uh-oh. Another math post! Feel free to ignore it.
Gary Robbins of Canada set a new course record at HURT (20:12) this week. But just how good is that? Comparing trail races is the holy grail of running math geeks.
I think I've found the best way to do it. One can linearize race results by plotting the finish time against the cube root of the place - don't ask why it works; I've spent 20 years justifying it. It works better as a first approximation than anything else does. For the H.U.R.T. 100 Mile, places 6-14 and 27-47 fall on a straight line (there's a weird divergence in between, due to the constraints of the model). The equation is 314.463x(cube root of place)+1027.59=minutes. The intercept, 1027.59, is the theoretical limit of fastest finish time, in this case 17:07.
Twice this time, or 2055, is the expected finish time of the average runner and that runner's expected place is the cube of (intercept/slope)= 34.89. A check of the results shows that this is close.
The effective field size is twice this place, or 70 runners. The expected finish time of runner #69.78 is 38:42, which is an expected cut-off time for the race. HURT is notorious for its short cut-off of 36 hours and its corresponding low finish rate.
The slope plus the intercept equals the expected winning time (22:32), which is almost always higher than the actual winning time. [It's worth noting that Kyle Skaggs' record at Hardrock is faster than the intercept!]
For those looking for a quick and dirty method, the intercept is approximately three times the eighth finisher's time minus twice the 27th runner's time (1052). For larger races, another approximation is 4 x the 27th runner's time minus 3 x 64th.
The intercept time should be the same for any race, year after year, with a variation due to weather. A runner can compare his time at one race to another by comparing fractions of intercept times.
For example: the 2007 Superior Sawtooth 100. The equation is 447.2364n(1/3)+1013.32=T.
T1=24:21 (23:17 actual)
T(last)=38:10 (cut-off=38 hours, 23 official finishers)
From this, one can see that HURT is about 1.5% harder than Superior (i.e. 1027/1013). The two are almost equivalent, though HURT has a reputation as a hard race and Superior is relatively unknown outside the midwest (where it's known to be hard).
No one did both races, so it's impossible to check how well they compare that way.
How would Wynn's winning time that year compare? 23:17x1027.6/1013.3= just under 24 hours, or third place. Does that mean Wynn would've finished third? No. One can't justify that; the method compares, it doesn't predict.
I'm going to try to record some top performances this way and see if my results match those of Ultrarunner magazine.
Big change in life today
4 days ago