How King and Queen Race Results Are Calculated

Note: This article was originally written by Earl Brown when he was K&Q Competition scorekeeper from 2008 to 2011. It was edited by Matthew Studholme in May 2016.

To calculate results for K&Q races, age differences are first eliminated by using the age-grading tables published by the World Masters Athletics (WMA). You can manually age-grade a race yourself by going to this website. There you can pick a race distance (or even field events, like the high jump, if you want) and then enter an age, sex, and event result. After that, click on the "Age-grade" button. This will then show the age-graded results and age-performance %. For example, in the 2009 Phipps Bend 5K, Molly Allen (38-years-old woman) ran a time of 18:20 (a PR!). Plugging these results into the calculator on the WMA site and using the distance as "5kmRoad" from the "Road" drop-down menu followed by pressing the "Age-grade" button, you'll find that Molly's time converts to an "age-graded result" of 17:54 and an "age-performance %" of 82.64%. (Note that this site will also list the world record for that distance and sex, called the "Open std" and the world record for that age and sex, called the "Age std".) The "age-graded result" is theoretically an equal performance by a person of that sex in their early 20's. The "age-performance %", which is listed on our K&Q results as "%World", is a percentage of the world-record for that distance for that particular age and sex. A rough estimate of what these world percent numbers mean is as follows:

This WMA calculator site is interesting, because after calculating a race result, you can convert it to a different age, sex, or distance. For example, after plugging in Molly's Phipps Bend 5K results, and pressing the "Age-grade" button, change the age to 53, the sex to male, and then press the "Result" button (not the "Age-grade" button). This will then show that a 53-year-old man (like me) would have had to run a time of 18:17 (seen in the "Time/distance/height" box) to equal Molly's performance.

To finish the calculation for K&Q race results, the age-graded results calculated above are then normalized to a 10K time, that is, they are converted to times that would probably have been the results had the race been a 10K. There are many different ways to normalize times (it's basically all guess work!), but we use something called the "Riegel formula", which was published by Pete Riegel in the early 80s in an article called "Athletic Records and Human Endurance" published in American Scientist. You can manually normalize your age-graded result calculated above by going to this site, which also lists Riegel's formula. There input the distance for that particular race, the calculated age-graded time from the WMA calculator site, and then pick 10 km for "What is my predicted time for". After that click on the "calculate" button. For example, Molly Allen's Phipps Bend 5K converted to an age-graded time of 17:54. So, on the "Race Conversion Calculator Page", type 5 (because Phipps Bend is a 5K) in the box after "I have run:" (be sure the adjacent box is set to "kilometers") and in the box on the next line type in "17:54" (that is "0:17:54"). Then on the third line, in the box after "What is my predicted time for:" type in 10 (be sure the adjacent box is set to "kilometers") and click on the "Calculate" button. This normalized 10K result should match closely the result listed on the Individual K&Q Results Page for that person. The article The King and Queen Web Pages has more information about how to use the Individual Results Page to see individual race results.

The final calculation is to figure out which combination of 6 races that totals up to at least 25 miles gives the fastest average time. Depending on how many races you have run, this may not be a simple thing to figure out manually. If you ran all 31 K&Q races in 2009, then there are (I think) 73,6281 possible combinations of 6 races! Of these combinations, how many give race totals of at least 25 miles?! (By my guess, it's 2,654! Check out this file to see a list of the combinations of 6 K&Q races that add up to at least 25 miles.) Since I can't do this manually, I wrote a computer program that calculates every possible combination of 6 races from the total number of races run by a particular runner. For each one of these combinations, if the 6 races add up to at least 25 miles, then the average time for those 6 races is calculated and compared to all combinations that total at least 25 miles and the best (fastest) average is saved. You can manually check your results on the Individual K&Q Results Page. If you find a combination of 6 races that you ran that total at least 25 miles and gives a faster average time than the result listed, please let the K&Q competition scorekeeper know. That won't be easy, though. Good luck!!!