Comparing performance

[I got tired of trying to make pretty images for this. Please bear with it.]

One of the big challenges of running is figuring out if one run at one distance is better or worse than another at another distance. There are apps that claim to do this and some of them work very well for some people. None has worked for me. I had to devise my own system and I think it can work for others.

If you plot World records (men, women, age class doesn't matter much) on a log-log plot, you get this:

There's a steep line up to 800m or a mile, then it flattens into another straight line to the marathon or 50K, then rises steeply again. The marathon itself is marked with an x, it's an anomaly below the straight line; this is because of the number of people who have raced the distance at a high level because one can win one major race and retire if you're from Kenya or Ethiopia. 

If you plot all of your runs, races and training, you get a plot like this.

I have 600+ races and 10000+ workouts, so the data is good (if messy), but you may have to make this just a thought experiment for yourself. The lowest dots should be your fastest races at different distances and should form a straight line.

If that line is parallel to the record line, you're equally good at all distances. The line is then

1.085 log (miles) + log (mile time) = log (minutes)

This is essentially the same as the charts made by J. Gerry Purdy in the 1960s and published in the classic Computerized Running Training by Gardner and Purdy, easily found online. This works best for those whose best races are 5K to 10K.

If the slope is shallower, 1.06 rather than 1.085 in the above, it matches the charts made for Jack Daniels in the 1960s and easily found in any of his works. This works best for those who are by nature marathoners. It's what's used in a lot of sports trackers.

In my case, the line is steeper, 1.10 rather than 1.085 and this is common for 800m/1500m specialists. There is no published charts for this, but the math isn't terrible. 

There should be a line in the center of all the training dots parallel to your races that is your average training run regardless of distance. [Linear regression isn't the best way to find this, as one tends to cut bad runs short and not do truly easy long runs.] For me, race times are 0.79 times this average and I find this 80% (rounding) average run is typical for other runners. 

So, if you have races or common favorite runs that are accurately measured, you can figure out what that compares to at other distances. 

If you imagine looking down the average line from one end, most performances are close to the line and then it spreads out in a normal curve of error. 

There will be statistics in future posts.