Joined: Jun 18, 2018
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February 8th, 2019 at 12:58:13 PM permalink
Begging the Wizard to help out on this one.

College basketball fans know this year, the Pac-12 is mediocre on some days, average at its best.

It's also headed toward a situation that begs a question on probability.

Ken Pomeroy currently has the final projected Pac-12 standing as such ...

Washington: 16-2
Arizona: 10-8
Arizona State: 10-8
Oregon State: 10-8
USC: 10-8
Utah: 10-8
Colorado: 9-9
Oregon: 9-9
Stanford: 9-9
UCLA: 9-9
Washington State: 4-14
Cal: 1-17

I don't think a 3-way or 4-way tie in a 12-team league is all that uncommon. This projection calls for one five-way tie and one four-way tie, with only a game separating the two clusters. So my question is, in a 12-team with an unbalanced schedule (only 18 games -- if everyone played each other twice, there would be a 22-game league schedule), what are the odds of having a 9-way tie for second at 10-8?
Joined: Dec 23, 2009
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February 8th, 2019 at 1:23:58 PM permalink
The only way to answer this question is if you assume all results are completely random.

Since they arenít, Iím not sure what help that answer would be to your question.
Joined: Jun 22, 2011
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February 8th, 2019 at 3:57:35 PM permalink
If you assume the home team will win 65% of the time (which is pretty much how RPI works), I ran a random simulation of about 10 million seasons.
Of these, 6,839,823 seasons had a sole winner.
Second place teams:
1 teams: 3307808
2 teams: 1998069
3 teams: 911355
4 teams: 406937
5 teams: 171080
6 teams: 39652
7 teams: 4040
8 teams: 558
9 teams: 258
10 teams: 66
In this simulation, a 5-way tie for second happened about 1/40 of the time.

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