Fanblogs.com - Latest Comments in BCS Standings - Nov. 9th 2008

Re: BCS Standings - Nov. 9th 2008

GotliebTX — Sat, 15 Nov 2008 15:34:58 -0000

Unfortunately for me, I'm a geek of the computer kind and my math skills have all eroded into binary and hex. Adding 1s and 0s is my forte'. That may have had something to do with the iterative approach I took to calculating Win Factor.

Re: BCS Standings - Nov. 9th 2008

GotliebTX — Sat, 15 Nov 2008 15:25:44 -0000

1) Ball State wasn't in the top 25. Their competition really is that bad this year. Central Michigan was actually higher in Win Factor up until recently even though they had two losses (to Purdue and Georgia).

2. I don't claim to understand these rankings as well as you do. I also don't have the statistical background to really "get" these other calculations. I understand that they serve the same purpose but I believe most college football fans aren't savvy enough to understand, and ultimately trust, these to actually generate "standings" vs "rankings" or "ratings". There is a reason scoring in football(and almost every physically competitve sport) is in integers. Percentages are more difficult to compare on the fly. Could you imagine a basketball game where a free throw was worth .33, a field goal was worth .67, and the "3 pointer" was worth 1.0? I'd be lost the third time down the court.

3. Appalachian St. beating Michigan would have put them in the standings with a Win Factor of 1 (their win over Michigan). Any other FBS team beating them would have gotten 1 win added to their Win Factor just like any other team. The wins State compiled against FCS foes would not accrue.

4. www.collegewinfactor.com

5. Not sure what you mean here. They are treated equally yes. A win is a win but if you are in a tougher conference there will be more Win Factor wins to play for. That is why the Big 12 dominates the upper end of the standings this year.

6. Again, I thought this part through very carefully. Though your opinion on the loss factor as a tie-breaker is valid, I deemed the Win Factor 2 to be more in the spirit of the ranking and better at connecting all the teams in the pool. Win Factor (and Loss Factor) only connects you to teams you have faced in direct competition (1 degree of separation). Bringing in Win Factor 2 adds a second degree of separation and your connection now includes the competition of your competition. Forgive me if I've bastardized the use of the term separation, but it is how I understand the word.

7. Thanks. I worked very hard on stripping it down to the minimums and still keeping the essential elements intact. My hope is that the simplicity will make it understandable to the common fan.

Re: BCS Standings - Nov. 9th 2008

Ben Prather — Sat, 15 Nov 2008 12:38:25 -0000

I am just a math geek who has dabbled into and researched football rankings from time to time.

Rule of succession:

If a coin is not known to be fair the best estimate of the probability of heads given W heads in N tries is given to be:

P=(W+1)/(N+2)

The variance(square of the standard deviation) of the actual probability relative to this estimate can be found (on wikipedia, for example) to be:

SD^2 = P(1-P)/N

Re: BCS Standings - Nov. 9th 2008

Ben Prather — Sat, 15 Nov 2008 12:22:06 -0000

1) My point in bringing up Ball State was that they were missing from your initial listing.

2) Peter Wolfe and the Colley Matrix are the only two BCS formula's that have enough details about the method available to be reproducible. Both, like your win factor, are reductive in phylosophy. This means they attempt to best match the existing results for the season. For rankings that are reductive, projected out comes are a fair comparison.

Peter Wolfe uses a maximum likelihood analysis based on a logit distribution. This completely describes his rankings up to how he eliminates the unbounded behavior of undefeated and winless teams.

Wes Colley uses an adjustment to LaPlace's rule of succession that accounts for, I would argue to little, SOS. His method, like the one I described, is recursive, the final rankings are used in the formula to define the rankings. His are linear and can be solved exactly using matrices, though iteration gets close enough much faster.

Neither of these methods use the percentage type analysis you describe, but Massey, Anderson & Hester and Billingsley clearly do.

I would be surprised if your win factor did not out perform the Colley Matrix. by this measure.

It would be unfair to use projected outcomes to compare a reductive ranking to a predictive ranking such as Sagarin's predictor. His ELO-CHESS algorithm used for the BCS is not predictive, and also performs poorly if used as such. Massey's rankings are a hybrid and performs very well, both his wins only methods and his MOV method.

3) So last year you would have added Appalachian State and the teams that beat them?

4) Do you have a website your win factors are published at? Massey has a nice website comparing various methods available on the WEB and I would be interested in seeing how yours compares.

5) The main problem with the win factor as described is that it treats all 9 win teams the same, whether BYU, Oklahoma or Tulsa. Even your win factor ranking admits this is not the case.

6) The loss factor, defined to be the losses of the teams you lost to would be very much in the spirit of the win factor. If you lose to a team with few or no losses it would not make much difference at all, but a loss to a team with a few loses it would be significant. USC's loss to Oregon State should sting more than Texas' loss to Texas Tech. This is, IMO, a better tiebreaker than the win factors of teams beat. Rank based on wins, break ties based on losses.

7) I like the simplicity of your method compared to the results. It would be hard to find a simpler method that produced that good of a ranking.

Re: BCS Standings - Nov. 9th 2008

GotliebTX — Sat, 15 Nov 2008 02:12:45 -0000

For predictive outcomes this is probably fine provided you exclude games that cross divisions (er subgraphs). I don't see Grand Valley State taking on Florida anytime soon. The exclusion itself may cause problems as some teams play down and others do not, leaving you with an unbalanced number of games for your calculations.

Are you a statistician? I don't think I remember "Laplace's rule of succession" from my college math classes. That's way too deep for me.

Re: BCS Standings - Nov. 9th 2008

GotliebTX — Sat, 15 Nov 2008 01:58:52 -0000

Again, it's all about the 'W's. If you look at the conference Win Factors below (total Win Factors divided by conference members), you will see that the MAC has faired poorly in non-conference play this year. The Mountain West on the other hand has done very well averaging over 3 FBS wins more per team than the Pac 10. Utah is the sitting on top of a rising conference. Ball State is playing an entirely different level of competition as evidenced by the lack of FBS wins available in their conference play. If you strip away all the non-essential factors and focus on wins over winners, Ball State is properly ranked in low 20's.

Your right about predicting outcomes, Peter's system is better at it because that's what it's designed to do. He is trying to capture how good a team is this week, Win Factor is trying to capture how good a team was all season long.

FYI, beating Western Kentucky only counts if the Hilltoppers actually succeed in beating one of the other official 119. ncaa.org does not list them as actually sponsoring at the Div 1 FBS level so I am treating them as an FCS team that is playing an expanded schedule. If the Hilltoppers win against an FBS opponent, they will get added to the bottom of the pile (right above Washington and Wash State) and everyone who beat them will get 1 more win in their Win Factor.

WinFactor Team Standings as of 12:51 AM EST on Saturday November 15, 2008
Week 12 In Progress: 7 of 50 Games Complete.

Conference Name Total Winfactor Members Winfactor Per Member
Big 12 243 12 20.25
Big 10 212 11 19.27
SEC 225 12 18.75
ACC 211 12 17.58
Big East 140 8 17.50
M West 147 9 16.33
Pac 10 128 10 12.80
Ind. 37 3 12.33
WAC 105 9 11.67
MAC 143 13 11.00
C-USA 115 12 9.58
SunBelt 55 8 6.88

Re: BCS Standings - Nov. 9th 2008

GotliebTX — Sat, 15 Nov 2008 01:40:06 -0000

Ben,

You bring up good points but what's different about Win Factor is that losses are treated simply as missed opportunities By eliminating losses, the equation (if you can call adding 10 integers an equation) becomes instantly understandable as a scoring system and not a computerized rating. There are no percentages in the basic rankings table unlike all of the computerized rankings used by the BCS. Even without the percentages, it still compensates for SOS (Strength of Schedule) and disregards MOV (Margin of Victory). It is the simplest yet most balanced way of scoring a season. It is not designed at all to be predictive of future competition.

To your other astute point, I thought about using exactly the "loss factor" you described as a tie-breaker but felt that it ran counter to idea behind a Win Factor, which is to encourage teams to seek out the best competition in non-conference games and beat them however they can. Blowing out that Sunbelt cupcake isn't going to reward you at all. Squeaking by a potential conference champion from a rival conference will pay off big time (FYI, Utah would be #1 right now if they had beaten Boise State instead of Utah State).

Finally, to answer your last question, WF2 stands for Win Factor 2 or Win Factor Squared(though this is not literally a squared function). This is the second tie-breaker behind H2H (Head to Head) competition. It is simply the sum of the Win Factors of defeated opponents. This raises the pyramid of scores another order of magnitude which creates greater separation between close teams. It also increases the commonality of opponents between teams in different geographical regions as it allows for two degrees of separation. I actually considered taking this a step further with a Win Factor 3 but after careful consideration decided that if two teams are that close, they should either play it out on the field or remain tied in the rankings. In the unlikely event this happens in the top spot, there would be co-champions.

Thanks for your thoughtful analysis of my post.

Re: BCS Standings - Nov. 9th 2008

Ben Prather — Fri, 14 Nov 2008 20:13:48 -0000

Also, Ball State has a win factor of 21 or 22 depending on if you count Western Kentucky. This #19-25 ranking is remarkably low for a ranking that has Utah #2.

I don't think it beats Peter Wolfe's ranking if used to project the winners of games.

Re: BCS Standings - Nov. 9th 2008

Ben Prather — Fri, 14 Nov 2008 19:58:22 -0000

I like the results But I don't think the idea is complete.

It would be better if a parallel loss factor was determined, the number of FBS loses of teams you lost to. The ranking would be win factor - loss factor. For Example Texas lost to Texas Tech who has no losses, so they have a loss factor of 0. Bad example. Take USC. They have a single loss to Oregon State who has 3 losses so they have a loss factor of 3.

At the very least loss factor is a compelling tie breaker.
What is the WF2 you use for a tie breaker?

Re: BCS Standings - Nov. 9th 2008

GotliebTX — Fri, 14 Nov 2008 19:15:23 -0000

Darn it. Is there any way to format these posts into columns?

Re: BCS Standings - Nov. 9th 2008

GotliebTX — Fri, 14 Nov 2008 19:14:01 -0000

Ben,

Win Factor is incredibly simple but effective. It is simply the sum of all FBS wins of defeated opponents. Here is the math that currently puts Utah in 2nd place overall.

UTAH
Week  Defeated                       Conference        FBS Wins  
1 MICHIGAN                                Big 10                     3 
2 NEVADA-LAS VEGAS             M West                   5 
3 UTAH STATE                            WAC                       1 
4 AIR FORCE                              M West                   7 
6 OREGON STATE                     Pac 10                   6 
7 WYOMING                                 M West                  3 
8 COLORADO STATE                M West                  3 
10 NEW MEXICO                        M West                   4 
11 TEXAS CHRISTIAN               M West                  8 
                                       UTAH's WinFactor is ==> 40

Re: BCS Standings - Nov. 9th 2008

Ben Prather — Fri, 14 Nov 2008 10:55:56 -0000

Did I miss the definition of a win factor?

I have a similar ranking produced as follows:

Each team has a rank between 0 and 1, the higher ranking the better.

Add the ranks of the teams you beat to get a teams win score.

Add 1- the ranks of the teams that beat you to get a teams loss score.

Each team's rank is then defined to be:
rank = ( 2*(win score) + 1 )/( 2*(win score + loss score) + 2 )

If you play only average teams this reduces to LaPlace's rule of succession. It weights wins by the strength of the opponent, a win agianst a team with a rank of 1 counts double, with a rank of 0 does not count at all. Losses are the opposite. A loss to a team with a rank of 0 counts double while a loss to a team with a rank of 1 does not count at all.

An error measure can be found and used to determine the probability one team will beat another.

The recursive definition is fun to solve. Using Peter Wolfe's game data and c++ this can be done quickly.

Texas Tech is favored to beat Oklahoma 56% of the time. Utah is favored to beat SDSU 99.999% of the time. BYU is favored to beat Air Force 75% of the time.

A major flaw is that Grand Valley State is in the top 5 when all NCAA teams are ranked together, showing that large and weakly connected subgraphs are not handled appropriately.

Utah is #3, showing its over dependence on W-L record.

Re: BCS Standings - Nov. 9th 2008

Ben Prather — Fri, 14 Nov 2008 10:51:11 -0000

I wonder how in the world TCU falls below BYU.

That makes no sense to me.

Re: BCS Standings - Nov. 9th 2008

GotliebTX — Tue, 11 Nov 2008 23:50:14 -0000

I'd really like to see that Ball State vs Texas matchup. They'd have to reset the scoreboard at halftime.

Re: BCS Standings - Nov. 9th 2008

NMLSooner — Mon, 10 Nov 2008 09:19:15 -0000

So if the playoffs started next Saturday:
8 North Carolina @ 1 Alabama
5 Boise State @ 4 Penn State
6 Ohio State @ 3 Oklahoma
7 Oklahoma State @ 2 Florida
8 Michigan State @ 1 Texas Tech
5 Georgia @ 4 Utah
6 Missouri @ 3 USC
7 Ball State @ 2 Texas

Re: BCS Standings - Nov. 9th 2008

Cougar_Fan — Mon, 10 Nov 2008 00:56:15 -0000

I wonder why Air Force hasn't received more love in the polls? They've been impressive and only lost at the last second to a good Navy squad and to #7 Utah.

Re: BCS Standings - Nov. 9th 2008

GotliebTX — Mon, 10 Nov 2008 00:21:42 -0000

Ben,

Utah's win was clutch. Their win over TCU coupled with several wins by their downline(defeated opponents) combined to push the Utes into the #2 spot in the Win Factor rankings.

Recapping the top five spots, Texas held on to the top spot by getting several wins from their downline and picking up 2 by beating up on over-matched Baylor. The Utes victory pushed them into the #2 spot as I mentioned above. Utah actually leapfrogged Tech into that spot as their downline continued to pile up wins. Texas Tech's was less helpful coming up one win short of the Utes for third even after thumping OSU at home. Florida and Oklahoma round out the top 5 spaces with solid wins each.

Here is the Win Factor Top 25.

"WinFactor Team Standings as of 1:24 AM EST on Sunday November 9, 2008"

Week 11 Complete

Rank Team Name Conf WinFactor Comment
1 TEXAS Big 12 45
2 UTAH M West 39
3 TEXAS TECH Big 12 38
4 FLORIDA SEC 36
5 OKLAHOMA Big 12 34
6 ALABAMA SEC 33 Owns WF2 advantage over OHIO STATE
7 OHIO STATE Big 10 33 -
8 SOUTHERN CAL Pac 10 32 Owns WF2 advantage over BOISE STATE
9 BOISE STATE WAC 32 -
10 PENN STATE Big 10 31 WF2 advantage over MICHIGAN STATE
11 MICHIGAN ST Big 10 31 WF2 advantage over GEORGIA
12 GEORGIA SEC 31
13 PITTSBURGH Big East 30
14 NORTH CARO ACC 28 Owns WF2 advantage over MISSOURI
15 MISSOURI Big 12 28 -
16 TCU M West 27
17 CALIFORNIA Pac 10 24
18 CINCINNATI Big East 23
19 VIRGINIA TECH ACC 22 WF2 advantage over VIRGINIA
20 VIRGINIA ACC 22 WF2 advantage over VANDERBILT
21 VANDERBILT SEC 22 WF2 advantage over OKLAHOMA STATE
22 OK State Big 12 22 WF2 advantage over NEBRASKA
23 NEBRASKA Big 12 22 WF2 advantage over AIR FORCE
24 AIR FORCE M West 22
25 WAKE FOREST ACC 20 Owns WF2 advantage over EAST CAROLINA

Re: BCS Standings - Nov. 9th 2008

MAYDAY13 — Sun, 09 Nov 2008 18:36:19 -0000

Ben what did i tell you?

Re: BCS Standings - Nov. 9th 2008

Ben Prather — Sun, 09 Nov 2008 17:50:52 -0000

Though BYU lost ground in the rankings they actually gained .0009 BCS points. Several teams filled some gaps immediately in front of them causing them to go down in rank.

I apparently underestimated Ball State and Michigan State's opponent strength. Next week Utah might lose ground with SDSU killing thier SOS.