Assumptions
(1) Only teams ranked in the Top 20 now have a shot for an at-large bid
(2) The Big and SEC likely to get 5 or 6 of the at-large spots.
(3) The Big XII needs for the ACC or Notre Dame to implode. The Northern Illinois loss by ND is not enough to disqualify them (although it should).
(4) The Big XII at large team can have no more than 1 loss. Thus AT LEAST one team in Arlington must be undefeated.
What the league should hope for
(1) Oklahoma State either beats both KSU and Utah or loses to both. Worst case scenario for Big XII is a split. Best case is for the league is for TWO undefeated teams in Arlington (a guaranteed at large bid IMO). This realistically only happens if OSU loses both games.
(2) Have only one team from the ACC. Every Clemson and Louisville loss helps. Have Miami win the ACC championship.
(3) Eliminate SEC and BIG teams currently behind Utah, KSU, and OSU. Multiple losses for OU, Michigan and Notre Dame.
(4) Have TWO teams from the grouping of Mizzou, Tennesee,,Oregon, Penn St, and USC go into a major swoon. Every loss by teams in this grouping helps the Big XII.