Ok. I'm building a spreadsheet to do different types of advanced calculations involving projections, standard deviations, etc based on playing in a single table tournament.

If I think that I'm 20% better than the average field, how would I fill in the following values?

I want to create a pdf that states the probability of me finishing in each respective position (10 player tournament).

If I'm 20% better than the average field, I know that 1st place will be 0.1*1.2, which is 12%. How would I go about calculating how to spread the remaining 88% through positions 2 through 10. The structure of the tournament, in theory is winner-take-all, and 2nd place pays nothing. I would love to discuss and learn a thing or two. I think I'm just having a brain fart.

1st place - 12%
2nd place -
3rd place -
4th place -
5th place -
6th place -
7th place -
8th place -
9th place -
10th place -

And also, some thoughts I have had would be 0.88/9*1.2 which comes to 11.73%. If I do this all the way down, my sum of probabilities comes to something like 101.1%. Any help is appreciated. Thanks.

Here is something I came up with pretty quickly. I would think there might be more sophisticated methods.

“Better” can be defined a number of ways. I’ll define it is as having a win probability better than the 9 other players. Then if you have an E% edge,

(1+E)*P + 9*P = 1, where P is the average win probability for the field.

So for a 20% edge,

10.2*P= 1, P = 1/10.2 = 9.8% for each of the 9 opponents.

Your win probability = 1.2* 9.8% = 11.8%.

Depending how you use this, having the same edge on all opponents may not be a very good idea.

One modificaton for splitting the edge between 2 groups would be

f1*(1+E1)*P+(1-f1)*(1+E2)*P + 9*P = 1,

where f1 is the fraction of the 9 players in group 1.

Then solve for P and get the weighted average for hero win probability. While this accommodates different edges it still gives each opponent the same win probability, and that may not be realistic but maybe okay for practical use.

This approach can be extended to more than 2 groups.

Since you mentioned spreadsheet and advanced stats such at standard deviations for an STT, maybe this will inspire you. I developed just such a program for Sit'n'Go. It probably doesn't do exactly what you are planning but Excel along with it's VBA programming language (used for the simulation) can do a lot of things. Here is a sample pic showing part of the spreadsheet.