Race Time Predictors. An explanation.

It is possible to suggest a predicted time based on a recent race result, this is based on research and observation from runners and race results. There are 4 main methods quoted online where the calculation method is widely known (where else would anyone else look!! Actually online is better than in books and publications since most sites offering the information also have a handy calculator built in - which is what I have done). There are 2 other methods that I am not considering here. The Purdy points method - it looks too complicated for me to programme how to do it and I would end up copying the code which isn't morally good. The other is the McMillan method, the calculation for this isn't widely available (OK it is on only 1 site really and then you have to dig a bit to get the formula), and like copying the code for the purdy points system, copying the formula wouldn't be a good thing to do.

The ones I am considering are:
The most quoted is the 'runners world' method (or Riegel Method)
The Cameron method
The Harwill method
The WMA Age Grading method (also the Howard Grubb method).

On the prediction page I put in the method I first used to guess my race speed, I'll call it the Steven method (might as well get some mention for this)

The last one I have put in is based on the average race times, I'll call it the Average race method.


Riegel Method
This was one of the first predictors, developed in the 1970's and says that the further you run, then your time decreases exponentially and this is described in a formula. This makes it easy to use, just type it into a calculator and one formula gives you a predicted time. The formula used is:
T2 = T1 (D2 / D1) ^ 1.06, where T is the time, D is Distance (1 for the race you know, 2 for future race) and ^ 1.06 is the exponential slowing.

Cameron Method
Based on the worlds 10 fastest times at each distance and again breaks down to simple formulas (though a bit more complicated than the Riegel Method). The formulas used are:
a = 13.49681 0.048865*olddist + 2.438936/(olddist^0.7905)
b = 13.49681 0.048865*newdist + 2.438936/(newdist^0.7905)
newtime = (oldtime/olddist) * (a/b) * newdist

These 2 methods and you rate of slowing is a factor of the increase in distance. What I mean here is that if 2 runners run at the same speed but for different distances, when the distance doubles, the one who runs the longer distance will slow down more.

Harwill Method
This says that as you double the distance your speed slows by a fixed amount per mile (16 seconds a mile slower), this change of speed is uniform regardless of your starting speed - which I think is a flaw in the method.

Steven Method
I started saying - based on my race times - that as my distance doubled my race time was doubled plus the number of miles in the new distance. Simple to work out but doesn't quite work because for everyone - just people who run at the speed I used to run at. Perhaps I can modify this one day to take into account the runners speed.

Age Grading
This is quite a popular thing at the moment. What it says is that you run at a proportion of the speed of the world record for a runner of your age (there are world records for all ages of people, plus the ultimate fastest ever at the distance). So you might be running at 50% of the world record for a 35 year old, and then you can compare yourself to a 90 year old - if they run at 60% of their world record then they are the faster runner - even if they were slower on the course. So that is how they come about and the World Masters Athletics keep a list of these records, these are designed to even out the ravages of age a bit. Howard Grubb produced an age grading website and it seams that everyone has just copied his code and bunged it into their own sites, newer age grade tables appear on Alan Jones's website. These 2 sites plus the data from the World Masters form the basis of my age grade tables. Anyway for my purposes is to get your age grade for your first race and then to apply the age grade to your second distance to predict your time.

Average race time
This says that if you finish a race at the centre of the pack then in a different race you are also likely to finish in the centre of the pack. So knowing the average race time for the new and old race lengths you can predict the new time.

The age grading and average time methods are also good ways to predict a finishing time since they are using proportions of race speeds rather than saying you will slow down by a set amount. This works well whether you are at the front or the back of the pack


I have only considered the 4 most popular road races - the 5km, 10km, half marathon and marathon and have made an assumption that each is twice as far as the next shortest.

Each predictor uses a different formula and is based on different observations. This means that each one will give a slightly different result to the others. The largest differences are races a long way from the known race (say 5km predicting a marathon). Each runner runs differently and I know of runners who slow down a lot, maintain a steady pace and even speed up when the distance increases. I put the results on for all the methods and you can choose the best to suit your running style, I have also put an average on of all of them - this might be more accurate for you.

Last thing to note: The predictions here use the formulas and methods described above, and so do other sites. This should suggest that all the results are equal - they arn't quite since the programming and tables used are different. This is a prediction method and is not an exact science, the numbers just give your mates a rough time to get out of the pub to watch you pass that's all




So how DO race time predictors compare?

Bet you can guess where I am going with this bit....

If you have 6 methods all meant to be giving the same result then surely the results should all be similar. A bit of an afternoon with a spreadsheet and these formulas and this produced the following charts. I have gone for entering basic data - based on a 30 year old man, running 2 distances in various times, how do the predictions compare. I am comparing 5km times and marathon times, any large differences between the methods will be clearer the further you are away from the 'actual' time. So marathon and 5km times


Comparison of predictions from 5km Race times

Comparison of predictions from marathon Race times
Axis are: Y axis (up-down) - predicted time, X Axis (left-right) 'actual' race time
Line from top to bottom: Marathon prediction, Half marathon, 10k and 5k

What they show
All 6 methods give very similar results. There is a greater variation from a short race to marathon prediction between the results, but this is similar to real life - I don't think you should use a 5km result to predict a race 8 times longer - there are so many other variables to consider.

The McMillan and Purdy points methods give similar results to the others based on the few test times I have tried (1 fast, 1 medium and 1 slow time for each of the 4 distance).

Time predictors give a very similar result to each other



So how do these compare to REAL runners
So you know how the theoretical predictions compare, but what about real runners

The Power of 10 website publishes runners and their race results (a handy website to keep a track on those PB's!). For my purposes this is a useful set of actual race times. Going through the website I noted down runners times where they had run 3 out of the 4 of my race distances. This was quite a lot of work - more than I had anticipated when I started looking at this bit. This gave me quite a list of runners race times over several distances (my first list was 500 runners... I have added more as I get time to). Now I can compare real runners to the predicted race times! When I looked at this I only looked at the runners absolute PB for the distance - whether they were on the same day or 5 years apart. My thought for comparing PB's is that this is as fast as the runner can go, comparing races within a certain time of each other allows for variations due to weather, courses, feeling off, a hard run the week before, running with friends, hills, rain, sun, and all the other excuses I have used in the past

This gave these charts.

Comparison of race times and the predictions from a 5km race time

Comparison of race times and the predictions from a 10km race time

Comparison of race times and the predictions from a Half Marathon race time

Comparison of race times and the predictions from a marathon race time

The 4 charts show actual race times for each distance and the corresponding runners race times for the other distances, the solid lines are the predicted times based on the charts distance finishing times

As before the top line is the marathon, then the half marathon, the 10km race and then the 5km race. The solid line is the predicted race time from the 5km race result or marathon race result and the dots are the actual times of the runners. X-Axis is the race distance race time.

The predictions follow that actual times runners get however there is a variation from predicted to actual. This is to be expected - different courses, weather conditions and so on can do this


Conclusions

  • Race time predictors all give similar results
  • Race time predictors give a straight line graph pretty much, so really a simple equation can be used for a race time predictor
  • Runners who run with the same race time will finish another race in similar times - but not identical times
  • The further you are away from your timed race, the less accurate a prediction will be
  • Due to the length of time it takes to complete them, the marathon and half marathon show the greatest variation between a prediction and actual race result. Runners can run several short races a year fast and have a greater opportunity to gain a PB (The values I used to compare the predictions with), and perhaps one marathon a year for the average runner - so an off day with the marathon and the time predictions will be out
  • If you are going to predict future races, the half marathon is the best race to predict them from