around this topic.  However, Billat, et al describes this concept well in the article "Training effect on performance, substrate balance and blood lactate concentration at maximal lactate steady state in master endurance-runners." (Figure 3, in particular).

I have been using this relationship for a few years to understand how my body adapts to various types of run training (e.g., speed work vs low-aerobic).  I have also used this relationship to predict my potential run split times in my recent Ironman races.  In fact, I predicted my 2016 IM-Boulder run split to within 1-minute using this technique.

My Data

During the period of August 12, 2018 to September 9th, 2018(today) I tracked this data in my long runs (14-20 miles) along the same course.  To keep the analysis consistent and simple, I took the same segments along the route (Easley Road, which is flat) on the "out" (segment-1) and back (segment-2).  My run strategy has been the same for each of these runs; out is at Maffetone (relaxed) pace and back is slightly harder than Ironman pace.  Numerically, these effort levels correspond to ~135BPM out, and ~146BPM (capped at 149BPM) coming back.  Here is a visual of an 18-mile run last week.  The change in effort level is apparent at the start of lap 10 (mile 10).

This data is also presented as an XY-scatter in the image below.  This chart is comprised of 8 runs during the aforementioned period.  One can appreciate the good (but not great) relationship between heart rate and pace.  This analysis is about where I had historically left off.  That is, this data gave me the information I needed -- answering the question of, "how fast can I expect to run at a given HR"?

However, historically what I have been most curious about is what influences the slope and intercept of this relationship.   Billat, et al show that training over a relatively short period (6-weeks) improved the intercept with the slope remaining unchanged (figure 3 in their article).  The particular training in that study was steady-state threshold intervals.  I suspect that any training along this line (easy through threshold) will have a similar affect.

The slope & intercept data from these runs is presented below.  For each run, I calculated the slope and intercept.  While not monotonic, I am seeing a large change in the intercept over the last month or so.  But what is also apparent is that there is a change in the slope as well.  I found that fact unusual, and NOT present in the Billat study.  Also, why was there such a large change in the intercept?  Why, over a short period of time, is there such a large change in slope?

When trying to understand data, I often rely on pictures, or plots.  So, I created a simple XY-scatter of the slope and intercept to see if there was nay sort apparent relationship.  What I found was completely unexpected and incredibly fascinating -- there was a near-perfect correlation between the slope and intercept.  How could there be such a high-fidelity relationship?  Every run lies on this line.

As I thought about this further, I realized that this relationship meant that each run could be represented by an individual line, and these various lines would all intersect at a singular point -- near 147BPM.  What is the significance of this heart rate?

What is also presented in the table above is the pace at 147BPM.  I'll cover later why I chose that specific heart rate.  But, I had noticed a concerning trend in the pace at 147BPM -- it was declining!  That concerning trend is apparent in the chart below.

I was training well, running well, but it appeared my fitness was declining.  My first thought was concern of over-training, but other training and physiologic parameters did not support that theory.  Of course, one of the obvious reasons for slowing down is a higher training load.