Dual Forecast Maths

[blackpoolbison]

Hello, I'm playing with a spreadsheet and I can't figure out what I'm doing wrong, but I can't get the eventual possibilities to add up to 100% so something is up. There are 4 teams, 2 can qualify for a total of 6 possible outcomes.

To Qualify Market (2 qualify):
Team A: 0.8
Team B: 0.6
Team C: 0.4
Team D: 0.2

Dual Forecast Options (order not important):
AB = A * B/(B+C+D)
AC = A * C/(B+C+D)
AD = A * D/(B+C+D)
BC = B * C/(A+C+D)
BD = B * D/(A+C+D)
CD = C * D/(A+B+D)

is wrong. very wrong. but I'm not sure how to get the right result. I guess it might involve 1 minus the other outcomes somewhere but I'm not certain where in order to get the right result. working backwards from the answers I know are right isn't helping. can anyone assist?

[blackpoolbison]

I now think this is impossible with only this information. I think you need to take the win probablity from the qualify probability to get the 2nd place probability and then multiply all the possible outcomes, ie AB+BA, AC+CA, AD+DA, BC+CB etc etc.

If anyone knows better please let me know!

[blackpoolbison]

Is this right??

(Aw*([Bw-Bq]/[Bq+Cq+Dq]))+(Bw*([Aw-Aq]/[Aq+Cq+Dq])) = AB/BA dual forecast %

A/B/C/D=team
w/q=win or qualify %

Thanks!