Creating good athletic divisions

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A perennial problem with any athletic event is designing a fair reward structure. Say you're organizing an amateur mass-market athetic event like a road race. What divisions can people win in? The obvious and natural thing to do is to simply have everyone in the same division; the first X people across the line are winners and everyone else.... isn't. The problem here is that this restricts the pool of potential winners to a fairly small group, say men between 20 and 40. There's practically no athletic event at which even the best women are competitive with the top rank of men and there's a fairly sharp performance peak around 30-35 (depending a bit on what the sport is).

Now there's nothing necessarily wrong with just giving awards to those people but it's clearly a turnoff for people to be "competing" against others whom they have no actual chance at beating. And turning competitors off isn't a good way to get more people to enter your event. So, there's a lot of incentive to find some reward structure that gives a broader class of people a chance to win something. This even crosses over into professional sports where it feels unfair to force people to compete against others who are clearly qualitatively different—though it's worth noting that within gender (the most common division) variation greatly exceeds between gender variation and yet nobody thinks it unfair that I have to compete against men with 2:30 marathon times.

The three most common divisions that are used to partition up contestants are gender, age, and weight. All of these have the advantage that they seem superficially fair because they're either uncontrollable (age and except for edge-cases gender) or only marginally controllable (weight), which gives the appearance of fairness. In my experience the next most common division is "local contestants", which is also not really controllable and clearly arbitrary.1 All of these divisions also have the advantage of being (mostly) readily verifiable.

This sort of division works well for some sports but not as well for others. In martial arts, for instance, weight matters and there are often weight classes, but there's enormous skill variation between athletes. If you let white belts compete against black belts what you get is less a match than a rout. In martial arts with strict ranking systems you can just pair up people of the same rank (or maybe one-up or one down) against each other. 2. In less formal sports, sometimes how long you've been training is used as a proxy. Since most dojos don't keep particularly good records of when people have trained or what rank they have attained, and those records aren't centralized, it's pretty easy to sandbag. The theory here is that it's better to be a winner in the beginner's division than be a loser in the advanced division, so you claim you're a beginner.

One way of countering sandbagging is to turn it into a repeated game. Bicycle racing is divided into 5 "categories". The way you move up from one category to another is by winning races. If you're too dominating in a category you get promoted to the next one. What makes this work is that people tend to race each other repeatedly, so they tend to find their own level. Obviously you can sandbag a little bit, but you can't win very often because you'll eventually get moved up.

This doesn't work as well in non-iterated situations. An interesting case I ran into recently is rock climbing. A typical bouldering competition involves a bunch of problems of various difficulties, with harder problems being worth more points. Because climbing is so skill-based, it makes sense to have divisions, but it's so hard to compare people's skills that the competitions I've heard of (note: I've never done one but I've spoken to people who have worked them) have competitors self-sort into divisions. Obviously, this is incredibly susceptible to sandbagging. Competitions deal with this by promoting people who look too good into the next division.

Unfortunately, this strategy is inherently unstable because it's precisely the people you would expect to win (the best people in the division) who are most likely to get bumped out for being too good. A related problem is that there's a lot of variation in experienced difficulty for problems that are nominally the same grade, so it's precisely when you're having a good day and the problems seem to be easy for you that you have to worry about being declared too good. And of course you can still sandbag some by figuring out where the line is and climbing right up to it. What mostly seems to suppress this sort of thing is that it's considered unsporting. This works in a small community, but in my experience once the stakes get big (or even not so big) people seem to lose their sense of sportsmanship. Do any readers who've done comps have a read on how much people try to game the rules?

1. It's also interesting to look at the evolution of sports, which seem to accrete finer divisions. For example, the Ultimate Fighting Championship used to be totally open but later weight classes were added. A while back triathlon introduced the "clydesdale" division for heavier athletes (the female version is called Athena). Clearly, heavier athletes are at a disadvantage but it seems to me that this division is still regarded with a bit of suspicion.
2. A related problem in martial arts is that you need to keep the divisions fairly small because otherwise the tournament requires two many matches to converge on a single winner.

3 Comments

Chess players have ratings assigned by a central authority (national or whatever) using e.g. the Elo scheme, based on performance in games vs other rated players. Players can then be partitioned into sections by maximum rating at tournaments.

It works very well to keep a level playing field and to retain incentive for less able players.

Couldn't the same be done for any two-"player" martial art for example? For athletic events you could just use a central authority to track performance based on times and some clever weighted average or something.

How random; I just spent all weekend setting for a comp at my gym...

Our answer is basically to cheat. The only division at sign-up time is by gender. After everybody is done climbing, we look at the resulting point distributions, and divide the men's and women's fields into beginner, intermediate, and advanced categories. It generally works out that it's pretty obvious where those divisions should go. It's nominally possible to game this system if you keep track of how many points other people are racking up, but I don't think anybody really does.

I was just at a collegiate dance competition this weekend (e.g., waltz, rhumba, foxtrot). Division into levels there is basically self-selected; the interesting thing is that the advanced levels actually offer the best opportunities to place -- at the competitions I've been to (in the (south)west), simply competing in the gold syllabus category would put you in the top 5. But dance is fairly performance based, and I think that the shame of having to publicly dance above your actual level means that college competitors end up clumping mostly at the bronze level (just one step above the very newcomers)

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