The Big Percent

Runners often talk about a course being a 'PB' course - that is a course where a runner generally runs faster for the same distance than another course, but are they really, and just how much faster is a course compared to another? Is there a way of saying one course is, say 10% faster than another? Using the Parkrun series of training runs as examples, it is possible to give each course a figure to show it's speed compared to other courses. I am calling this figure the 'big Percent'

Parkrun is an ideal event to show how this works, each are the same length, measured the same way, they run every week so that effects of weather are reduced, and there are a lot of results available to look at. To get a good value of speed for a course the more results and more races that you can use the better the results will be.

Men and Club Runners are faster than Women and Non-club runners on average (If an average club runner takes 100% of time, then an average non-club runner takes percent to complete the same route). To compare like for like it is better to reduce all variables apart from the course to an even comparison. There are 4 types of runner:
Male Club Runners Female Club Runners Male non Club Runners Female non Club Runners

Ignoring age (Too hard for me to work out - not enough data you see). Comparing all the runs, each class of runner is given a % value of a base value. For the Parkrun events my base value is the fastest for that class of runner in any Parkrun. For example, if average 5k runners in run 1 finish in 20 minutes, and in course 2 in 22 minutes, course 2 is 91% of the speed of course 1. In longer distances I am going to use the average value for that race distance as a base value.

Add the percents for each class together and divide by 4 and this gives each course a number out of 100 that shows how it compares to the other courses. This is a more accurate measure than just averaging all the runners since it takes into account courses that might be dominated by one type of runner (for example, Ladies only races would suggest a slow course if just the average was used - no club running men to improve the average).


Alternative method.
The other way of suggesting which are the fast courses is not practical to do, but that is to compare all the runners who have run both courses, and compare the times of identical runners running different courses - assuming that they run them both with the same effort and so on. Not practical to do or useful since you might not have any runners to compare and those that you do will be such low numbers that an unusual result for a runner would skew the results greatly. I have done the sums for the Parkrun series though - See the bottom of this page.


To show how this works here are some of the Parkruns examples that I have looked at:


Overall
Male Club Runner
Female Club Runner
Male No Club
Female No Club
The Big
Location
Average
Average
percent
Average
percent
Average
percent
Average
percent
Percent





How does it compare to real runner?
The Big Percent compares the average times for all the runners from one course to another, the higher the number the faster the course. You can do a similar thing for individual runners and add all of them together. So if a runner has run course 1 and course 2, you can say that the runner completes course 2 slower than course 1, and work out how much slower. There are several ways to do this, for example comparing one run from each runner on a course (fastest run for each course, consequetive runs and so on), or comparing many runs from each runner and using an average of these.

I am going to do an average method but to only use runners who have run the course several times (a runner might run their local course every week and run a different course once, when they have visited friends, after a Friday traveling, a night out and leaving the hotel without breakfast - not the best comparison to a run where they get out of bed refreshed and ready to go). I will use runners who have run the course 7 times or more. Ideally I would use runners who have run more than one course more than 10 or more times - but that really does reduce the number of runners to a small amount (the more times they run, the more consistent their average times and so gives a better result) - the more runners the better the numbers become.

If I work out the Big Percent for a route and the comparative runners speeds with that route and other routes, there should be a correlation between the 2. The numbers won't match exactly since I am comparing humans who change over time but they should be close.

Anyway, the Big Percent and Runners Percent have a correlation of: 0.4. Not quite as high a correlation as I would have thought to be honest. However if you take into acount only the more mature events, for example 3 years old, this correllation between runners percent and Big Percent rises to 0.72 - which is statistically OK to say the 2 are related.

The update for this takes quite a while to do, 20 minutes for each of the 80 and more Parkruns, so not surprisingly I am not going to update this every week


Parkrun time prediction
Now Using the big percent value, you can predict your time on another course - divide your known time by that courses big percent value and then multiply it by the new course big percent value to get a prediction

So if I ran Middlesbrough in 25 minutes I am likely to run Bushy Park in 25 x (Middlesbrough) / (Bushy) minutes (about 22:51)

This is giving me shivers - I can feel another handy calculator coming on.... eurgh.. but I'll leave this for now.