Over the past few years, I've tried to find a way to analyze trail ultras mathematically and the progress I've made has been, let's say "limited." The sport is refractory. I found a way to compare races that works quite well most of the time, but completely falls apart for some races; I know why it fails, but that doesn't make me any happier about it.
Game theory (now a branch of decision theory) can do a good job of describing most sports. Bill James created "sabermetrics" as a method of turning baseball statistics into information useful for team management. Games, however, are required to have a few basic principles:
1) Rational, independent participants, competing to win.
2) Clear goals and rules.
3) Determinacy (the ability to make decisions based upon observations).
Here's where I'm having problems.
1) Only a very small minority of competitors in trail races are trying to run their best, much less try to win. The standard has become to finish comfortably enough that they can run in a race again in a week or two. People use most races as training runs, aiming for only one or two serious attempts at a fast time, if they ever do attempt to run fast. Many top racers intentionally do not compete against each other, choosing to go for easy wins, rather than to risk finishing second or third and many more drop out of races rather than finish with a sub-standard time. [As to whether there's anything rational in the sport... well, maybe.]
2) The goal of runners may be to become well-known and admired, rather than to win "important" races. Running a large number of races (I'm guilty here) or winning very small but particularly difficult races or being the first or the fastest to do something outside of racing has become the way to notoriety. Is the goal to run as well as one can, or to get noticed and then perhaps sponsored? After the Western States 100, people were arguing about how Kilian Jornet would have done if he hadn't done so many long and difficult runs just before it. Karl Meltzer's running the 2000 miles of the Pony Express route just because it struck him as something to do that no one else had thought to do. The most famous ultrarunner is Dean Karnazes, but just what has he done since 2006? (Best placing: second in the Canadian Death Race, whatever that is).
3) There is little improvement in times due to learning the sport. Races are often won by newcomers. Brian Peterson won the Superior Sawtooth 100 as his first attempt at the distance and credited his doing well to "really nailing the nutrition" from his experience in his two runs of 50 miles before it; the rest of us who have food problems will always have food problems. [People tend to swear by a product or two once they have some success, but the product itself isn't important. Getting inured to the product is what counts.] Helen Lavin won that same race in her first attempt at the distance, breaking the women's course record by hours; I remember hearing her making predictions of what she'd do (and being exactly right), but without much to base the expectations upon - it turns out the best predictor of one's time in an ultra is one's own gut feeling, not experience or training. If one is prone to a problem (like hand swelling), one goes through a ton of information to try to solve it, but to my knowledge no one ever "solves" it, they just accept it and the top runners never have to deal with it. If one runs a trail ultra and fails to finish (or finishes much more slowly than expected), one tries to learn from one's mistakes - but each race brings its own problem and the only thing one learns is that one can tolerate more discomfort with each experience of discomfort.
Still, trying to break such a monster of a sport into something manageable and capable of analysis has its charms. I'll keep working on it.
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