Thursday, February 20, 2014

Race for the 2 seed

Having analyzed the possibilities for the 1 seed, I now turn to the other double-bye, that great boon that so far has prevented every 2 seed since the new format was adopted from ever hosting a tourney game.

As things stand now, there are 15 games left and the standings are as follows:
                   W   L   Games left
Green Bay         11   2   VU, @OU, @UDM
Cleveland State    9   4   UWM, YSU, @VU
Valparaiso         8   4   @GB, YSU, @WSU, CSU
Wright State       7   6   UDM, VU, @UIC
Milwaukee          6   6   @YSU, @CSU, UIC, @UDM
Youngstown State   5   7   UWM, @VU, @CSU, OU
Detroit            6   7   @WSU, UWM, GB
Oakland            5   8   @UIC, GB, @YSU
UIC                0  13   OU, @UWM, WSU
First of all, the number of RPI 1 seed scenarios has been reduced to 5, and in each of them RPI will decide the top 3 seeds, so we can dispense with them, except to say that as of this writing, Green Bay's RPI is 62, Cleveland State's is 92, and Valpo's is 162 according to Real Time RPI's Daily RPI. So if that ranking remains the same and Green Bay wins that tiebreaker, CSU would end up with the 2 seed because in each case they sweep Valpo (who ends up with the 3 seed).

If Green Bay ends up with the 1 seed, 52.2 % of those scenarios have Cleveland State locking up the 2 seed. Once again: between Cleveland State and Valparaiso, if one wins out, they necessarily finish at least 1 game ahead of the other because (a) they are currently tied in the loss column, and (b) they have one more game against each other. So CSU can lock up the 2 seed by finishing 12-4 for sure. Certainly they can finish tied with Valpo at 11-5 or 10-6 and still get the 2 seed. The first thing that needs to happen is that the Vikings sweep the Crusaders to avoid losing the tiebreaker via record against Green Bay. At 10-6, there's also Wright State and Milwaukee to possibly contend with. A 4-way tie at 10-6 results in the 2 seed for CSU (who would then lose to Milwaukee and YSU, splitting with former and being swept by latter) if Wright State and Milwaukee both win out (obviously), Valpo beats Green Bay and YSU (since they must lose to WSU and CSU), but also only if Oakland beats YSU (since YSU can now ruin the Vikings' fun), and Detroit beats Green Bay (who thus finishes 12-4) so they finish ahead of YSU (since Detroit is an important tiebreaker helper for the Vikings).

Result: in the 4-way head-to-head, WSU and CSU both are 4-2 while Valpo and Milwaukee are both 2-4, so we reduce it down to just the Raiders and the Vikings. They split with each other; they each were swept by Green Bay, by definition they both have the same record against Valpo/Milwaukee. Oakland is neutral since both teams swept the Golden Grizzlies, so it doesn't matter what their record is. That only leaves Detroit and YSU, and in this subset Detroit finishes 7-9 and YSU finishes 6-10. CSU swept the Titans while Wright State can do no better than sweep, so CSU wins the tiebreaker.

Factoring Milwaukee out to leave a 3-way tie at 10-6, that still leaves CSU beating Valpo and losing to Milwaukee and YSU, so while Valpo still falls out to the 4 seed, CSU still needs Detroit to finish ahead of YSU to guarantee the 2 seed over Wright State (with CSU splitting with Milwaukee the Panthers become neutral like Oakland, since WSU also split with them) for the same reasons as above.

Instead factoring out Wright State to leave a 3-way tie at 10-6, Milwaukee falls out to 4th, and Valpo is eliminating in the remaining tiebreaker by being swept by CSU. Much simpler. It doesn't matter this time where Detroit and YSU finish.

Factoring both out to leave a 2-way tie is likewise simple as CSU wins the tiebreaker by virtue of sweeping Valpo.

Obviously if they tie at 9-7, that means Valpo beats CSU to split with them, and then in any tiebreaker CSU has a problem because they were swept by Green Bay while Valpo has split with them. So that's out if CSU wants the 2 seed.

Valpo gets the 2 seed in 36.4 % of the scenarios where Green Bay is the 1 seed. This one is long and involved, much like the one for CSU, so I'm going to punt for now and just do all the rest. Suffice to say, whatever is left over when you cover everything else in this post -- that's where Valpo gets the 2 seed ;)

Milwaukee gets the 2 seed in 5.5 % of the scenarios where Green Bay is the 1 seed. They must finish 10-6 in order to have a chance. If Valpo also finishes 9-7 or 8-8, they can only end up in a tie with CSU and/or WSU. Having split with both in this subset, it comes down to common opponents, and Milwaukee is the only one of the 3 to beat Green Bay, so they win any tiebreakers. Only Valpo is a deal-breaker for the Panthers.

RPI must be consulted in 1.5 % of the scenarios where Green Bay is the 1 seed. If WSU beats Detroit to split with them, YSU beats CSU to sweep them, WSU beats Valpo to sweep them and also beats UIC, we have WSU and CSU at 10-6 (If Milwaukee also finishes 10-6, then they get the 2 seed as shown above). They split with each other, they were both swept by Green Bay, they both swept Valpo and split with Milwaukee. They both swept Oakland and UIC. In all cases in this subset, Detroit and YSU end up tied at 8-8 or 7-9, and both teams are 2-2 against that pair, so we have to consult RPI. Best guess at this time is that CSU ends up winning that tiebreaker, but we'll have to wait and see.

Wright State gets the 2 seed in 1.4 % of the scenarios where Green Bay is the 1 seed. They need to beat Detroit and Valpo, and they need to finish tied with or above Valpo, CSU, Detroit, YSU, and Oakland (i.e, 10-6 or 9-7) and ahead of Milwaukee (unless it's a 5-way tie with Valpo, CSU, and YSU at 9-7). At 10-6 they must finish ahead of Milwaukee, so they can only afford 2-way ties with CSU or Valpo. Valpo they eliminate head-to-head. If they tie with CSU, Valpo and Milwaukee are neutral individually, so they can be ignored. Same goes for Oakland and UIC. Familiar theme: it comes down to Detroit and YSU. For Wright State to win this tiebreaker, YSU must finish ahead of Detroit. If Detroit finishes ahead of YSU, it goes to CSU as shown above. Even if the two finish in a tie, CSU can still win the tiebreaker if they beat YSU to split with them. If they get swept by YSU, then we have to resort to RPI as mentioned above.

If Valpo ends up with the 1 seed, Green Bay gets the 2 seed in 100 % of those scenarios, so that's done. Green Bay can finish no worse than 11-5, and CSU can finish no better than 11-5 if Valpo has the 1 seed, so the best CSU can do is tie Green Bay and they lose that tiebreaker every time.

If CSU ends up with the 1 seed, Valpo gets the 2 seed in 50.3 % of those scenarios. In all of these, they lose to CSU and beat Green Bay, YSU, and WSU. Beating Green Bay means winning the tiebreaker with them, so that explains that breakdown as much as necessary.

Green Bay gets the 2 seed in 49.7 % of the scenarios where CSU is the 1 seed. In all of these, Valpo loses at least twice more (to CSU and either WSU or YSU or both), leaving Green Bay alone at 11-5 in 2nd place.

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