I have 6 coworkers competition in a NCAA bracket. I'm trying to find out how to calculate who has the best chance of winning. For example currently the score card looks like:
Player 1. Current Right Picks: 14 Current Wrong Picks: 11
Player 2. Current Right Picks: 17 Current Wrong Picks: 7
Player 3. Current Right Picks: 16 Current Wrong Picks: 9
Player 4. Current Right Picks: 16 Current Wrong Picks: 7
Player 5. Current Right Picks: 13 Current Wrong Picks: 12
Player 6. Current Right Picks: 18 Current Wrong Picks: 5
Player 7. Current Right Picks: 14 Current Wrong Picks: 9
Now the reason they don't all add up to the same number is because some people picked a team to win in multiple rounds but they ended up losing in the first round which means they can't be right later on.
I know that each player's best possible score is 63 - current wrong picks.
Essentially I'm trying got get a formula that show each players chance of winning the entire bracket, i.e. have the highest possible score against the other players.
Thanks!
What if you just estimated a person's outcome with $$\text{Current Corrects}+\frac{\text{Remaining Undecided}}{2}$$
It's not great because if you pick a team to go all the way and it loses in the next round, it takes out a lot of your possible points, but off the top of my head, it is decent.
As far as probability of each perosn winning, you would need a distribution of possible outcomes for each person, which would get pretty hairy.