Thursday, February 18, 2016

#HLMBB double-bye possibilities: VU, WSU, UWM, UWGB, OU

First of all, a slight correction to #HLMBB 1 seed possibilities: Valpo, Oakland, and Wright State, caught by a member (agibson) of the Valpo Fan Forum:

Wright State can get the 1 seed if they win out, Valpo goes 1-3 or 0-4, and Oakland goes 1-2 or 0-3. They will either win the regular season title outright or share the title only with Valpo, and in that case they obviously win the tiebreaker.

This is not quite true. If there's a 3-way between Valpo, Wright State, and Oakland at 13-5, and Valpo beats Oakland tomorrow, and Milwaukee is alone in 4th place, Wright State gets the 1 seed. The head-to-head-to-head tiebreaker is a wash because while Wright State is swept by Oakland, Oakland is in turn swept by Valpo, and Valpo is swept by Wright State. The sweeps cancel each other out and the common opponent tiebreaker is needed. If Milwaukee is alone in 4th place (most like at 11-7), Wright State becomes the only team to sweep Milwaukee. Regardless of Milwaukee's final record, in this subset of scenarios Valpo's lone remaining win is against Oakland, which means they lose at Milwaukee next Friday. Oakland has already split with Milwaukee. Hence, Wright State wins the tiebreaker for the 1 seed in this situation as well.

Certainly, if Oakland beats Valpo and Valpo beats UIC, Milwaukee, or Green Bay then as stated above, Oakland wins the tiebreaker by virtue of their 3-1 record against the other 2 teams.

Now then, the breakdown of the 2 seed is still completely up in the air, or at least so it seems to me at this late hour. Wright State, Green Bay, Valpo, Milwaukee, and Oakland all could end up with the 2 seed, and if I tried to figure out the conditions for each, I'd never make it to the ARC tomorrow night for the Valpo-Oakland game, so I'm going to punt on that and -- since there is no longer more than a token difference between 1 and 2 seed -- just try to summarize what it takes for each team to secure a double-bye.

The easiest team to start with is Milwaukee. They have no shot at the 1 seed, so this is basically about the 2 seed for them.

For starters, they have to win out and finish 11-7. The only of the other 4 teams they play is Valpo, so that means Valpo loses at least once more. Since Valpo already has 12 wins, it means Oakland must lose out (handing Valpo their 13th win among other things). Wright State also needs to lose at least 2 of their remaining 3, or they also end up with at least 12 wins. Basically, if Milwaukee is the 2 seed, Valpo has to be the 1 seed. Green Bay likewise has to lose at least once. If all 4 teams tie at 11-7, that would ruin it because Oakland wins the tiebreaker (sweeping both Wright State and Green Bay while splitting with Oakland is impossible to beat).

Actually, Wright State needs to lose out as well as Oakland, because in a 3-way tie with them and Oakland, Milwaukee loses the tiebreaker due to their 1-3 record against the other two. However, if it's just Milwaukee and Oakland and Valpo sweeps Oakland, Milwaukee would win the tiebreaker by splitting with Valpo. There are 240 of the 262,144 remaining scenarios in which this happens.

The next easiest team to consider is Green Bay. They also have no shot at the 1 seed because they can't win the 4-way 12-6 tie that would be necessary as explained in my previous post. They do have to win out in order to have a chance at the 12 seed since the best they can do at 11-7 is tie Oakland and they lose that tiebreaker (they split with Milwaukee and Wright State so those 2 don't change anything). In fact, Green Bay's lone chance at a double-bye consists of winning out while Wright State and Oakland both lose out, so that Green Bay is alone in 2nd at 12-6 (Valpo has to win at least one more game in this situation since Oakland loses all their remaining game). There are 1024 scenarios in which this happens.

The next easiest team to consider is Wright State, but it gets more complicated. The simple part is that they have to win 2 of their remaining 3 games. But there are no obvious restrictions on the final win totals of the other 4 teams.

Obviously, if they win out, they only have to contend with Valpo and Oakland. Here are the only ways Wright State would be denied the double-bye at 13-5:

1. Oakland and Valpo both finish 14-4 or better
2. Wright State ends up in a tie with only Oakland and Valpo all alone in 1st. Oakland wins the tiebreaker for the 2 seed. Obviously if Valpo finishes behind them, both teams get double-byes

If Wright State loses 1 of their remaining 3 games to finish 12-6, then there can't be two or more teams with 13 or more wins if they are to get a double bye. If Green Bay wins out to tie them, then Valpo needs to lose out (meaning Oakland also wins at least 12). In a 4-way at 12-6, as shown Tuesday, Oakland and Wright State get the double bye because Green Bay and Valpo are both 2-4. If Green Bay loses at least once, that reduces it to the same situation as when they win out. The above 2 conditions remain the only ways that Wright State is denied the double-bye (only change 14-4 to 13-5 in condition 1).

There are 41,472 scenarios in which Wright State gets the double-bye.

In the remaining 219,408 scenarios, Valpo and Oakland keep the double-byes all to themselves.

This mess will sort itself out a little bit over the weekend.

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