Suppose some random tie-breaker is used and Team B advances. Team Z then loses to Team B in the championship but would have beaten Team A. Is that really fair to Team Z?
yes that is completely fair to all 3 teams because it is within the spirit of the single game elimination format.team Z has earned a 50% chance at the championship and 50% at 2nd place.
as long as you you give him his head to head matchup (50% chance at 1st, 50% chance at 2nd, 0% chance at anything else) then that is fair. i am facing the lowest point scorer of the playoff teams in my championship. if he lost the last game, i would be playing the highest point scorer. either outcome would have been fair from everyones point of view
I still think the best way is to split up the prize money in half and have two championships. Team Z vs Team A and Team Z vs Team B. If Team Z beats them both he's the undisputed champion. If he splits or loses both games then you have co-champs.
Doing it this way does not penalize Teams A and B by some tie-breaker created after the fact when none was in place. It gives each of them a shot of 1/2 the first place money which is better then no shot at all. It guarantees Team Z at least 2nd place with a chance to win half or all of first place.
I think that's a fair compromise that doesn't grossly reward or penalize any of the teams more than the others.
this is fair to team A and B but unfair to team Z and here is why...lets say 1st is $300, 2nd is $100, 3rd is $0
team Z: has already earned $100 for 2nd place, worse case scenario for him in either a normal head to head matchup, or your scenario
$100+...
Z beats A and B: .5*.5 = 25% at $200 = $50 expected dollars for team Z
Z beats A, looses B: 25% at $100 = $25 expected dollars for team Z
Z looses A, wins B: 25% at $100 = $25 expected dollars for team Z
Z looses A, looses B: 25% at $0 = $0 expected dollars for team Z
$100+(50+25+25+0) =
$200 expected dollars for team Z
in a normal head to head matchup
Z beats A: $100 + (50% at $200) = $200 expected dollars for team Z
Z looses A: $100 + (50% at $0) = $100 expected dollars for team Z
$200+100 =
$300 expected dollars for team Z. anything less is penalizing team Z
team Zs expected earnings decrease by 33% in your scenario
**there is one way this scenario is fair though.
If and only if 2nd place is exactly half of what 1st place, or zero is AND 3rd place is half of what 2nd place is or zero
ex:
400, 200, 0
400, 200, 100
400, 0, 0