2021 Binomial Reduction Week

"It is a part of Miss Havisham's plans for me, Pip … I am to write to her constantly and see her regularly, and report how I go on— I and the jewels — for they're nearly all mine now."

- Estella, Great Expectations by Charles Dickens

BLUF: 32.4% likelihood (1:2 odds) Michigan goes to Indy per FPI, 26.7% (1:3 odds) per Sagarin Index, and 28.4% (2:5 odds) per S&P+.

This will be a brief diary entry. With the close of the season fast approaching, the possible range of remaining wins and losses can be counted on one hand - two fingers, to be precise. This significantly reduces the scenarios by which your ever-lovin’ Maize’n’Blue Team #142 might advance to its first B1GCG. Granted, the probability of them doing so is generally not favorable, but it’s not zero, either.

There appears to be some confusion among the threads with discussions of three-way tie-breaker scenarios, but at this point, a three-way tie in the B1GE is impossible. Only a couple two-team head-to-head tiebreak scenarios remain. The following charts show the likelihood of Michigan beating out Ohio State in the final B1GE standings based on the Week 11 ratings from FPI, the Sagarin Index and S&P+. The sum total probabilities are noted in the colored boxes in the center charts.

To further parse the center charts, the Difference in non-Head-to-Head Wins axis can be broken out as the following scenarios, all of which are evaluated from the condition that UM beats OSU. To be clear, there is no possibility for UM to advance to Indy without defeating the Buckeyes:

-2 => Michigan loses to Maryland AND OSU beats MSU (least-likely outcome per FPI)
        => UM (7-2) beats OSU (8-1)
        => UM is still out regardless of The Game, as is MSU (7-2 or 6-3)

-1 => Michigan beats Maryland AND OSU beats MSU (most likely outcome)
        => UM (8-1) beats OSU (8-1)
            => MSU (7-2 or 6-3) is out
            => UM (8-1) advances over OSU (8-1) by H2H tiebreak

UM’s likelihood of advancing by this sequence of events is 29.7%, 24.8% and 26.5% as per FPI, SAG and S&P+, respectively.

 0 => Michigan beats Maryland AND OSU loses to MSU (least-likely outcome per SAG and S&P+)
        => UM (8-1) beats OSU (7-2)
            => OSU (7-2) is out
            => MSU (8-1) advances over UM (8-1) by H2H tiebreak with MSU win over PSU
            => UM (8-1) advances over MSU (7-2) with PSU win over MSU*

In this scenario, if PSU beats MSU (FPI: 45.7%, SAG: 61.8%, S&P+: 45.5%), UM will advance to Indy. So UM's likelihood of advancing by this scenario (including beating OSU) is 2.7%, 1.9% and 1.9%. Add these figures to the Mode -1 FPI, SAG and S&P+ UM factors, respectively, to account for the PSU beats MSU factor.

The Bottom Line? The likelihood of UM advancing to Indy  are 32.4% (1:2 odds) per FPI, 26.7% (1:3 odds) per Sagarin Index, and 28.4% (2:5 odds) per S&P+