A popular competition is the NFL eliminator or survivor pool where you choose a team each week and if they lose you are out but if you win you survive to next week but you cannot choose the same time twice in a season.
I think there is a way to identify which pick is the most "value" in terms of your chances of winning the competition if you know(or can estimate) a) how may contestants have picked each team and b) each team’s chance of winning. The general approach you want to pick a good team with little support and avoid good teams with a lot of support and hope that your team win and the other good team lose elsewhere to reduce the number of opponents.
Mathematically your chance of winning the competition overall is equal to your chance of your pick winning this week divided by the number of contestants left if you do win. Call this your survival factor, the aim is to pick the team with the highest survival factor.
For many eliminator pools (ESPN Yahoo) you can see what percentage of people have picked each team.
To work out each teams survival factor I do the following
a) for each game multiply the chance of the favorite winning by the number of people who have picked them add to this the chance of the underdog winning multiplied by the percentage of people who have picked them. This gives the average number of survivors from this game.
b) Then take each team in turn and divide their winning chance in that game by the number of survivors using the average number of survivors from all other games plus the support for this particular team.
This is a one week at a time approach but I think that as it is impossible to predict future matches several weeks in advance this is probably as good a way as any.
Using the current yahoo survivor pool selections and the moneyline from Football Locks.com Tennessee are way too popular and the Giants are too unpopular so I am going for the Giants.
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