Should Michigan fans have rooted for OSU over Northwestern

Submitted by m1jjb00 on

Summary

A simulation suggests that Ohio State beating Northwestern increases Michigan’s chances at that time of winning the division by 5 percentage points and the Big Ten championship by 1-1/2 pp.  Such a win also improves on average Michigan’s bowl placement when it doesn’t win the division.  On the other hand, what’s true for Michigan is also true for Michigan State.  And perhaps more importantly, a win over Northwestern greatly improves Ohio State’s chances of a great season. 

 

Details

So, events have overtaken the question, but the argument that I should have rooted for OSU over Northwestern, which played out in some forums in the week before the game, remains stuck in my mind.  Before getting to the relevant analysis, I’m compelled to make two points.

  1. Whom I root for is of no practical consequence to anyone else, especially how Michigan’s season actually plays out.1  I can understand an argument that I should give to charity or be nice to my neighbor, but why I “should” do something that doesn’t matter strikes me as a strange concept.
  2. Being happy that OSU beats Northwestern makes sense because it increases Michigan’s chances of winning the division.  Taking pleasure in an OSU loss makes sense because, obviously.  The choice depends on how I weigh the tradeoffs.  Determining whom to root for solely on how it affects Michigan’s chances of winning the division at the exclusion of all other considerations may work for some people, but there’s no basis to argue that I “should” have those same preferences.2

Still, there’s an unresolved issue that can be analyzed.  How much does the outcome of the OSU-Northwestern game affect Michigan’s chances of winning the division?  For that matter, how does it affect other considerations, like MSU’s chances, OSU’s chances of going undefeated, etc.?3 Armed with those answers, everyone can draw their own conclusions over whom they should have liked to win.

To answer this question, I picked a probability structure for the Big Ten games as scheduled, used a random number generator to establish outcomes, programmed the Big Ten’s tie-breaking procedures, and repeated 5,000 times.  To calculate the effect of the OSU-NW game, I let the rest of the season stand and calculated the season outcomes when NW wins and when OSU wins.  I also let stand the actual outcomes of the Minnesota-Iowa and Wisconsin-Ohio State games that occurred the week before.

The left-hand side of the Table 1 details the results for Michigan.  When Northwestern wins the game, Michigan wins the division about 25% of the time; when Ohio State wins, Michigan wins the division about 30%, for a 5 percentage-point differential.  (Keep in mind that with four teams in the division that at the time were thought to have reasonable chances of winning the division, any one team’s odds aren’t going to be large.)The differential for the Big Ten championship, however, is much smaller at 1-1/2 points.  That’s because an OSU win increases its chances of winning the Leaders Division, and Michigan’s chances of beating OSU in the championship games are assumed to be smaller than those of beating anyone else out of that division.

Table 1

Probabilities of U of M / MSU Season Outcome

 

Michigan

 

MichiganState

 

NW W

OSU W

 

NW W

OSU W

B1G winner

11.6

13.1

 

4.2

4.8

Division winner

25.3

30.3

 

12.9

16.7

    Helped

0.6

5.5

 

0.2

4.0

    Unaffected

     24.7

 

     12.7

 

 

 

 

 

 

B1G order, non-div winner

 

 

 

 

    Helped

7.0

11.2

 

2.9

11.5

    Unaffected

    50.7

 

     63.9

 

It’s interesting to observe that there are a small number of times when a Northwestern win helps Michigan win the Legends.  That can happen in the following case: MSU beats Michigan but loses to Northwestern and say Iowa.  Michigan beats Northwestern and loses to a team in the Leaders Division.  And Northwestern loses to one other team other than OSU and Michigan.  If Northwestern beats OSU, then there’s a three-way tie that Michigan wins because each of the winners are 1-1 against the others, but either Michigan has the best division record or at least MSU is knocked out for having the worst division record, and then Michigan wins head-to-head against Northwestern.  On the other hand, if Northwestern loses to OSU, then it’s just a tie between Michigan and Sparty, which Sparty wins by the head-to-head match up.  Even so, the more common outcome is that a Northwestern win hurts Michigan’s title hopes, rather than helping.

One may also be interested in knowing how a Northwestern win affects Michigan’s bowl placement when it doesn’t win the division.  (I use a simple rule that considers non-conference wins and a tie-breaking procedure that looks at head-to-head records to determine the order, but then gives Michigan the benefit of the doubt otherwise.)  The outcome of the NW-OSU game is of no consequence for Michigan’s bowl placement the large majority of the time.  Otherwise, a NW win helps Michigan sometimes, but hurts it about 4 pp more often.

What’s true for Michigan is also true for Michigan State, which may be relevant for some people.  An OSU win increases MSU’s chances of winning the division by 3-3/4 pp and winning the Big Ten by 0.6 pp.  As with Michigan it also helps its bowl placement on average.

Obviously, a win against Northwestern also makes it more likely that OSU has an outstanding season, which could also be an important consideration.  An OSU win over Northwestern increases the probability OSU wins it division by almost 19 pp and the probability it wins the Big Ten by 13 pp (Table 2).  It increases its chances of going to a BCS game by 26-3/4 pp (Big Ten winner or 10-2 record or better.)  And finally, what some may consider a nightmare scenario, Ohio’s chances of going undefeated go from zero to 15% with a win against Northwestern.

 

Table 2

Probabilities of OSU Season Outcome

 

NW W

OSU W

Division winner

70.3

89.0

    B1G winner

42.1

55.2

        13-0

0.0

15.1

        12-1

14.7

26.8

        11-2

21.4

12.2

    B1G loser

28.2

33.8

        12-1

0.0

9.6

        11-2

10.0

16.5

Division non-winner

29.7

11.0

        11-1

0.0

0.1

        10-2

7.8

5.2

BCS

59.9

86.6

 

Methodology

For each scheduled Big Ten game (other than OSU-Northwestern and the two games the week before) I model the probability of the home team winning as depending on the difference in fixed strength parameters plus a home premium.  A more sophisticated model could allow for match up issues that mean win probabilities aren’t transitive. 

Table 3 describes these parameters, the probability Michigan beats them on a neutral field and the average Big Ten wins in the simulations.  They aren’t meant as an accurate gauge of the relative strengths of the teams as much as an expression of what I take to be the relative strengths of the teams as perceived by the fan base at the start of the Big Ten season.  Home teams won 56.9% of their Big Ten games in the 2003-2012 period, so the home-field premium equals 6.9 pp.  Home team i beats visitor j in the simulation if the draw of a random variable (distributed uniformly between [0,1]) is less than or equal to ½ + ½ (Pi - Pj) + h.  The outcomes of all the games are assumed to be mutually independent.   The results are little different quantitatively, and are qualitatively the same, if I shock the strength parameters for each simulation with a uniformly random variable between [-0.10, +0.10].

Table 3

Assumed Relative Strength

 

Strength

Probab.

v. Mich.

Avg. Wins

Iowa

0.15

0.18

2.7

Michigan

0.80

 

5.1

MichiganState

0.55

0.38

4.6

Minnesota

0.10

0.15

1.5

Nebraska

0.70

0.45

5.2

Northwestern

0.80

0.50

5.1

Illinois

0.10

0.15

2.0

Indiana

0.40

0.30

3.6

OhioState

0.95

0.58

6.3

PennState

0.55

0.38

4.2

Purdue

0.05

0.13

2.1

Wisconsin

0.85

0.53

5.5

Probabilities versus Michigan are calculated on a neutral field.  Average wins for Northwestern and OSU take the outcome of their game as 50-50.

 

Endnotes

1.       My theology doesn’t leave room for God choosing the victor based on a prayer vote or my prayers alone, but I can see if others go in a different direction.  I’m also excluding the metaphysics of Scott Adams of Dilbert fame who argues that you can effect changes in the universe over which you otherwise have no control by simply writing down an affirmation for 15 straight days.  See the end of The Dilbert Future: Thriving on stupidity in the 21st century.

2.       Economists call a preference structure where one needs to be satiated in one dimension before appreciating other dimensions as lexicographic preferences.  They’re not logically excluded, but they’re not how I roll.  The spirit of this piece is that life has tradeoffs.

3.       There are two things I’m not going to consider.  First, I’ll ignore whatever effect the game has on BCS rankings as it’s probably small and related to the order in the Big Ten standings anyway.  Second, another reason to root against a team is because you’d like an indication that the team is bad and is more likely to lose future games.  An OSU loss will make you feel better about the Game as you update your win probability using Bayes’ Theorem.  This thought experiment doesn’t lend itself easily to such considerations.  It takes pairwise probabilities as “known” in advance.

Comments

TennBlue

November 15th, 2013 at 1:40 AM ^

that rooting doesn't actually have any effect on the outcome of the game.  Hence, it really doesn't matter who you root for.  Therefore, there is no valid reason ever to root for Ohio State.

UMxWolverines

November 15th, 2013 at 1:45 AM ^

Um, no? Why would I root for a team that is our biggest rival and had a 17 game win streak going at the time? 

Strength of schedule means dick unless you're playing for a national title...which we weren't going to be doing. 

Soulfire21

November 15th, 2013 at 8:59 AM ^

Well that's all good and dandy, in general we want our divisional opponents to lose to increase our chances of winning the division, but all of this winning our division stuff comes with the caveat of having to win games yourself.

akim

November 15th, 2013 at 10:38 AM ^

I feel that while the content of the post is reasonable and brings up a good question, the timing of this post is pretty bad in the context of the season.

I say just focus on winning, and view this game as a win-win either ohio loses or northwestern loses and you can rejoice in either one.  In this particular instance, NW over Ohio so to end the win streak.

VintageBlue

November 15th, 2013 at 11:00 AM ^

Say you're standing in front a nut kicking machine.  The machine is repeatedly kicking you in the nuts. You have a metallic taste in your mouth and begin thinking that a fork in the eye would be a more enjoyable experience.

 

In that situation do you think a blue shirt or black shirt would have been more approriate?

goblue52

November 17th, 2013 at 1:47 PM ^

On the one hand I'm glad that OSU beat Northwestern because it could have put OSU higher in the rankings and forced them to play a better team, perhaps ensuring a loss. But my favorite team in the Big Ten after Michigan is Northwestern. After Oregon lost they only dropped 3#'s. A loss to Northwestern probably wouldn't have knocked OSU too far up in the polls. So I say Northwestern all the way.