Post Week 10 Transitive Rankings-No Upsets, No Changes

As every college football message board debater knows, winning football games is transitive. In other words, if Team A beats Team B and Team B beats Team C, the fans of Team A are perfectly within their rights to talk trash to fans of Team C. Obviously, Team A could have completely wiped the floor with Team C, they just didn't happen to play each other. If Team D happens to lose to Team C, they are also deserving of as much scorn as possible. Thus one way of ranking teams just counts how many teams' fans are permissible trash talk targets (minus those in the reverse situation).

Very little changed from last week.  The only "upset" was Michigan beating Illinois and even that was predicted by the margin based rankings.  The rankings now allow FCS teams on paths, but doesn't count transitive wins/losses over FCS teams.  In other words, Minnesota doesn't get a loss to South Dakota in their record, but since Fresno State beat Cal Poly who beat South Dakota, Minnesota does get a loss to Fresno from that path.  


1 Wisconsin 109-10 (#9 in the country)

The Badgers remain the best team with a "bad" loss.  For the Badgers to move up, one of the top 8 has to lose.  

Most Interesting Chain:  Mississippi State (#8) is the lowest transitively unblemished team, but they don't have a short route to Wisconsin.  They get their transitive win from: (Mississippi State, UAB, Southern Miss, Louisiana Tech, Utah State, Brigham Young, Washington, Oregon State, Arizona, Iowa, Michigan State, Wisconsin)

Next Week: Indiana.  Wisconsin beat Iowa who beat Indiana.  


2 Nebraska 105-14 (#12)

Nebraska's win over Iowa State probably doesn't look particularly notable, but transitive rankings love the Big 12 this year.  Ten of the twelve current teams in that conference are in the top 25 of the country, including Iowa State at #21.  (Sagarin has a slightly more dim view, with only 9 Big 12 teams in the top 27).  

Next Week: Kansas.  Nebraska beat Kansas State who beat Kansas, but Kansas beat Colorado who beat Hawaii who beat Nevada who beat California who beat UCLA who beat Texas who beat Nebraska.  


Iowa 102-17 (#14)

Staying on the Big 12 theme, Iowa's win over ISU is worth as much (40 transitive wins) as their next best two wins combined (MSU 22 and Michigan 18).  Transitive rankings overvalue out of conference wins, but no one expected that early win to be at all respectable.  

Next Week: At Northwestern.  Iowa beat MSU who beat Northwestern.  


Michigan State 101-18 (#17)

MSU still only has one win over teams in top 30, which holds them back.  Their second best win remains Northwestern, as the Illinois and Michigan wins split a lot of the same territory because of their cycle with Penn State.    

Next Week: Bye. 


Ohio State 96-23 (#21)

OSU has the same problem as MSU.  No one is counting the Miami win as a season-definer now (Miami is #47 in transitive rankings).  However, if OSU beats PSU and especially Iowa the next two weeks, they should rise substantially.  

Most Interesting Chain:  OSU actually has transitive wins over much of the SEC from the OSU-Purdue-Northwestern-Vanderbilt-Mississippi-Kentucky-South Carolina-Alabama-Arkansas/Florida chain.  This is obviously a long chain, but since OSU's only "bad" loss is from OSU-Wisconsin-MSU-Iowa-Arizona-Oregon State-Washington/UCLA, the Buckeye's path to the SEC teams is shorter than anything they have back to OSU.  

Next Week: Penn State.  Ohio State beat Illinois who beat Penn State.  



For the next 3 teams, Michigan beat Illinois who beat Penn State who beat Michigan.  This short cycle prevents any of these teams from rising much higher than the others, since they all have many of the same wins and losses.  

6t Michigan 81-38 (#35t)

Michigan's win over Bowling Green State (actual motto: Moving forward by degrees) is worth a surprising 18 transitive wins, mostly over MAC and CUSA teams.   BGSU beat Marshall who beat 6-4 UTEP and 7-4 Ohio.  

Most Interesting Chain: Michigan's win over FCS UMass actually gives them some transitive wins over FBS teams.  UMass beat JMU who beat Virginia Tech who is now 7-2.  

Next Week: At Purdue.  Michigan beat Illinois who beat Purdue.  


6t Illinois 81-38 (#35t)

Illinois has a death of a thousand cuts.  None of their losses are bad, but each of them contributes a little bit.  The Missouri loss in particular became much worse after Missouri lost to Texas Tech this week. 

Most Interesting Chain: Like Michigan, Illinois' FCS win also gives them some FBS transitive wins.  SIU beat Illinois State and Northern Iowa, both of whom beat North Dakota State who beat Kansas.  

Next Week: Minnesota. Illinois beat Penn State who beat Minnesota.  


Penn State 79-40 (#37)

The third member of the trio drops out of the tie due to transitive losses to Kentucky, Georgia, and San Diego State.  Illinois doesn't have the loss to Georgia, Michigan doesn't have the loss to SDSU and neither of them (transitively) lost to Kentucky.  

Next Week: At OSU.  Penn State beat Northwestern who beat Vanderbilt who beat Mississippi who beat Fresno State who beat Utah State who beat BYU who beat Washington who beat Oregon State who beat Arizona who beat Iowa who beat MSU who beat Wisconsin who beat OSU.  


9 Northwestern 58-61 (#60)

Transitively speaking, Northwestern could probably lose the rest of their games and not move much.  Based on their second half play the last 4 games, that seems to be the intention.

Most Interesting Chain:  Illinois State is worth 7 transitive wins to Northwestern, since they beat North Dakota State who beat Kansas (who beat Georgia Tech and Colorado).  This as much as the Minnesota (4) and Central Michigan (3) wins combined. 

Next Week: Iowa.  Northwestern beat Vanderbilt who beat Mississippi who beat Fresno State who beat Utah State who beat BYU who beat Washington who beat Oregon State who beat Arizona who beat Iowa.  



10t Purdue 39-80 (#81t)

Purdue and Indiana are tied, but their approaches are completely different.  Purdue has a decent win over Northwestern, but two pretty horrible losses to Notre Dame and Toledo. 

Most Interesting Chain:  Purdue has a transitive loss to New Mexico, who before this week was thought to possibly be the worst team in FBS.  1-8 New Mexico beat 2-8 Wyoming who beat Toledo who beat Purdue.  

Next Week: Michigan.  Purdue beat Northwestern who beat Vanderbilt who beat Mississippi who beat Kentucky who beat South Carolina who beat Alabama who beat Penn State who beat Michigan.


10t Indiana 39-80 (#81t)

In contrast, Indiana doesn't have a bad loss for this ranking (Northwestern is the worst team to beat them, but NU is at least in the top half of FBS teams), but their wins are over #98 Arkansas State, #114 Western Kentucky, and #120 Akron (out of 120 teams).  

Most Interesting Chain: Indiana has transitive losses to 10 of the Big 12 from the Illinois-Missouri-Nebraska/Texas Tech chain and has wins over the two others (Colorado and Kansas).  

Next Week: At Wisconsin.  Indiana beat Arkansas State who beat FAU who beat UAB who beat Southern Miss who beat Louisiana Tech who beat Utah State who beat BYU who beat Washington who beat Oregon State who beat Arizona who beat Iowa who beat Michigan State who beat Wisconsin.  


12 Minnesota 18-101 (#105)

Minnesota took a hit this week because of the change allowing FCS teams on paths.  The Gophers now have 39 losses to FBS teams through that South Dakota loss, as USD is now 4-6 overall.  

Most Interesting Chain: The only BCS team ranked lower than Minnesota is Washington State.  However WSU has the head-to-head transitive win: WSU beat (FCS) Montana State who beat Weber State who beat UC Davis who beat South Dakota who beat Minnesota.  

Next Week: At Illinois.  Minnesota beat Middle Tennessee State who beat ULM who beat (FCS) Southeastern Louisiana who beat Tennessee-Martin who beat Eastern Kentucky who beat Jacksonville State who beat (FBS) Mississippi who beat Kentucky who beat South Carolina who beat Alabama who beat Penn State who beat Michigan who beat Illinois.  


This is the same order as Sagarin's rankings except for flipping Wisconsin and Nebraska.  



Wisconsin over Indiana

Illinois over Minnesota

Nebraska over Kansas

Michigan over Purdue

Iowa over Northwestern

OSU over Penn State


Transitive rankings obviously aren't perfect.  One issue is that they unreasonably value long chains.  In some sense, the best information comes from the closest connection.  As an alternative, here are rankings according closest connection record.  These rankings consider only the shortest connection of the type "Team A played Team B played Team C".  If Team A beat Team B who beat Team C, then Team A gets a win over Team C.  If Team A beat Team B, but Team B lost to Team C, then the Team A vs Team B match-up is considered a no-result.  Confused?  Consider Purdue and South Carolina.  The shortest connection is Purdue-Northwestern-Vanderbilt-South Carolina.  Purdue beat Northwestern who beat Vanderbilt, but Vanderbilt lost to South Carolina.  So Purdue (and South Carolina) get a transitive tie.  

National Rank Team Shortest Connection Record
5 Nebraska 64-2
14 Wisconsin 52-1
15 Michigan State 52-3
16t Ohio State 49-2
16t Iowa 54-7
29 Michigan 38-11
45 Penn State 30-18
46 Illinois 24-13
59 Northwestern 23-22
74 Indiana 9-20
76 Purdue 17-31
91 Minnesota 5-36



The final set of rankings looks at the closest connection and takes the net score along that path to determine the winner.  Home field advantage is considered as 3 points and victories have a max margin of 28 points.  

National Rank Team Margin Chains Record
11t Ohio State 98-21
11t Nebraska 98-21
14 Iowa 97-22
29 Wisconsin 83-36
30 Michigan State 82-37
34 Illinois 80-39
38 Michigan 78-41
41 Penn State 76-43
75 Northwestern 48-71
84 Indiana 40-79
89 Minnesota 37-82
91 Purdue 36-83


All of the in conference games now have common opponents, so these predictions are simply average point differential against those common opponents, adjusted for home field.  


Iowa -11.5 at Northwestern

Indiana +14.5 at Wisconsin

Minnesota +13.5 at Illinois

Michigan -7.5 at Purdue 

Penn State +15.5 at Ohio State

Kansas +20 at Nebraska

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