"There's only one hard and fast rule in running: sometimes you have to run one hard and fast."

Monday, December 27, 2010

Trail ultras and game theory

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.


Glaven Q. Heisenberg said...

I suspect there's only so much that any rational analysis can tell you (or "one") about an activity as quintessentially irrational as attempting to run 100 miles or more. I'm not saying analysis isn't worth it or that it can't tell you anything. But can the rational really fully encompass the irrational? Can it even capture the essence of it?

Next maybe you can do a mathematical analysis of speaking in tongues, who does it best, and why.

wildknits said...

Looking forward to reading your thoughts on this.

It may be hard to tell, but I do really enter races to see how well I can do at that particular distance. I tend to be very competitive, at least with myself.

Right now I intend to have another go at both the Voyageur 50 mile and Wild Duluth 100k as I think (know) I can run better races than I did in 2010.

Oh yeah... rational analysis of an irrational sport.... ;->

mike_hinterberg said...

Very interesting. My limited understanding of game theory (and Wikipedia's entry) generally suggests an interaction between 2 or more players. Indeed, like you suggested, winning (or placing) in most public races, for most people, is more about time/finishing goals and seeing what one can get out of their training.

That is, you could get most of the 'information' about a performance of an individual based on their training on the same (or similar) course, independent of the interaction between opponents. The extras of an ultra seem to be more about camaraderie and convenience (not having to carry liters of water and thousands of calories) more than interpersonal strategy -- for most people.

Contrast that with baseball or checkers, where playing a game against yourself just doesn't make sense...ultras, especially, seem to be an individual performance outside of the top 5% or so.

But, if you could re-define the 'game' as to being one that maximizes the goals you mentioned: racing against oneself, racing at 85% capacity as a training run, etc., you might get some results and mathematical equations out of it?

Otherwise, I think a big machine-learning/neural network approach might also get us what we ultimately want: the ability to predict finishing times without having to actually run the damn distance anymore!

Fast Bastard said...

Steve, I agree with your post, but you also have to admit that the charm of ultras is the irrationality.

There is a lot of talk about money in ultra running. In the four years I have been aware of ultra running as a sport, it has certainly become more mainstream and sponsorships and prize money seem to be on the rise.

But it's still such a "poor" sport that the biggest stars can't just pick a spring and a fall ultra, like the top marathoners do. This leads to a culture, where most people race frequently, with little focus on peaking for a goal race.

Once money becomes a major factor in ultras, I think we will see an influx of elite marathoners moving up to ultras. I think you'll agree that a 2:15-2:20 marathoner could win most ultras pretty easily.

Money in ultra running would make for some cool, competitive races, but the irrationality would be gone.