Hello everyone.

The past year or so I've been generating projection models for various sports to predict the performance of individual players. The approach varies by sport.

I've stumbled onto one situation where I need to significantly improve my abilities in order to finalize the projection model I'm imagining. It's been years since I've taken a college statistics course so I'm a little rusty.

The problem I'm trying to solve is basically as follows (it will be applicable to several other scenarios, essentially any sport where a large group of individual athletes compete against one another)

Say 100 people are competing in a race, and the following info is provided for each contestant:

- % chance of finishing first
- % chance of finishing in the top 5
- % chance of finishing in the top 10
- % chance of finishing in the top 20

(these will of course vary based on the contestant pool and basic handicap information provided)

With this information, I would like to calculate:

1) Each contestant's exact projected finishing position (mean finishing position? median?)

2) The standard deviation of each contestant's finishing position, or any other method which would allow me to generate a distribution model of each contestant's finishing position.

I have all the data and have no issue with managing it to solve the problem. I just don't know where to begin solving this for even one contestant. I've been using a rough model to date (using the %s to calculate an arbitrary "score" and then ranking the contestants based on that score) but it's a little amateurish and I know I can refine it much further.

Thanks for any help you can provide!