Age grading is something that may be familiar to parkrunners. Those percentages in the results that seek to level the playing field by comparing your time to the world record time for your age and gender. They give the example of four parkrunners: a 9 year old girl who finishes with a time of 29:15, a 23 year old male with a time of 21:30, a 65 year old man on 27:57, and a 75 year old woman with a time of 40:25. Although their finish times are different they all share exactly the same level of performance/fitness when age and sex are taken into account. To be specific, they all have exactly the same age-graded percentage of 60%.
Our friends at Thirsk and Sowerby Harriers implement age grading in their own championships, and I thought it might be nice to do the same at GVS. For example, check out the results for Peak Forest, a →9.7km ↑247m fell race. The 1-2-3 using times alone was Gavin-Thomas-Lucas. But, taking ages and genders into account, the best performance was still Gavin, youthful Thomas falls right down the table, to be replaced by Moira.
| name | time | # | age grade | # |
|---|---|---|---|---|
| Gavin Peach | 44:45 | 1 | 73.6% | 1 |
| Lucas Jones | 49:23 | 3 | 71.3% | 2 |
| Moira Hunt | 69:43 | 13 | 69.2% | 3 |
| Paul Barton | 51:50 | 4 | 67.4% | 4 |
| Brian Holland | 62:54 | 11 | 66.2% | 5 |
| Wayne Grant | 52:25 | 5 | 66.1% | 6 |
| Thomas Penn | 47:26 | 2 | 65.4% | 7 |
| Julia Carter | 61:59 | 10 | 62.6% | 8 |
| Mary Jones | 65:03 | 12 | 61.7% | 9 |
| Neil Colquhoun | 53:29 | 6 | 60.6% | 10 |
| Anna Aspinall | 60:15 | 7 | 59.0% | 11 |
| Liz Roberts | 61:18 | 9 | 58.0% | 12 |
| Roy Whittle | 60:26 | 8 | 57.8% | 13 |
| Elizabeth Gilmour | 78:15 | 17 | 56.7% | 14 |
| Peter Rowe | 76:10 | 15 | 55.9% | 15 |
| Paul Hunt | 69:44 | 14 | 55.3% | 16 |
| Chris Tetley | 77:53 | 16 | 52.4% | 17 |
But how are these percentages calculated? Keep reading for the boring details.
The Boring Details
parkrun don’t publish the tables they use to calculate their age grading. What’s more, parkruns are all 5km. What’s even more, this was a gnarly fell race with some serious ascent. How can we get round these issues?
How long (effectively) is Peak Forest fell run?
Peak Forest is a 9.7km fell run, with 247m of ascent. Naismith’s rule of thumb would use the formula
9.7 + ɑ ⨉ 0.247
with ɑ=8 to say that this is an equivalent distance of 11.7km on the flat. But that formula would only apply to strictly uphill runs; in Peak Forest, there’s also 247m of descent. Hm. Up and down races, whilst not as hard as just up races, are harder than flat races. What’s more, gnarly fell races are much harder than their road equivalents. Somewhat arbitrarily, then, we’ll use the above formula with ɑ=8 (fell), ɑ=6 (trail) and ɑ=4 (road).
But what’s the world record for an 11.7km race?
parkrun don’t publish the tables they use to calculate age gradings. But World Masters Athletics do. For females and males, a variety of estimated world records are published for road racing distances from age 5 to 100, and 1 mile to 200 km.
For example, Moira is [age redacted]. You can read across to see the estimated 11.3 km (7 mile!) world record is 46:22, and the 12 km world record is 49:38. WMA recommend extrapolating with
u = (log 11.7 – log 11.3) / (log 12 – log 11.3) = 0.57
46:22 ⨉(1-u) ⨉ + 49:38 x u = 48:13
as the world record for someone of Moira’s age over 11.7km.
And finally
If we divide through Moira’s time into the world record time
48:13 / 69:43 = 69.2%
this is the age grading. It means that when the world-record holder finishes, Moira is 69% of the way around the course. Not bad!