Race for the 3 seed

Having analyzed the possibilities for the 2 seed, I now turn to the single-bye. In truth both the 2 and 3 seeds do have the capability of hosting the championship game if the 1 seed falls in the semifinals, but otherwise, all games they play are road games. Compensation for the leg up and extra rest, I guess.

As things stand now, there are 11 games left and the standings are as follows:

                   W   L   Games left
Green Bay         12   2   @OU, @UDM
Cleveland State    9   4   UWM, YSU, @VU
Valparaiso         8   5   YSU, @WSU, CSU
Wright State       8   6   VU, @UIC
Milwaukee          6   7   @CSU, UIC, @UDM
Youngstown State   6   7   @VU, @CSU, OU
Oakland            6   8   GB, @YSU
Detroit            6   8   UWM, GB
UIC                0  14   @UWM, WSU

With their victory Thursday night over Valpo, Green Bay has now clinched the 1 seed and 2nd/3rd round hosting duties. They will play the 2nd game on Saturday night, after 6 other teams have already been eliminated. To reiterate: Cleveland State is the only team left who can hope to match their record and the Phoenix swept the Vikings, so they win the tiebreaker. Another obvious impact from yesterday is that with their loss to the Penguins in OT, Milwaukee has been eliminated from contention for the 2 seed. They still have a shot at the 3 seed.

In 47 % of the scenarios with CSU as 2 seed (1293 out of 2048), Valpo gets the 3 seed by beating WSU, or by finishing ahead of them. By beating WSU, they win any tiebreaker with them because of their split with Green Bay. If they lose to WSU, then they must beat CSU and YSU while WSU loses to UIC (which seems unlikely).

In 50.2 % of the scenarios with CSU as 2 seed, WSU gets the 3 seed by beating Valpo and finishing tied with or ahead of Valpo. Since both here and in the previous paragraph, the team in question has to finish at least 9-7, and since YSU split with both teams, the only relevant 3rd party is Milwaukee. If WSU, Valpo, and Milwaukee end up 9-7, the winner of next Tuesday's game at the Nutter Center will get the 3 seed by virtue of tiebreakers. The winner would be 3-1 and the loser would be 2-2, while Milwaukee in either case is 1-3. Note: if YSU instead of Milwaukee is 9-7, it would come down to Valpo's win over Green Bay to break the tie.

In 1.5 % of the scenarios (20) with CSU as 2 seed, YSU gets the 3 seed by finishing 9-7 (beating Valpo, CSU, and Oakland) and UIC beating WSU and CSU beating Valpo and Milwaukee loses at least once more and WSU beats Valpo. Thus Valpo and Milwaukee finish no better than 8-8 leaving YSU tied with WSU at 9-7. They split with each other and were both swept by Green Bay, but whereas WSU split with CSU, YSU sweeps CSU to win the tiebreaker.

In 1.3 % of the scenarios (16) with CSU as 2 seed, Milwaukee gets the 3 seed by finishing 9-7 (beating CSU, UIC, and Detroit), Valpo finishes 8-8 (losing to WSU, CSU, and YSU), and WSU loses to UIC to finish 9-7. This puts Milwaukee in a 2-way tie with WSU or a 3-way tie with YSU (the latter of which is irrelevant because YSU split with both Milwaukee and WSU). Milwaukee wins the tiebreaker because they are the only one involved to beat Green Bay.

In 78.1 % of the scenarios with Valpo as 2 seed (576 out of 2048), CSU gets the 3 seed. I'll tackle the other 21.9 % extensively and leave this one as what happpens if none of that happens.

In 10.4 % (60) of the scenarios with Valpo as 2 seed, WSU gets the 3 seed by finishing 9-7 (beating either Valpo or UIC but not both), CSU finishing 9-7 (losing to Valpo, Milwaukee, and YSU), YSU loses to either Oakland or Valpo, Milwaukee loses to either Detroit or UIC, for starters. This puts WSU in a 2-way tie with CSU at 9-7. If they beat Valpo, they win the tiebreaker immediately because they will sweep Valpo while CSU will split with Valpo. So let's look at WSU losing to Valpo and beating UIC: They were both swept by Green Bay and they both will split with Valpo. They both will split with Milwaukee, they both swept Oakland, and they both sweep UIC, so those teams don't matter (none of them can finish higher than 8-8). It comes down to Detroit and YSU. Detroit favors CSU by +1 and YSU favors WSU by +1, so the additional requirement is that YSU finish higher than Detroit (if they tie, RPI must be consulted, see below).

In 5.6 % (32) of the scenarios with Valpo as 2 seed, Milwaukee gets the 3 seed by finishing 9-7 (beating CSU, UIC, and Detroit), CSU finishing 9-7 (also losing to Valpo and YSU), and YSU finishing 8-8 or worse. In a 3-way tie with CSU and YSU, YSU's sweep over CSU keeps Milwaukee from winning the tiebreaker. In a 2-way tie with CSU, Milwaukee's win over Green Bay wins the tiebreaker.

In 2.8 % (16) of the scenarios with Valpo as 2 seed, Youngstown State gets the 3 seed by finishing 9-7 (beating Valpo, CSU, and Oakland) and CSU finishing 9-7 (losing to Milwaukee, YSU, and Valpo). In a two-way tie with CSU, YSU wins the tiebreaker because they sweep the Vikings. WSU and Milwaukee each split with both teams, so they add nothing.

In 3.1 % (18) of the scenarios with Valpo as 2 seed, RPI will be needed to settle things if WSU finishes in a two way tie with CSU at 9-7 and Detroit and YSU finish tied at 8-8 or 7-9 as mentioned above: Milwaukee, Oakland, and UIC are neutral, Detroit favors CSU by +1 while YSU favors WSU by +1 (so they cancel each other out if Detroit and YSU are tied).

In 55.3 % (94) of the scenarios with WSU as 2 seed, CSU gets the 3 seed by WSU beating Valpo and several other factors. I'm going to cop out again and look at the other possibilities instead.

In 37.6 % (64) of the scenarios with WSU as 2 seed, Valpo gets the 3 seed by beating CSU and losing to WSU (finishing 9-7 or 10-6) and CSU finishing 9-7 (also losing to Milwaukee and YSU) for starters. If Valpo beats YSU, that's enough to get the 3 seed (they lose the head-to-head tie with WSU for the 2 seed). If Valpo loses to YSU, then there are still Milwaukee and YSU who can finish 9-7. If YSU finishes 9-7, WSU must finish 10-6 (because YSU's sweep of CSU and split with WSU pummels Valpo in the tiebreakers -- if WSU is out of the equation, Valpo's sweep of Milwaukee cancels out YSU's sweep of CSU). One way or another, Valpo ends up in a 2-way tie with YSU, and Valpo's win over Green Bay wins that tiebreaker.

In the remaining 7.1 % (12) of the scenarios with WSU as 2 seed, YSU gets the 3 seed by finishing 9-7 (beating Valpo, CSU, and Oakland), Valpo finishing 9-7 (also beating CSU and losing to WSU), CSU finishing 9-7 (also losing to Milwaukee), and WSU to also lose to UIC. As mentioned above, with WSU also in the tiebreaker, YSU wins the tiebreaker (their 3-1 against WSU/CSU overtakes Valpo's 2-0 against Milwaukee).

That leaves 9 scenarios where RPI must be consulted to determine the 3 seed, and then only because RPI is need to determine the 2 seed. Luckily I covered this already in the above linked post.