Logic Test: (Modified) Swiss Tournament Elimination
So the setup is this:
12 Teams participate in a Modified Swiss tournament; each team will play each other team (11 rounds).
The outcome of each match is both binary (Win/Loss) and Score (0-4).
Total score of a match is either 4 or 5; if it is 5, the score was 2-3 in favor of one team or the other. (4 sets are always played; if tied, a 5th is played to break the tie). Thus, the possible Set-Score outcomes of any given match are 0-4, 1-3, 2-3, 3-2, 3-1, and 4-0.
The final placement of teams is determined by their Total Match Score first, Total Set Score second, and Head-to-Head Winner in event of ties.
The top 4 teams are advanced to a playoff.
What programmatic rules can be made to determine if a given team has been mathematically eliminated?
No team can be mathematically eliminated before the halfway point. (All 4 top teams could fail utterly for the rest of the tournament, and the bottom 4 teams could go perfect)
Any team currently in the top 4 is not mathematically eliminated.
Any team which has <4thplacewins> - <wins> > <games_remaining> is mathematically eliminated.
Any team which has <4thplacewins> - <wins> = <games_remaining> and <4thplacesetwins> - <setwins> > <gamesremaining> * 4 is mathematically eliminated.
Any team which has <4thplacewins> - <wins> = <games_remaining> and <4thplacesetwins> - <setwins> = <gamesremaining> * 4 and lost to 4th place team is mathematically eliminated.
Is there a circumstance where these 4 rules would generate a false 'positive' (elimination)?