Thursday, June 12, 2008

WS Pace Chart

I took the results and splits from last year's WS race and did some calculations with them. For all finishers, I figured out what percentage of their total finishing time was spent in each segment of the race, based on the data from the WS web site.

I used last year's data because last year's course is the same as this year's course (I believe) and both years will be low-snow years. Last year was cooler than average, so a hot day this year may invalidate some of this data.

After calculating the percentages by segment, I grabbed the median value from each data set. The sum of the medians was 99.14%, so I divided each segment percentage by 99.14%, so I'd end up with 100%. From this, I calculated an expected arrival time for each runner at the major (timed) aid stations, based on a pace of 16, 18, 20, 22, 24, 26, 28 and 30 hours.

I like to give my crew something like this for every race (usually only for 24-30 hours though), so they can use this to estimate when I'll be at the next aid station. They can also see if I'm picking things up relative to the pack or if I'm falling off. I added the faster split segments this time in case any fast readers happen across my blog.

Please note that my times for the 24 hour pace are slightly different than what you'll find on the WS web page.

Click on the image to see it in a larger and more readable size.


Jamie said...

You just saved me a lot of work... thanks!!!

firepotter said...

Excellent work!

Here is a version of last year's splits on Google Doc.


Andrew said...

This is really nice. I have a question about method. I don't quite understand how you calculated the median values. (I'm sure this is my fault since I'm a math dummy.) Are the median values for 24 hour runners taken from those who finished in over 22 but under 24 hours, over 22 but under 26 hours, all under 24 hour finishers? I ask because one of my projects this week is to sit down and calculate median times for the last ten 24 hour finishers (since I will be at the back of the 24 hour pack if I'm in it at all).

Damon said...


I used all finishers, and calculated the median percentage of time used for each split. I ignored time spent in aid stations to keep it simple, and I only bothered with one time at the river crossing, on the near side.

In the past, I've used a different technique, where I would break finishers down by time ranges around a number. For example, if I wanted 24 hour estimates, I might take all finishers from 23-25 hours and examine them. I'd plot data points and ask Excel to generate a 5th order polynomial for me. That can give you more accurate data for a narrow time range, but the reduced number of data points risks being less statistically valid. I would often have data sets with fewer than 30 records, and those are particularly suspect.

Because 16 hour runners and 30 hour runners might run the course very differently, in terms of time spent on particular segments, my method this time is probably best for runners near the mid-point of the finishers. I simply used all finishers and then took the median percentage time used for each segment. I decided that using averages could be thrown off a bit by bizarre splits if a runner took a nap at an aid station somewhere.

Then, when I summed the median times, I got 99.14%. So, I divided each percentage by .9914, to normalize those percentages to 100%. From that, I took the percentage for each segment, and multiplied it by a projected finishing time.

I started with the spreadsheet that firepotter mentioned in his comment.

I have now modified the spreadsheet somewhat for my crew, but I can e-mail you what I have, if you like. You could then use that as the starting point for what you need.

I went with a simple technique this time that had lots of data points, rather than smaller samples around a single finishing time range.