Transitive Rankings Post Week 6: Look to the West
by nuftw on Oct 11, 2010 1:51 PM EDT
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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).
We've reached the unfortunate time of the year when we must deal with cycles. For instance, Hawaii beat Louisiana Tech who beat Utah State who beat Brigham Young who beat Washington who beat Southern California who beat Hawaii. They way these rankings cope is by giving the transitive win to the team with the shorter path. USC beat Hawaii directly, so they get a win (even though Hawaii beat LA Tech who beat USU who beat BYU who beat UW who beat USC).
The unfortunate result is that teams might be ranked lower than teams they beat directly (which is unavoidable with cycles). However, these rankings still guarantee that a team is higher ranked than a team they beat (transitively), unless there is a cycle involving those two teams.
1 Boise State 86-0 (5-0)
2 Texas Christian 82-0 (4-0)
3 Oregon State 81-2 (3-2)
These teams are all here for the same reason: Oregon State's win over previous #1 Arizona. Unlike voters, the transitive rankings don't forget that Boise State and TCU both have wins over Oregon State. A team is never ranked lower than a team they beat (unless there's a cycle). SI's Stewart Mandel calls the Beavers the most underrated team.
4 Oregon 76-0 (5-0)
Beating Washington State doesn't do anything, but the Stanford win is now worth 59 transitive wins.
4 Arizona 79-3 (3-1)
The California win is currently Arizona's best for transitive purposes (if you haven't figured it out yet, transitive rankings currently love the Pac-10). Iowa might pay off more in the future though.
6 Nevada 75-0 (5-0)
Nevada beat Cal as well.
6 Nebraska 75-0 (4-0)
The Washington win still helps a little, but beating KState is what propelled Nebraska into the top 10.
8 Kansas State 74-1 (3-1)
KSU's win over UCLA still looks pretty good, but ISU contributes the bulk of the transitive wins (ISU beat Texas Tech and a surprisingly game Northern Illinois).
9 Auburn 72-0 (6-0)
No reasonable person should have Auburn below Alabama. Auburn beat South Carolina, Alabama did not.
9 Stanford 73-1 (4-1)
56 of Stanford's wins are from USC or UCLA. Beating ND helped a lot in the polls, but not here.
9 Oklahoma 72-0 (5-0)
FSU's win over Miami bumped their value up some, but Oklahoma's best two wins are still Air Force and Texas.
12 California 73-5 (2-2)
12 Louisiana State 68-0 (6-0)
14 Utah 67-0 (5-0)
15 South Carolina 67-1 (3-1)
16 Iowa 66-4 (3-1)
17 Michigan State 61-0 (5-0)
18 Virginia Tech 61-1 (4-1)
19 UCLA 69-10 (3-3)
20 Ohio State 58-0 (6-0)
Ohio State's schedule has held them back a bit so far. Miami isn't as good as once thought.
20 North Carolina State 60-2 (4-1)
22 Missouri 57-0 (4-0)
23 Michigan 57-1 (4-1)
23 Alabama 58-2 (5-1)
23 Air Force 57-1 (4-1)
23 Iowa State 64-8 (2-3)
27 Texas 66-12 (3-2)
28 Mississippi State 55-2 (3-2)
28 Florida State 54-1 (4-1)
30 West Virginia 53-1 (3-1)
WVU is the Big East's highest rated team here. The next highest is #66 Pitt. Had Marshall finished off that upset, the Mountaineers would be 90th.
30 Oklahoma State 52-0 (5-0)
Worst undefeated team? When 4 of your wins are over Tulsa, ULL, Troy and Washington State, it's a possibility. A more fitting description might be "Least Impressive So Far of Any Undefeated Team".
32 Notre Dame 55-4 (3-3)
32 Wisconsin 52-1 (4-1)
32 Illinois 53-2 (2-2)
35 Maryland 52-2 (3-1)
35 Arkansas 53-3 (3-1)
37 Navy 51-5 (2-2)
38 Colorado 52-7 (3-2)
38 Texas A&M 50-5 (2-2)
38 Texas Tech 61-16 (3-2)
41 Arizona State 50-6 (1-3)
42 Baylor 59-17 (3-2)
43 Penn State 51-11 (2-3)
43 Wyoming 54-14 (1-3)
45 Northern Illinois 51-12 (3-2)
46 Toledo 53-15 (3-3)
46 Houston 52-14 (2-2)
48 Temple 50-17 (3-2)
48 Purdue 52-19 (2-2)
50 Northwestern 51-20 (4-1)
51 Georgia Tech 55-25 (3-2)
51 East Carolina 55-25 (3-2)
51 Kansas 55-25 (2-2)
51 Southern Mississippi 55-25 (3-2)
51 North Carolina 55-25 (3-2)
56 Florida 28-4 (4-2)
Transitive ranking also agrees with Mandel's assessment of Florida as the most overrated team.
57 Miami (FL) 16-3 (2-2)
58 Central Florida 13-5 (2-2)
59 Texas-El Paso 16-15 (4-1)
60 Indiana 2-3 (2-2)
Indiana continues to be the most boring team, transitively speaking. Their wins are over teams that are 0-11, their losses are to teams that are 9-1.
60 Southern Methodist 16-17 (4-2)
60 Georgia 13-14 (2-4)
63 Tennessee 12-17 (1-4)
64 Boston College 2-8 (1-3)
65 San Jose State 0-7 (0-4)
SJSU will probably have the title of "Best Transitive Record by a Winless Team" for as long as they remain winless. Their losses are to Alabama, Wisconsin, Nevada, and Utah. Next week, Boise State comes to town.
66 Pittsburgh 2-10 (1-3)
67 Mississippi 46-58 (3-1)
67 Hawaii 46-58 (3-2)
69 Vanderbilt 45-59 (2-3)
70 Louisiana Tech 44-59 (1-4)
71 Southern California 44-60 (4-2)
72 Connecticut 43-60 (2-3)
72 Tulsa 13-30 (2-3)
74 Clemson 12-31 (1-3)
75 Rice 12-32 (1-5)
76 Brigham Young 41-62 (2-4)
76 Rutgers 41-62 (2-2)
78 Washington 41-63 (2-3)
78 San Diego State 41-63 (2-2)
78 Fresno State 41-63 (2-2)
78 Army 41-63 (4-2)
Army is the lowest team with a winning record. Having a best win of Tulane will do that.
82 Tulane 39-64 (1-3)
82 Utah State 39-64 (1-4)
84 Wake Forest 1-33 (1-4)
85 Kentucky 16-70 (3-3)
85 Syracuse 15-69 (2-1)
87 Minnesota 12-69 (1-4)
88 Cincinnati 11-69 (1-3)
88 Louisville 13-71 (2-2)
88 South Fla. 13-71 (2-2)
91 Miami (OH) 10-71 (3-3)
92 Memphis 12-75 (1-5)
93 Colorado State 7-72 (1-5)
94 Buffalo 4-70 (1-3)
95 Idaho 6-73 (2-2)
96 New Mexico State 1-70 (1-4)
96 Virginia 0-69 (0-3)
98 Duke 0-70 (0-4)
98 Florida International 1-71 (1-4)
98 Washington State 0-70 (0-5)
101 Western Michigan 3-74 (1-3)
102 Kent State 1-73 (1-3)
103 Ball State 2-75 (1-3)
103 Nevada-Las Vegas 1-74 (1-5)
105 Central Michigan 1-76 (1-4)
106 New Mexico 0-77 (0-6)
106 Western Kentucky 0-77 (0-5)
106 Akron 0-77 (0-5)
109 Louisiana-Lafayette 9-87 (2-3)
109 Middle Tennessee State 9-87 (1-3)
109 Troy 9-87 (3-2)
112 Arkansas State 7-89 (2-4)
112 Alabama-Birmingham 7-89 (1-4)
112 Louisiana-Monroe 7-89 (1-3)
115 North Texas 6-90 (1-5)
115 Florida Atlantic 6-90 (1-4)
117 Ohio 2-95 (2-3)
117 Bowling Green State 2-95 (1-5)
117 Marshall 2-95 (1-4)
120 Eastern Michigan 0-104 (0-6)
EMU looks like they have secured the 120 spot. Only 8 teams have a win but do not have a transitive win over the Eagles.
Longest Shortest Cycle: (The longest cycle which is the shortest involving a particular team)
Army beat Tulane who beat Rutgers who beat Connecticut who beat Vanderbilt who beat Mississippi who beat Fresno State who beat Utah State who beat Brigham Young who beat Washington who beat Southern California who beat Hawaii who beat Army.
Right now, this group is clumped #67-#82 region, though it will be more spread out as time goes on.
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I was thinking about this
Suggest giving a fraction of the victory to each time, as a ratio of the shortest path distance.
Example:
Team A’s shortest path over Team B is 1 (they beat B)
Team B’2 shortest path over Team A is 5
A gets 5/6ths of a win, B gets 1/6th of win. For simple chains, A beats B beats C beats etc beats A, this still works out to .5 wins per team, but for complex chains, it rewards the team with shorter paths while giving everyone in the chain some credit.
Conference homers are the lowest form of fandom. That is why the SEC has so many of them.
Congratulations
You have reinvented the Colley Matrix.
http://www.colleyrankings.com/method.html
(That’s a good thing. The Colley Matrix is a pretty good computer ranking method)
by The Commenter Formerly Known as Not You on Oct 11, 2010 5:21 PM EDT up reply actions
Ummm...dont think so
Actually, I may have, but having read it, I didnt realize thats how it worked.
He fooled me with all the matrix math.
And, yeah, Ive always liked Colley’s method.
Maybe the matrix is an easier way to do the same calculation than calculating shortest paths for every connection. Huh. Cool if true.
Conference homers are the lowest form of fandom. That is why the SEC has so many of them.
I don't think it is.
Best I can tell, it’s just WPct (modified by adding a win and a loss against an average team, just to make the numbers converge) + SOS – 0.5, with SOS calculated from the opposing ratings and not just their records.
Yeah, that goes with my thoughts on Colley
Of course, that is the right way to calculate SoS, not basing it on records.
Some people dont grasp the concept of “iteration”.
Conference homers are the lowest form of fandom. That is why the SEC has so many of them.
I keep running your proposed method and Colley through my head
and getting the same results. So either my head is stupid (Which it’s been accused of many times, mind you), or it’s a complicated way of calculating the matrices in the same way…
Or I’m just not choosing a complicated enough example, which is also likely, but that falls under my head being stupid. I can’t do big matrices in my head… stupid head…
by The Commenter Formerly Known as Not You on Oct 12, 2010 11:16 AM EDT up reply actions
Proof they arent the same
Boise is #1 according to “my” suggestion (which is same as transitive rankings for non-loopy teams) and #5 in current Colley.
Conference homers are the lowest form of fandom. That is why the SEC has so many of them.
Oh, duh.
I was just comparing the looping.
Yeah, chalk it up to my head being stupid.
by The Commenter Formerly Known as Not You on Oct 12, 2010 1:09 PM EDT up reply actions
I’ll implement that at some point and see if it changes much. My gut reaction is that if a team beats another directly, they should get full credit for the win.
Transitive Rankings: It's not who you beat, it's who they beat. Post Week 5: Big Ten and all FBS
Reality has a little-known Northwestern bias
NU prez knows how to get PUMPED
Eh, a chain is a chain
If they chain over you, they deserve some transitivity credit.
3 ways to do it:
1. Everyone in chain gets equal credit – ends up kind of silly
2. Shortest chain gets all credit
3. Shortest chain gets bulk of credit
- seems better than #2 to me. In simple chains all three work out the same. With #3, the more complex the chain, the more credit a direct win is worth.
At this point, I doubt it makes much difference at all. When it would matter would be 2008, when Florida is part of the loop due to losing to Ole Miss. But, actually, I doubt #2 v #3 makes much difference. Fractions here and there.
Conference homers are the lowest form of fandom. That is why the SEC has so many of them.
I agree #1 doesn’t really work. #3 complicates the rankings (unnecessarily IMO) because it requires a number of choices like “How much better is a direct win than a win with 1 intermediate steps?”
The gray area to me is the comparisons where the chains are equal length. Right now, I’m breaking the tie by counting which direction has more paths. (This works out to record against common opponents in the length 2 case). A simpler way would be to just give each side a tie.
Just for fun, here is the final top 10 for 2008 if done in this way:
1 Utah 119-0 (12-0)
2 Alabama 116-2-1 (12-2)
3 Florida 113-2-4 (12-1)
4 Boise State 111-7-1 (11-1)
5 Southern California 110-7-2 (12-1)
6 Oklahoma 107-8-4 (11-2)
7 Texas 105-7-7 (12-1)
8 Texas Christian 105-10-4 (10-2)
9 Oregon State 94-12-13 (9-4)
10 Oregon 94-13-12 (10-3)
10 Georgia 91-10-18 (9-3)
Florida’s losses are to Utah and Mississippi. Their ties are with Iowa (length 3), Navy (length 3), Wake Forest (length 2) and USC (length 5).
Transitive Rankings: It's not who you beat, it's who they beat. Post Week 6: Big Ten and all FBS
Reality has a little-known Northwestern bias
NU prez knows how to get PUMPED
This is where fractional makes a difference
Bama above Fla ends up as result of way you do it.
Florida has a loss to Ole Miss. Alabama doesnt, because they beat Ole Miss directly. If done with my idea, Alabama would get 2/3rds of the points vs Ole Miss instead of the full pt, because they have a length of 1 to Ole Miss and Ole Miss has a length of 2 to them.
You have Alabama at 116.5 vs Florida at 115.0. With fractional pts within the loop, I think that either tightens up or Florida takes the lead. Just in the case of Ole Miss, it makes 2/3rds of a point difference. Bama falls to 116.17 and Florida rises to 115.33 (they get 1/3 vs Ole Miss do to having a 2 length chain to them).
Your method penalizes Florida for a “bad” loss without really penalizing Bama for losing to a team with a bad loss.
The bigger problem with this method is that a team with a wretchedly bad schedule can end up on top as long as one team they beat is in the loop and everyone else is in the loop. Not that Utah’s schedule was wretchedly bad.
Conference homers are the lowest form of fandom. That is why the SEC has so many of them.
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