Extreme sports: What are the risks?

An upcoming sky-dive has our resident statistician contemplating whether risky pursuits are a good idea.

I have a confession to make: I am feeling a little nervous. I am making a TV programme for the BBC about chance and uncertainty, and for some reason the producers have told me that I need to do a sky-dive – presumably while they stand safely on solid ground, sipping tea and enjoying the spectacle of me floating gently to earth. Probably.
But as I ponder the wisdom of such an undertaking, the statistician in me has been keen to explore the real dangeers of various seemingly high-risk pursuits. There is seemingly no shortage of people apparently willing to scale great heights, or hurl themselves down from them – including me, it seems – turning extreme sports into a multi-billion dollar global industry.
Comparing these risks is not a clear-cut task. It is usually fairly straightforward to count the dead bodies. But do we consider these as a proportion of everyone who takes part, or those that attempt more dangerous forms, or per day of activity? And even then it is often difficult to get solid data on how many people are getting up to whatever pursuit turns them on.