Can MU earn a first round bye?

West Virginia, Villanova and UConn appear to be in the drivers seat to earn three of first round byes in Big East tournament this year. The race for 4th place, however, and it's all-important first round bye in the Big East tournament is still very much up in the air. Based on the remaining schedule, MU definitely has a chance.

Other teams in the hunt--Georgetown, Pittsburgh, Seton Hall and Syracuse.

For MU to have a shot, there is no room for error. We need to sweep our home slate, and take two of three on the road from Rutgers, ND, and Louisville.

At 4-4, Syracuse isn't mathematically out of it, but looks to have the toughest path:
Home: Cincy, UL, WVU, VU
Away: UConn, St. Johns, Georgetown, DePaul
For the sake of argument, lets project 3 of 4 at home (losing to West Virginia), with road wins at St. Johns and DePaul. That gives them 9-7 on the season.

Seton Hall is 5-3 after today's win over Rutgers
Home: UConn, West Virginia, Notre Dame, Cincy
Away: USF, St. Johns, Pitt, DePaul
A strong finish and they could take ND and Cincy at home, and USF, St. Johns and DePaul on the road. Losses are likely versus UConn, WVU and @Pitt. They would finish 10-6

Georgetown is 7-2 after today's win over Pittsburgh, and probably has the easiest path to the 4th place finish.
Home: St. Johns, WVU, Rutgers, Syracuse
Away: MU, Villanova, USF
Lets say they take SJU, Rutgers and Syracuse at home, and USF on the road. That puts them 11-5.

Pitt is 6-3 after today's loss at Georgetown.
Home: WVU, UC, PC, Seton Hall
Away: PC, MU, WVU
West Virginia is their biggest rival--it seems fair to project a split. Then, they likely take UC, Providence twice and Seton Hall. Final record: 11-5.

Marquette is currently behind all these teams in the standings, with a record of 6-4.
Home: Pitt, Georgetown, Providence
Away: Notre Dame, Louisville, Rutgers
If you've read this far, you already see projections that MU will take the rematch with Pitt, as well as the Georgetown game at home. Taking care of business against Providence, the season rests on the three road games. If MU can take two of three against UL, ND and Rutgers, they finish 11-5 as well.

If the season breaks out this way, it would put three teams tied at 11-5 at the end of the season: MU, Georgetown and Pittsburgh.

How does the tiebreaker work?
From the Big East tie-breaking forumula,

Teams are viewed as a “mini-conference” when comparing head-to-head results. The team with the best record (as determined by winning percentage, even if unequal games) vs. the other teams in the mini-conference gains the advantage.

The mini-conference would look like this:
MU: 2 -1 (split with Pitt, win over GT)
Georgetown 1-1 (win over Pitt, loss to MU)
Pitt: 1-2 (split with MU, loss to GT)

Everything has to go right for MU down the stretch, but MU still has a chance to be the 4th seed in the Big East tournament, earning the first round bye.