I'm not sure I believe the hypothesis, but I think most of the skills we value are mental, rather than physical, and so a contest designed to test these things would likely be considered a game, rather than a sport (e.g. something like forum mafia incorporates a lot of skills rationalists value, or I'd make the case for mahjong).
We value making probability estimates based on limited information, changing your mind appropriately when the information changes, and avoiding being influenced by others. We don't like blindly following orders (something that's necessary in many current team sports). I suspect many of us dislike arbitrary tribal affiliation (required for any kind of sports fan-experience really), the win-lose structure that means each match gives a risk of an unhappy result, and the value placed on physical ability.
So a rationalist sport would want to have physical ability relatively unimportant (secondary to skill and intelligence), either no teams or fluid teams, and some positive-sum scoring structure where it's possible to play risk-aversely and do well. And even then, that might be something we'd enjoy playing, but you wouldn't get the fan dynamics of mainstream sports.
On the contrary, I always liked sports that compensate for mental work. Also, physical activity can be healthy and, as they say, mens sana in corpore sano... (For example, running is said to be healthy for the brain and I found it very useful for forcing my brain to pause. One problem is that in the long term running destroys your knees, so after two marathons I will reduce long-distance running in the future.)
This has some tradition, for example Alan Turing (maybe the greatest computer scientist of all time?) and Bobby Fischer (maybe the best chess player...
This post is a bit of an experiment; Most of the time, Discussion post lay out an idea and this idea then get commented upon. This post, on the other hand, will be purely about discussion on a topic. If this works out well, I'll might post more of these in the future.
On to the meat of this post:
I got this idea from a reddit post on /r/LessWrong.
To quote:
So have at it.
I only ask for one thing and that is to hold off on proposing solutions for 24 hours before giving suggestions for actual sports. In the first 24 hours, please discuss what makes current sports unappealing to rationalists and what aspects a sports designed for aspiring rationalists should have.
Edit: The 24-hour window has closed and solutions and suggestions can now be given.