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Archive for the 'BCS' Category

Checkdowns: Joe Posnanski on Bye Teams Losing & the NFL vs. the BCS

Posted by Neil Paine on January 18, 2011

Joe Poz had an interesting post yesterday about the phenomenon of teams with a 1st-round bye losing half their opening playoff games since 2005. This randomness plays into why most of us hate the BCS even though in some ways a BCS-like method is "fairer" to teams based on their regular-season performance. Doug once found that the NFL's best team only won the Super Bowl about a quarter of the time, and Joe wonders what it means when we're basically OK with that.

19 Comments | Posted in BCS, Checkdowns

CFB: Auburn’s Place Among BCS Champions

Posted by Neil Paine on January 13, 2011

Note: This post was originally published at CFB at Sports-Reference, S-R's new College Football site, so when you're done reading, go over and check it out!

Whenever a team wins a championship, the temptation is always to compare them to other champions from the past, and the 2010 Auburn Tigers are no exception. Using the Simple Rating System (SRS), let's take a look at where the newest title-holders stand among BCS champs...

On Monday, ESPN asked its users to rank the BCS Champions from #1-13, coming up with this list:

Team Total Pts #1 Votes
2005 Texas 147,259 3,238
2004 USC 141,467 2,710
2009 Alabama 138,222 2,104
2001 Miami-FL 130,473 2,474
2008 Florida 119,697 1,071
2006 Florida 102,270 478
2010 Auburn 92,789 1,042
1999 Florida State 87,367 446
2002 Ohio State 82,755 629
2003 LSU 79,905 404
2000 Oklahoma 78,115 388
1998 Tennessee 74,067 525
2007 LSU 73,156 200

The SRS, though, comes up with a different ranking:

Year School Conf W L T SRS SOS
2001 Miami-FL Big East 12 0 0 26.169 5.741
2004 Southern California Pac 10 13 0 0 26.062 8.788
2008 Florida SEC 13 1 0 25.370 6.701
2005 Texas Big 12 13 0 0 24.977 5.686
2009 Alabama SEC 14 0 0 23.693 7.747
1999 Florida State ACC 12 0 0 23.495 6.208
2000 Oklahoma Big 12 13 0 0 21.555 5.812
2003 Louisiana State SEC 13 1 0 20.847 4.033
2010 Auburn SEC 14 0 0 20.648 7.031
1998 Tennessee SEC 13 0 0 19.955 4.955
2006 Florida SEC 13 1 0 19.661 7.886
2007 Louisiana State SEC 12 2 0 18.414 6.659
2002 Ohio State Big Ten 14 0 0 18.134 4.739

7 Comments | Posted in BCS, Best/Worst Ever, College, Simple Rating System, Statgeekery

NCAA: SRS ratings through eleven weeks

Posted by Chase Stuart on November 14, 2010

Oregon and TCU stumbled this week, barely hanging on against inferior conference opponents. Boise State and Auburn obliterated hated rivals and left no question about their ability to win. What do the SRS ratings say compared to last week?

Rank Team Gm MOV SOS SRS Rec Conf ConRk SOS Rk
1 Oregon 10 29.3 43.1 72.3 10-0 P10 1 26
2 Boise St 9 27.9 36.6 64.5 9-0 WAC 1 76
3 Stanford 10 17.3 47.1 64.4 9-1 P10 2 8
4 TCU 11 26.8 37.3 64.1 11-0 MWC 1 66
5 Alabama 10 16.3 44.5 60.8 8-2 SEC 1 14
6 Ohio State 10 22.3 37.3 59.6 9-1 B10 1 65
7 Auburn 11 16.2 42.5 58.7 11-0 SEC 2 29
8 Oklahoma St 10 15.4 41.9 57.3 9-1 B12 1 33

Comments Off | Posted in BCS, College

NCAA: SRS ratings through ten weeks

Posted by Chase Stuart on November 7, 2010

As usual, all game results courtesy of Peter R. Wolfe. The top three teams have stayed on top for a few weeks, but the order has now changed. Courtesy of the Win of the Year by the Horned Frogs on Saturday, TCU moves ahead of Boise State in the SRS. Full explanation of the SRS available here.

Rank Team Gm MOV SOS SRS Rec Conf ConRk SOS Rk
1 Oregon 9 31.7 41.7 73.4 9-0 P10 1 43
2 TCU 10 28.8 38.8 67.5 10-0 MWC 1 62
3 Boise St 8 27.3 38.5 65.8 8-0 WAC 1 67
4 Stanford 9 18.4 46.5 64.8 8-1 P10 2 8
5 Alabama 9 16.2 44.3 60.5 7-2 SEC 1 23
6 Ohio State 9 22.4 37.0 59.4 8-1 B10 1 74
7 Auburn 10 16.3 42.0 58.3 10-0 SEC 2 40
8 Nebraska 9 15.8 42.4 58.2 8-1 B12 1 33
9 Oklahoma St 9 14.9 43.1 58.0 8-1 B12 2 31
10 Missouri 9 12.9 44.1 57.1 7-2 B12 3 26
11 Utah 9 18.6 37.9 56.5 8-1 MWC 2 70
12 Arizona 9 12.3 44.2 56.4 7-2 P10 3 25
13 Oklahoma 9 10.3 46.0 56.3 7-2 B12 4 11
14 Oregon St 8 2.4 53.8 56.2 4-4 P10 4 2
15 Arkansas 9 12.9 42.8 55.7 7-2 SEC 3 32
16 Southern Cal 9 6.3 49.1 55.4 6-3 P10 5 5
17 Texas A&M 9 10.8 44.5 55.4 6-3 B12 5 17
18 Nevada 9 18.9 36.1 55.1 8-1 WAC 2 79
19 Iowa 9 15.1 39.8 54.9 7-2 B10 2 55
20 Florida 9 9.9 44.6 54.6 6-3 SEC 4 14
21 Florida St 9 12.8 41.2 54.0 6-3 ACC 1 46

Comments Off | Posted in BCS, College

NCAA: SRS ratings through seven weeks

Posted by Chase Stuart on October 17, 2010

Regular PFR readers will recall that we published college football SRS ratings every week last season. With seven weeks in the books, and the BCS opening rankings coming out tonight, it made sense to start up the project for 2010. So how do we come up with SRS grades for college football teams?

PFR has used the Simple Rating System to grade college and NFL teams for years. All ratings or rankings are meaningless without explanation, and the link above explains what the SRS tries to do. The SRS version that I'm implementing below is most useful to predict future results; the SRS is predictive, not retrodictive. That means the SRS will have no trouble at all ranking a team that's undefeated and beat a team with one loss behind the very team it beat. Why? One, because we know that one game is just one game, and never is conclusive proof that one team is better than another; and two, because the SRS weighs each game equally. Of course, sample size issues are always present here; while I've waited for seven weeks before presenting the SRS, we really need to see a couple more weeks of action before we can have full faith in this system. For now, though, maybe they'll make you rethink your perception of a couple of teams.

So how am I calculating these simple ratings?

1) For each game, 3 points are given to the road team (unless it's a neutral site game). After that adjustment, all wins and losses of between 7 and 24 points are scored as however many points the team won by. So a 24-10 road win goes down as +17 for the road team, -17 for the home team.

2) Wins of 7 or fewer points are scored as 7-point wins and losses of 7 or fewer points are scored as 7 point losses, except that road losses of 3 or fewer and home wins of 3 or fewer are graded as 0 point ties. So a 21-20 home victory goes down as a tie for both teams. This is not as drastic as it sounds, because the SRS ultimately is not concerned with win/loss records. There is no distinction between a win and a loss (you don't need to make such distinctions in predictive systems) except for when the game is close. So three 10-point wins scores +30, just as two 20-point wins and a 10-point loss scores as +30. However, three 3 point wins (+9 before the adjustments, +21 after) is worth more than two 10 point wins and a 1 point home loss (+21 before, +13 after).

3) Wins/Losses of more than 24 points are scored as the average between the actual number and 24. This is to avoid giving undue credit to teams that run up the score. Oregon bludgeoned New Mexico on opening day, 72-0, but that "only" goes down as a 46.5 point win. Why? Because the game was in Eugene (dropping it to +69) and the average of 24 and 69 is 46.5. However, in FCS/I-AA games, there is no run-up-the-score modifier. Why? Otherwise, the elite teams could beat the FCS cupcakes by 64 points and go down in this system. Major thanks to Peter R. Wolfe for providing the game scores.

8 Comments | Posted in BCS, College

College Bowl Rankings

Posted by Chase Stuart on December 7, 2009

After a very exciting weekend in college football, there are only 35 games left: Army-Navy next weekend, and then the 34 Bowl games. Here are the college football ratings for each of the 120 teams in the FBS after week 14:

Rk team conf Gms MOV SOS SRS W L
1 Texas B12 13 22.5 45.5 68.1 13 0
2 Alabama SEC 13 19.1 47.4 66.5 13 0
3 Florida SEC 13 19.8 45.8 65.6 12 1
4 TCU MWC 12 24.8 38.3 63.1 12 0
5 Virginia Tech ACC 12 13.5 48.4 61.9 9 3
6 Oregon P10 12 13.0 48.1 61.1 10 2
7 Oklahoma B12 12 13.9 46.5 60.4 7 5
8 Cincinnati BigE 12 18.8 40.3 59.2 12 0

10 Comments | Posted in BCS, College

NCAA: SRS ratings through thirteen weeks

Posted by Chase Stuart on November 29, 2009

Last week's SRS rankings

Peter R. Wolfe's college games scores

While little changed at the top -- only Ndamukong Suh and the Cornhuskers stand in the way of the seemingly inevitable Texas-Floribama BCS Championship Game -- it was a wild rivalry week in college football. The only two one-loss teams both lost to their biggest rivals; Oklahoma State got smashed by SRS-favorite and Bedlam rival Oklahoma; Clemson, Utah, North Carolina and Ole Miss, all in the top 25 in the AP, lost battles to their in-state rivals, as well. Up top, Texas A&M and Auburn both came oh-so-close to pulling off big upsets, to the dismay of most of the population of Fort Worth, Cincinnati and Boise. There are now six undefeated teams in the FBS, zero one-loss teams, and nine two-loss teams (with six of them in BCS conferences, and half of those in the Big 10).

8 Comments | Posted in BCS, College

Bill James supports BCS boycott

Posted by Doug on January 8, 2009

Thanks to Dr. Saturday for the pointer to this Slate article, in which Bill James articulates his reasons for not liking the BCS.

I don't have time to comment on all the items in the article that deserve comment, so I'll just say that, like everything Bill James has ever written, it's worth a read. I do have a question, though, for those out there who are a bit more in touch with what James has been doing for the past decade or so:

When did James start to refer to himself as a statistical analyst?

Twice in this article, he makes it clear that he does in fact consider himself to be one. My (possibly erroneous) recollection is that James has always specifically denied that, opting instead for something along the lines of, "I'm not a stat guy. I'm simply a guy who likes to ask questions, and then exhausts all possible avenues (some of which might happen to be statistical) of answering that question." Can any of you serious sabermetricians --- I know you're out there --- shed some light?

9 Comments | Posted in BCS, College, Non-football

Elo ratings explained

Posted by Doug on December 10, 2008

About two and a half years ago, I wrote this:

As you probably know, the participants in the BCS championship game are determined in part by a collection of computer rankings. Those computer rankings are implementing algorithms that “work” because of various mathematical theorems. At some point, I’m going to use this blog to write down everything I know about the topic (which by the way is a drop in the bucket compared to what many other people know; I am not an expert, just a fan) in language that a sufficiently interested and patient non-mathematician can understand.

Since then, I have only written a handful of posts about the mathematics of ranking systems. Here they are:

Simple Ranking System

Another way to derive the simple ranking system

The Maximum Likelihood Method

Some discussion of the technical difficulties involved with the Maximum Likelihood method

Incorporating home-field and/or margin of victory into the Maximum Likelihood Method

I'm going to add another post to this list today by writing about a method that Jeff Sagarin cryptically calls ELO_CHESS. Sagarin's ELO_CHESS method is one of the six computer ranking systems that figures into the BCS, although as we'll soon see, we don't have quite enough information to reproduce his rankings exactly. That's OK. The point of this post is to understand the theory behind it.

First, a bit of background.

10 Comments | Posted in BCS, College, Statgeekery

College Bowl Pool Madness: My Picks

Posted by Chase Stuart on December 20, 2007

For anyone that missed yesterday's post, you still have until 9 PM EST to enter the Bowl Pool Contest. As of 3:30 EST, we've got 9 entries, so the competition to win some sponsorship dollars isn't too heavy. Join in!

Let's start with a few notes. I'm going to use the Sagarin Ratings and point spreads to make my picks. I'm using Sagarin's Pure Predictor ratings as the base, but I also need point spreads because Sagarin ratings are subject to a key problem: teams like Oregon (Dixon injury) are going to be vastly overrated. So the point spread helps to alert me to those things. To be clear, neither I, PFR, "Doug" nor sports-reference.com promote gambling or advise you to wager any money on any sporting event, ever.

First notes: here are the Sagarin ratings for the longshot games:

Cincinnati	85.63	Southern Miss	65.63	20.00
Florida		95.57	Michigan	80.80	14.77
Boise State	83.60	East Carolina	69.43	14.17
Southern Cal	89.44	Illinois	81.54	7.90
Georgia		85.05	Hawaii		79.91	5.14

So we get the same credit if Southern Miss upsets Cincinnati as if Hawaii upsets Georgia. But Georgia looks significantly more likely to fall. I expect Southern Miss and Michigan to get blown out. I think the other three teams probably all have small chances to win. FWIW, here's how these teams look according to the SRS:

Cincinnati	14.3	Southern Miss	-2.5	16.8
Florida		19.4	Michigan	 7.3	12.1
Boise State	 7.9	East Carolina	 0.0	 7.9
Southern Cal	17.0	Illinois	10.0	 7.0
Georgia		16.3	Hawaii		 8.1	 8.1

This confirms not to pick Southern Miss or Michigan. Carroll's record in Bowl games plus this game being in USC's backyard is a big plus, so I'm going to take the supremely talented Trojans. Their SRS is arguably deflated by an unhealthy team playing poorly in mid-season. And while I know nothing at all about East Carolina, Boise State's only losses are to Washington and Hawaii (#52 and #29 according to the SRS, respectively). East Carolina lost a close game to Va Tech (the week before the LSU thrashing), lost to Southern Miss (#73), lost by 41 to West Virginia, lost to North Carolina State (#77) and to Marshall (#101). Those are four bad losses. Their best win was at Houston, who isn't even any good. Boise State's best win was in Fresno State, and they have some history at Hawaii. It's a long travel for East Carolina fans. I know all these reasons are the reasons why East Carolina is a long shot, but I don't see a lot of upside here. So I'll grab Boise State, and even though I think Hawaii isn't any good (as I wrote here), it's good to have one longshot in there.

I'm still not sure if I'd rather join Cincinnati and Florida with one of these three teams, or if I prefer to match them both up with strong dogs. One problem with picking the longshots is you really lose out on pairing a strong dog with someone like USC.

2 Comments | Posted in BCS, College

College Bowl Pool Madness: Contest inside

Posted by Chase Stuart on December 19, 2007

I've got a good friend that is a big college football fan and a pretty snazzy programmer. Let's call him "Doug". Every year, "Doug" conducts a college bowl pool that's half for fun, and half so he can create a nerdy webpage. Here at PFR we'll be running the bowl pool for you guys, too, so feel free to join in on the fun and geekiness. The prizes are:

75 sponsorship bucks for 1st place
30 sponsorship bucks for 2nd place
20 sponsorship bucks for 3rd place

As for the rules, well, here's the e-mail "Doug" sent out every year:

There are 32 bowl games. For each game, one team will be designated the favorite and one team will be designated the underdog. In some games, the underdog will be designated a "longshot." The list is below, along with a sample entry.

Step #1: pick a winner for each game (straight up).

Step #2: group your picks into groups of 1, 2 or 3, subject to the condition that a group of two must have at least one underdog and a group of one must be a longshot.

To get credit for a group, ALL teams in the group must win. Whoever gets the most groups wins. Tiebreaker is whoever picks the most total games correctly (ignoring groups). [NOTE: I think there's a decent chance that the tiebreaker will come into play; that's part of the strategy.]

29 Comments | Posted in BCS, College

BCS Thoughts

Posted by Chase Stuart on December 2, 2007

The BCS Bowl Selections came out yesterday, and like almost every other year, many people are unhappy. I've got lots of random thoughts, so I figured I'd just start collecting them here.

  • No one got a bad deal here. Yes, if you root for Georgia, Virginia Tech, Oklahoma or USC (we'll get to Hawaii later), you are understandably disappointed today. On Sunday morning you thought your team might luck into the BCS Championship Game, and in the end LSU and OSU took those two spots. But all four schools lost two games each, and had multiple blemishes on their resumes. This is *not* 1998 Tulane, 2000 Florida State or Washington, 2001 Oregon or Colorado, 2003 USC, 2004 Auburn, Boise State or Utah, 2006 Michigan or Boise State. The '04 Tigers probably have the biggest complaint in BCS history, and no one this year has much to complain about. The argument boils down to "we weren't lucky enough to be selected", hardly a sympathetic complaint. Each team had more than enough chances to make the title game.
  • The BCS has increased my interest in college football. Maybe it's because I'm a math geek or maybe it's because I like controversy, but discussing who the top two teams are is pretty fascinating. It's probably not as fair as a playoff, but if it wasn't for the BCS, we wouldn't be talking college football this morning. Further, ...
  • If the BCS never came about, here's what we'd be looking at:
      Rose Bowl: USC vs. OSU
      Sugar Bowl: LSU vs ???
      Orange Bowl: Oklahoma vs. ???
      Fiesta Bowl: ??? vs. ???
      Those ???s would be filled by at large teams, of course. Maybe we'd get Oklahoma against Georgia, LSU against Virginia Tech, and Hawaii facing Kansas. Who knows. But we wouldn't be any closer to crowning a college football champion before the BCS came about.

After showing my pro-BCS stance, let me now get to my biggest pet peeve with the BCS and the polls. No one really knows how teams are supposed to be ranked. This bothers me and perplexes me more than just about anything in sports. How can we have polls where there's no guidance on how to rank the teams? While most rankings are easy, on the edges you really need some guidance. The big question is the retrodictive vs. predictive distinction: we don't know what the rankings are supposed to be. Are the polls supposed to be designed so that the team ranked X is always a favorite in a neutral site over the team ranked X+1? Should the polls reflect who has accomplished the most to date? Should they reflect who has looked the best to date? Should they reflect which team we subjectively think is the best team in the nation? I've got no idea, and frankly, it's impossible to rank the teams in a meaningful way until you know what you're ranking them on.

Here are a few examples:

1. USC of two years ago is 8-0 and ranked #1 in the country. Reggie Bush, LenDale White and Matt Leinart suffer season ending injuries in the 8th game. Where would USC be ranked after that? Where should USC be ranked after that?

2. Same situation, except it's the last game of the regular season when they get injured. So USC is 11-0 and #1. Where would USC be ranked after that? Where should USC be ranked after that?

3. Tim Tebow is injured in the off-season, and misses the first three games next year. UF goes 0-3. Tebow comes back, and UF is unstoppable, and rolls through the SECE and wins the SEC. UF wins every game the rest of the way, and looks to be unbeatable. Where would UF be ranked after that? Where should UF be ranked after that?

The answer is we just don't know. We're not sure if the BCS Title Game should reward the two teams that have accomplished the most this year, or the best two teams right now. And what do we do about when a team's losses occur? Should a 10-1 team that lost its last game be ranked behind a 9-2 team that lost its first two games, assuming equivalent SOS? Once again, I'm just not sure. There's no guidance.

With that all being said, let me explain why the BCS got it right:

  • Hawaii. You can tell who follows college football by asking them what they think of Hawaii. No, a 12-0 record against terrible opponents does not impress me. Sagarin ranks Hawaii as the 16th best team in the country, and the Warriors have the 137th toughest strength of schedule. Sagarin's ratings are not subjective (Hawaii isn't dropped automatically just because they play in the WAC; Boise State last year ranked 6th, and Utah in 2004 ranked 4th) Hawaii just isn't that good. There are only 119 teams in Division 1, which means over 20 teams not in Division 1 had a tougher schedule than Hawaii. Hawaii went into overtime in games against San Jose State (#113 in Sagarin ratings) and Louisiana Tech (#107 in Sagarin ratings). Hawaii simply isn't a great team; they're not even a very good team. Being undefeated isn't impressive when you're playing against inferior competition.
    Suppose the Cowboys played the Patriots, Colts, Chargers, Steelers, Redskins, Dolphins and Rams, and went 6-1. If Team X played the Jets, Dolphins, Bengals, Raiders, 49ers, Rams and Falcons, and went 7-0, would you think that Team X was better than the Cowboys? You'd be correct in saying you don't know -- Team X, in fact, could be as good as the Patriots. But what if I said that Team X went into overtime against the Dolphins and Rams, and got a lucky break when they beat the Raiders? You'd probably feel a lot more confident in saying the Cowboys were better than Team X. Teams can play in non-BCS conferences and still be one of the top two teams in the country. But one of the top two teams in the country wouldn't narrowly escape victory against non-top-100 teams, twice. Hawaii almost lost at home to Washington this weekend, which is hardly an impressive statement. A 49-0 blowout might have given the Warriors an argument that Hawaii can play with the big boys; a controversial one score win does not.
  • USC. The Trojans underwhelmed this year, and only the biggest of USC homers can cry foul. An out-of-conference schedule of Nebraska (#63), Notre Dame (#87) and Idaho (#168) underwhelms. Washington, Washington State and Arizona had losing records. The Oregon loss wasn't bad, but the Stanford loss is staggering. I understand the argument that USC is healthy now -- but did you think Florida in my hypothetical Tebow example should be in the championship game? The Trojans ended the season winning four straight -- over Oregon State, Cal, Arizona State and UCLA. The two California teams both have .500 records, and UCLA had lost three of its last four before playing USC. Cal lost six of its last seven games. Neither of those wins are impressive. Arizona State and Oregon State are good teams, but is that really enough to lift up USC? The Trojans didn't play a great schedule, had one of the worst losses of the season, and had too much to climb at the end of the year. No sympathy here.
  • Virginia Tech had two really bad losses. They got absolutely destroyed in Baton Rouge, and a home loss to BC (#19 in the Sagarin ratings) is not impressive. Yes, the Hokies avenged that last loss, and had a nice run at the end of the season. But where's the signature win? Clemson? BC? If you're not going to beat a top 10 team, and you're going to lose two games, you don't deserve to be called National Champions.
  • Oklahoma got a lot of late praise, since the Sooners just destroyed the #1 team in the nation. But while Oklahoma has the signature win, a loss to 6-6 Colorado, a late loss to Texas Tech, and the 59th best schedule in the nation sink OU's case. Beating Missouri twice is impressive, although we don't know how good the Tigers really are. But getting into a dogfight against Iowa State? Losing in Boulder? You can make the USC-when-healthy argument for the Texas Tech loss, but it's no more convincing here. Oklahoma was ranked 9th three days ago, and I don't think they deserve to jump all the way to two. A very good team, but the Sooners' awful OOC schedule dooms them. Maybe if the Hurricanes were the Miami of old, OU would be in the National Championship game. But without that, a weak SOS and two losses make it hard for fans in Norman to complain.
  • Georgia has the best case of all the snubbed teams. The Bulldogs weren't ever given a fair chance since Georgia lost its division, but that isn't fair. Georgia's a better team than Tennessee, and how the SEC decides its tiebreakers shouldn't control how the BCS picks its teams. I think Georgia would have had a terrific chance against LSU, and then we'd be excited for a Georgia-Ohio State championship game. As it stands, Georgia may have been the hottest SEC team but they weren't the best. LSU was clearly a better team over the course of the year, and accomplished more. LSU had a slightly harder SOS, and was closer in both its losses. A 21-point loss in Knoxville is way worse than a triple overtime defeat at the hands of Arkansas or Kentucky. Georgia was hotter than LSU, and may be the better team. But LSU had the same record, was closer in its two defeats, had the tougher schedule, and won the conference. LSU's win over Virginia Tech was also more impressive than anything Georgia's done.
  • LSU and OSU have their black eyes, but consider what they've done, too. LSU wasn't losing after regulation in a single game this year. Yes, we know they lost in overtime, but in terms of deciding how good the Tigers actually are, that's important. College football could still have the rule that games tied after regulation are counted as ties; in which case, no one would argue against LSU. They've got the two best losses -- by far -- of any two loss team. They also have the toughest schedule of any two loss team. They won the toughest conference in the country. I'm not much of an LSU fan, and I think they've been over hyped by the media -- but they're the most accomplished of the two loss teams. Ohio State and Kansas are the only one loss teams, and I don't think anyone is arguing for Kansas these days. The Buckeyes are not a controversial selection except by Big 10 haters, but consider: Ohio State didn't lose to the Stanford of its conference (USC), or a .500 team (Oklahoma, Georgia), or get blown out by anyone (Virginia Tech). A two-loss Buckeyes squad wouldn't deserve to make the title game, but OSU did not have a bad loss like everyone else in college football. Except the Tigers.

I'm going to close here with one final list, courtesy of Doug. It's the Simple Rating System for college football, with two caveats. All wins by less than 7 points are considered seven point wins, and all losses by over 24 points are maxed out at twenty-four. Why? The SRS usually underrates teams that win close games, so the seven point cushion helps. And in college football, some teams are less "classy" than others and run up the score against inferior opponents. I think a 24-point cap on a victory is a better indicator of true strength, and does not reward teams that run up the score. Finally, note that all 1-AA teams are grouped together as a single "team." This hurts Michigan, for example, and therefore hurts OSU a little bit, too. Note who is on top of the list:

The rating column shows how many points each team is better than the average team, and the last column shows the strength of schedule adjustment. Note that Washington, at +8.0, had the most difficult schedule in college football this year.

  Team                       Record      Rate      SOS
  1. Florida                  9-  3      19.4      6.7
  2. WestVirginia            10-  2      18.2      2.8
  3. LouisianaState          11-  2      17.8      5.3
  4. SouthernCalifornia      10-  2      17.0      4.1
  5. Oklahoma                11-  2      16.6      1.1
  6. OhioState               11-  1      16.5     -0.1
  7. Georgia                 10-  2      16.3      5.8
  8. Oregon                   8-  4      16.2      6.4
  9. Missouri                11-  2      15.7      3.5
 10. VirginiaTech            11-  2      15.3      2.5
 11. ArizonaState            10-  2      15.2      4.9
 12. Cincinnati               9-  3      14.3      1.2
 13. SouthFlorida             9-  3      14.2      3.6
 14. Kansas                  11-  1      13.8     -2.7
 15. Clemson                  9-  3      12.4      1.3
 16. Tennessee                9-  4      11.6      6.1
 17. Auburn                   8-  4      11.5      5.5
 18. BrighamYoung            10-  2      10.7     -0.8
 19. Arkansas                 8-  4      10.2      2.2
 20. BostonCollege           10-  3      10.2      1.8
 21. Illinois                 9-  3      10.0      1.2
 22. OregonState              8-  4       9.8      6.8
 23. PennState                8-  4       9.8      0.8
 24. Kentucky                 7-  5       9.4      5.4
 25. Texas                    9-  3       9.0      0.7
 26. Connecticut              9-  3       8.9      0.6
 27. UCLA                     6-  6       8.2      7.6
 28. California               6-  6       8.1      6.2
 29. Hawaii                  12-  0       8.1     -7.1
 30. MichiganState            7-  5       7.9      1.9
 31. Alabama                  6-  6       7.9      4.5
 32. BoiseState              10-  2       7.9     -5.4
 33. Utah                     8-  4       7.7      0.9
 34. TexasTech                8-  4       7.5     -1.8
 35. SouthCarolina            6-  6       7.4      6.1
 36. Michigan                 8-  4       7.3      2.2
 37. Virginia                 9-  3       6.9      1.7
 38. CentralFlorida          10-  3       6.4     -4.3
 39. WakeForest               8-  4       6.4      1.2
 40. Rutgers                  7-  5       6.4      1.4
 41. Wisconsin                9-  3       6.2     -0.0
 42. Arizona                  5-  7       5.8      6.3
 43. AirForce                 9-  3       5.7     -3.2
 44. Troy                     8-  4       5.7     -1.7
 45. FloridaState             7-  5       5.6      4.3
 46. GeorgiaTech              7-  5       5.5      1.6
 47. Louisville               6-  6       5.5      3.9
 48. OklahomaState            6-  6       5.4      3.9
 49. TexasA&M                 7-  5       5.4      3.0
 50. Purdue                   7-  5       5.2     -0.6
 51. Maryland                 6-  6       4.8      3.0
 52. Washington               4-  9       4.7      8.0
 53. TexasChristian           7-  5       4.1     -1.5
 54. MississippiState         7-  5       4.1      4.0
 55. Vanderbilt               5-  7       3.2      4.4
 56. KansasState              5-  7       3.2      1.5
 57. Colorado                 6-  6       2.8      3.8
 58. Pittsburgh               5-  7       2.3      3.5
 59. Indiana                  7-  5       2.2     -1.0
 60. FresnoState              8-  4       2.2     -2.8
 61. WashingtonState          5-  7       1.7      5.6
 62. NewMexico                8-  4       1.3     -2.4
 63. Nebraska                 5-  7       1.2      5.6
 64. EastCarolina             7-  5       0.0     -2.0
 65. NorthCarolina            4-  8      -1.0      2.5
 66. Miami(Florida)           5-  7      -1.0      2.2
 67. BallState                7-  5      -1.0     -5.0
 68. Stanford                 4-  8      -1.1      6.5
 69. Mississippi              3-  9      -1.3      6.2
 70. Tulsa                    9-  4      -1.4     -4.7
 71. Houston                  8-  4      -1.9     -6.6
 72. Iowa                     6-  6      -2.4     -1.1
 73. SouthernMississippi      7-  5      -2.5     -5.9
 74. BowlingGreenState        8-  4      -2.6     -6.7
 75. Northwestern             6-  6      -2.6     -0.4
 76. Navy                     8-  4      -2.7     -6.0
 77. NorthCarolinaState       5-  7      -2.8      3.3
 78. FloridaAtlantic          7-  5      -3.1     -1.7
 79. Nevada                   6-  6      -3.2     -5.3
 80. Wyoming                  5-  7      -3.2      0.4
 81. CentralMichigan          8-  5      -3.3     -5.9
 82. WesternKentucky          7-  5      -4.2     -8.2
 83. NotreDame                3-  9      -4.6      5.3
 84. MiddleTennesseeState     5-  7      -4.8     -3.2
 85. ColoradoState            3-  9      -6.2      0.3
 86. SanDiegoState            4-  8      -6.4      2.2
 87. Louisiana-Monroe         6-  6      -6.7     -3.9
 88. WesternMichigan          5-  7      -6.7     -4.3
 89. IowaState                3-  9      -7.3      2.3
 90. Memphis                  7-  5      -7.7     -8.0
 91. LouisianaTech            5-  7      -7.9     -2.0
 92. SanJoseState             5-  7      -7.9     -2.6
 93. ArkansasState            5-  7      -8.2     -4.9
 94. Ohio                     6-  6      -8.2     -8.0
 95. Miami(Ohio)              6-  7      -8.3     -4.7
 96. Nevada-LasVegas          2- 10      -8.7      1.2
 97. Buffalo                  5-  7      -8.8     -6.1
 98. Duke                     1- 11      -9.6      4.1
 99. Texas-ElPaso             4-  8      -9.7     -5.3
100. Syracuse                 2- 10      -9.9      5.4
101. Marshall                 3-  9     -10.1     -1.8
102. UtahState                2- 10     -10.6     -1.4
103. Minnesota                1- 11     -10.7      1.0
104. EasternMichigan          4-  8     -11.0     -4.7
105. Toledo                   5-  7     -11.1     -5.3
106. Akron                    4-  8     -11.3     -4.1
107. Kent                     3-  9     -11.4     -6.0
108. Baylor                   3-  9     -11.5      2.3
109. NewMexicoState           4-  9     -11.9     -4.5
110. Louisiana-Lafayette      3-  9     -13.2     -4.0
111. Army                     3-  9     -13.7     -2.4
112. Temple                   4-  8     -13.8     -6.0
113. Tulane                   4-  8     -13.9     -6.2
114. Alabama-Birmingham       2- 10     -14.1     -2.5
115. Rice                     3-  9     -15.1     -6.2
116. NorthTexas               2- 10     -15.6     -3.5
117. FloridaInternational     1- 11     -15.7     -0.7
118. SouthernMethodist        1- 11     -15.8     -4.8
119. Idaho                    1- 11     -16.5     -3.2
120. 1AAOpponent              9- 71     -16.7      0.2
121. NorthernIllinois         2- 10     -17.3     -7.5

36 Comments | Posted in BCS, College

Two promises

Posted by Doug on October 2, 2007

Back before the college football season started, I mocked the human polls and devised an algorithm to mimic them. I still haven't gotten around to catching up with what that "poll" would look like for the 2007 season, but I promise that I will do that at some point before too long. (<--- Promise #1)

Even without running it, though, it does seem clear that my algorithm isn't going to be as accurate as I hoped. So here I am admitting I was wrong. My apologies to all those graduate assistant strength-and-conditioning coaches and newspaper sports page interns. They have indeed been giving their rankings a bit more thought than I was giving them credit for.

Promise #2 is to someday (within the next two weeks) do the programming for a new rating system that I'm about to tell you about. I'm hoping that putting the promise in writing will make me more likely to keep it. It starts with a comment that was recently added to one of my old rating system posts, and is similar to other comments on rating systems. I can't find it at the moment, but I'll paraphrase it:

Does this system take into account the strength of the team at the time? For example, if the Patriots suffer some injuries and end up 8-8, then the Jets, Chargers, and Bills should get credit for losing to a great team --- a team that truly was playing lights-out at the time --- rather than some generic 8-8 team.

I think arguments could be made both fer and agin' that mode of thinking, but I'm going to set them aside for now and focus on the question: assuming you do want to incorporate at-the-time strength of opponents into your rating system, how do you do it?

Measuring at-the-time strength of schedule instead of overall strength of schedule necessarily means that you are treating the Week 2 Patriots as a different team than the Week 14 Patriots. It's possible, I'd even say likely, that both of those teams are of similar strength, but we don't want to assume it. If you take this thinking to its extreme, then you'd have to assume that there is no team called the "Patriots." Rather, there are 16 Patriot teams, one for each week. There may be some correlation between their strengths, but if you really want to go all the way with the at-the-time SOS philosophy, you can't assume it. And I guess that leaves you making no strength of schedule adjustments at all.

OK, so we don't want to be that extreme. If we're to conclude anything at all about strength of a team's schedule, we have to make some sort of assumption that every team bears some resemblance to its incarnation of the previous week, and of the next week. Consider this:

Week 1:  Vikings over Falcons by 21
Week 2:  Jags over Falcons by 6
Week 3:  Panthers over Falcons by 7
Week 4:  Falcons over Texans by 10

If we assume the minimum amount of continuity between the possibly-different teams that took the field wearing Falcon jerseys --- that is, if we want to allow the possibility that the Falcons' strength is continuously in flux --- then we don't want to infer too much about the relative strengths of the Vikings and Texans by comparing how they did against the Falcons. Those were different Falcon teams, after all. The minimum amount of continuity would be one game, so let's compare Falcon opponents only if they played the Falcons in consecutive games. So I can compare the Vikes to the Jags via the Falcons, and I can compare the Panthers to the Texans via the Falcons, but I won't (directly) compare the Vikings to the Texans.

Over the years I've learned that the simple rating system can do just about anything you want if you just figure out how to redefine what a "game" is. So I propose to regard this data as follows:

The Vikings are 15 points better than the Jags
The Panthers are 1 point better than the Jags
The Panthers are 17 points better than the Texans

Those are my games. And likewise there was a "Falcons-Lions game," which the Lions won by 24 points (do you see why?), and a "Falcons-Titans game," which the Titans won by 3, and so on.

And then I'll run the simple rating system on this collection of games. As you can see, there will still be an implied connection between the Week 1 Falcons and the Week 3 Falcons, but it will be indirect. And the connection between the Week 1 Falcons and the Week 17 Falcons will be so indirect as to be practically meaningless.

You need not write in to tell me that this is a pointless academic exercise; I already know that. But pointless academic exercises are my schtick, so I'm going to roll with it. I'm under no illusion that this will provide a better rating system, but I do think that, by taking a look at the teams whose traditional simple rating are very different from what this rating shows, we might find out some interesting things that we didn't know before.

6 Comments | Posted in BCS, College

Every game counts

Posted by Doug on September 27, 2007

As everyone knows, there are lots of reasons to dislike the BCS. But today I'll tell you one reason to like it. Or at least one reason I like it. The fact that the computer ranking algorithms play a real role in the process means that, at least theoretically, every one of the dozens of games played each Saturday has the potential to affect your team's chances of making the title game.

As an example, let's take a look back at 2004, when Oklahoma, USC, and Auburn were all undefeated. You'll remember that USC demolished OU in the championship game while Auburn ended up playing a consolation game against Virginia Tech in the Sugar Bowl. In that particular case, Auburn probably wouldn't have ended up in the title game even if they had ranked higher in the computer polls, but the possibility certainly exists that this year (or any year), a few thousandths of a point on a few of the computer rankings could determine who plays in the big game. My personal margin-not-included ranking algorithm, which is very similar to at least one of the official BCS computer polls, shows the following pre-bowl rankings for that season.

  1. SouthernCalifornia         12-  0       22.53 
  2. Oklahoma                   12-  0       20.46 
  3. Auburn                     12-  0       19.75 

Auburn played a slightly weaker out-of-conference schedule than Oklahoma, and the Pac 10 was stronger than the SEC that year, so that's how Auburn ended up third. They were third in almost all the computer polls if I recall correctly. But the margin between Auburn and OU was close enough that changing the outcome of just a game here or there could flop them. The only SEC / Big 12 matchup of the regular season was a very close Texas win over Arkansas. Had Arkansas won it instead, we would have had this.

  1. SouthernCalifornia         12-  0       22.66 
  2. Auburn                     12-  0       21.54 
  3. Oklahoma                   12-  0       16.88

The point is: every single interconference game, especially those between two BCS conferences has the potential to make significant changes in the rankings.

That's pretty obvious. What's less obvious is that even intraconference games can make a difference. Let's flip the Arkansas/Texas result back, so that OU outranks Auburn again. Now, if you flip the results of the North Texas / Middle Tennessee State game and the Louisiana Tech / UTEP game, Auburn jumps OU again. Why? Because the Big 12 played three games against North Texas, winning all three. So where North Texas finishes in their conference is relevant to determining the overall strength of the Big 12, which is obviously is a key factor in determining how strong Oklahoma is. Likewise, SEC teams played a couple of games against La. Tech, so an extra win by them raises their stature just enough to prop the SEC up just enough for Auburn to slip ahead of the Sooners.

Once you've got that in mind, you begin to realize that you might have a rooting interest in lots of intra-conference games that you never thought you cared about.

If you're an Ohio State fan, you have to root for Oregon (who beat a Big 10 team) to beat Cal (who beat an SEC team) this weekend. If you're a West Virginia fan (who doesn't have any particular animosity for any of your conference-mates), you were happy about the South Florida win over Auburn and disappointed about the Louisville loss to Kentucky, obviously, but you were also not pleased about Mississippi State's win over Auburn. If you like West Virginia, in fact, you are now a big fan of Auburn and Kentucky in all their SEC games and you like Michigan State (who beat Pitt) in the Big 10 and Oregon State (who lost to Cincinnati) in the Pac 10.

So while it's very unlikely that the outcome of the Washington / Arizona State game will be the deciding factor in getting Oklahoma or Texas into the championship game instead of Ohio State or Wisconsin, games are always more fun to follow if you have a rooting interest. And whether you know it or not, you almost always do.

8 Comments | Posted in BCS, College

Algorithmicizing the human polls

Posted by Doug on August 24, 2007

I still have not finalized the details of my attempt to algorithmicize college football's human polls. Since this project is too silly to post on any day other than Friday, and since this is the last Friday before the season starts, I guess I'd better nail it down right here.

In the above-linked post, I laid out a rough draft of an algorithm for ranking college football teams that would match up with the human poll at the end of the year. I knew that that formula in that post probably wouldn't end up being the finished product, and was hoping to get some suggestions from the readership (that's you). As usual, I did get good suggestions. In particular, both JKL and Pat noted that there needs to be a mechanism for vaulting teams up in the rankings when they beat a team ranked ahead of them, especially early in the season. They're right.

So here is the new system:

STEP 1: Build the preseason rankings - this will be done just as described in the earlier post:

1a. First rank all the BCS conference schools

1a(i). put them in order of last year's final poll (including the "others receiving votes" part)

1a(ii). order the non-vote-receiving teams by their 2006 winning percentage, with ties broken by perceived conference superiority: SEC > Big 10 > Big 12 > Pac 10 > ACC > Big East (note: since Notre Dame was "ranked" at the end of 2006, there is no need to make a special rule for them. Should the need arise in future years (yeah, like this thing is going to survive past week 3, much less into future years), they will be treated as a Big 10 team.)

1b. rank the non-BCS teams, first using last year's final poll, then ranking the rest by record, ties broken alphabetically (A's first)

1c. put all the non-BCS teams behind all the BCS teams to create the preseason rankings.

STEP 2: weekly adjustments

2a. deal with the losers first

2a(i). teams that lose by 9 or fewer points to a team ranked higher drop 2 spots.
2a(ii). teams that lose by 10 or more points to a team ranked lower drop 10 spots.
2a(iii). all other losing teams drop 5 slots.
2a(iv). all losing teams drop an additional 5 slots if they lost their previous game as well.
2a(v). all ties broken by the previous week's rankings. [for example, if the #1 team loses by 3 points, they should drop to #6. Meanwhile, if the #4 team loses to the #2 team by 3 points, they should also drop to #6. In this case, the former #1 would be #6 and the former #4 would be #7.]

At this point all the losers have a ranking. We need only order the rest of the teams, then fill them in to the empty slots in order.

2b. ordering the non-losers. (All references to "teams" below refer only to the non-losing teams.)

2b(i). starting with the lowest-ranked (worst) team, we look at each team in turn. If they beat a top 25 team, then they leapfrog int((.5 - .02r_1)r_2) teams, where r_1 is the previous rank of the beaten team, r_2 is the previous rank of the winning team, and int() is the greatest integer function (i.e. round down).

That's it. I'd like to point out that, even though it took a fair amount of verbiage, this isn't as complicated as it seems. The basic idea is: drop the losers down, move up the big winners, and fill everyone else in in the same order as the previous week.

I honestly have no idea how this is going to work out. I hope I'll be able to keep up with it throughout the season. Here is the preseason poll:

1. Florida
2. Ohio State
3. LSU
4. USC
5. Wisconsin
6. Louisville
7. Auburn
8. Michigan
9. West Virginia
10. Oklahoma
11. Rutgers
12. Texas
13. Cal
14. Arkansas
15. Wake Forest
16. Virginia Tech
17. Notre Dame
18. Boston College
19. Oregon State
20. Tennessee
21. Penn State
22. Georgia
23. Nebraska
24. Texas A&M
25. Georgia Tech
26. South Carolina
27. Maryland
28. Texas Tech
29. Kentucky
30. South Florida
31. Missouri
32. Clemson
33. Cincinnati
34. Purdue
35. Kansas State
36. Oklahoma State
37. UCLA
38. Oregon
39. Arizona State
40. Florida State
41. Miami (FL)
42. Kansas
43. Washington State
44. Arizona
45. Pittsburgh
46. Alabama
47. Minnesota
48. Iowa
49. Indiana
50. Washington
51. Virginia
52. Ole Miss
53. Vanderbilt
54. Northwestern
55. Michigan State
56. Baylor
57. Iowa State
58. UConn
59. Syracuse
60. Mississippi State
61. NC State
62. North Carolina
63. Illinois
64. Colorado
65. Stanford
66. Duke
67. Boise
68. BYU
69. TCU
70. Hawaii
71. Houston
72. Central Michigan
73. Navy
74. San Jose State
75. Ohio
76. Southern Miss
77. Nevada
78. Troy
79. Tulsa
80. Utah
81. Western Michigan
82. East Carolina
83. Middle Tennessee
84. Northern Illinois
85. Rice
86. Arkansas State
87. Kent State
88. La-Lafayette
89. SMU
90. Wyoming
91. New Mexico
92. Akron
93. Ball State
94. Florida Atlantic
95. Marshall
96. Toledo
97. UTEP
98. Air Force
99. Bowling Green
100. Fresno State
101. Idaho
102. La-Monroe
103. New Mexico State
104. Tulane
105. UCF
106. Colorado State
107. Army
108. La Tech
109. North Texas
110. San Diego State
111. UAB
112. Buffalo
113. Memphis
114. Miami (OH)
115. UNLV
116. Eastern Michigan
117. Temple
118. Utah State
119. Florida International

18 Comments | Posted in BCS, College

Are you sick of college football’s national champion being decided by rote, unthinking, mechanical algorithms? I have the solution.

Posted by Doug on July 27, 2007

Get rid of the human polls.

As I've said before, "The BCS" has become one of those abstract entities, like "bureaucrats" or "the government", that essentially means "something I don't like." So many people dislike so many different things about the BCS that it's almost impossible to have a conversation about it. In my opinion, the funniest kind of anti-BCS rant is the one that rails against the computer rankings. Computers don't understand football! Computers can't weight the myriad strengths and weaknesses of each team!! A computer has never felt the raw intensity of a Saturday night SEC game!!! How can it possibly tell us whether one team is better than another?

Those are legitimate points. As it stands now, though, the alternative --- the human polls --- is even more rote, mechanical, and formulaic, and even less likely to have involved serious thought. In fact, I'm pretty sure that the human polls actually are computer algorithms, and the code looks something like this.

Rankings = LastYearsRankings
For i = 1 to NumberOfWeeks  {
  For j = 1 to NumberOfTeams  {
    if (Team j lost a close game in week i OR Team j lost to a better team in week i)
      drop team j four slots in the rankings
    else 
      drop team j nine slots in the rankings
    }
  move everyone who didn't lose up to fill in the gaps
  }  

I'm going to test this out in 2007 by seeing just how close this ridiculously naive system can get to mimicking the final human poll.

I'll start by taking last year's final poll*, and then filling in the unranked teams in order of their records, with ties broken by perceived strength of conference (SEC > Big 10 > Big 12 > Pac 10 > ACC > Big East). I'll define a "close game" as one decided by less than 10 points and a "better team" as one that was ranked higher (according to this system) at the time of the game.

* - In order to account for the perceived divide between the BCS conferences and the non-BCS conferences, I will rank all the BCS teams from top to bottom, then I will rank the non-BCS teams from top to bottom. Then, for the initial rankings, I will place all the BCS teams ahead of all the non-BCS teams. I think this is about right. The pollsters will allow a non-BCS team to get pretty high up in the rankings if they keep winning. But they will always choose a BCS team over a non-BCS team with an equal record.

Final note: I reserve the right to make changes to my algorithm until the season starts on August 30th, but the system will maintain the ridiculous naivety of the one I'm printing here. Feel free to add suggestions if you have them.

13 Comments | Posted in BCS, College, Rant

Why there is no college football playoff

Posted by Doug on January 8, 2007

Disclaimer: I have a profound lack of understanding about the relationships between and the incentives of the various power brokers in this smoke-filled room. So anything I say in this post is possibly misinformed. The following is just my own attempt to make sense of things. Please chime in to correct any misstatements I make.

All that said, here is a very interesting article from Yahoo! Sports about why there is no college football playoff. It's a long article and, as you would expect, the situation is pretty complicated. But here is what I took from it.

The Big 10 commissioner, Jim Delany, is the key figure. He doesn't care about college football in general; he only cares about the Big 10, as well he should. But apparently, he's powerful enough to essentially veto any potential playoff system that doesn't benefit the Big 10 as much as the current system does. And, because Delany is such a good negotiator, the current system is pretty sweet for the Big 10.

So where does all his power come from? Here is a quote from the article:

Delany declared last year that the Big Ten, Pac-10 and Rose Bowl would abandon its BCS partners if they took even the slightest step toward a playoff.

My first reaction is: don't let the door hit you on the way out.

On second thought, though, it's not clear that the meta-conference consisting of the ACC, Big12, SEC, and Big East would win this power struggle. Under this scenario, there might be some sort of playoff involving everyone except the Big 10 and Pac 10. Then there would be a Rose Bowl pitting the Big 10 and Pac 10 champions, or possibly even a playoff among more than two of the top teams from those conferences. It might look an awful lot like 2003, when USC and Michigan played in the Rose and LSU and Oklahoma played in the official championship game.

Now, suppose you're FOX or ABC and you're negotiating the contract for the 4-team or 8-team non-Rose playoff. You may have the #1 and #2 teams in the country in your playoff, but you may not. And even if you do, there is a decent chance that one or both of them would get eliminated before the championship, leaving the Rose Bowl looking nearly as legitimate as your title tilt. This season, what if LSU and Louisville were playing in your championiship game while USC and Ohio State were playing in the Rose? Not good. And the more grave concern would be the kind of scenario that would have unfolded if USC hadn't lost to UCLA this year: the Rose Bowl gets #1 and #2, while numbers 3, 5, 7, 8, 9, 10, 11, and 12 play in your playoff. That's a disaster.

Of course, it's also a potential disaster for whoever owns the rights to the Rose Bowl, which makes this a risky strategy by Delany. Success is cyclical and virtually all of the Big 10's and Pac 10's BCS success is attributable to just two schools. During the first few years of the BCS, the 10s Big and Pac were no more relevant than the modern-day Big East.

It seems to me that the real heart of the matter is the Pac 10. While the Big 10, Pac 10, and Rose Bowl together make a formidable alliance, the Big 10 on its own is powerless. So the question is: once the current Rose Bowl agreement expires, what's in it for the Pac 10? What incentive do they have to hang with Delany while the other five conferences back a dumptruck full of money into their driveway?

Overall, though, the Yahoo! article reinforces what I've always thought: a playoff is coming. Slowly, but it's coming. The current system is better than what we had ten years ago, but not as good as what we'll have ten years from now. I wish those tens were twos, but I'll live.

10 Comments | Posted in BCS, College

Maximum likelihood with home field and margin of victory

Posted by Doug on December 19, 2006

Before reading this entry, make sure you've read part I and part II in the maximum likelihood series.

How to incorporate home field into a maximum likelihood model

In the basic model, we are trying to maximize the product of all R_i / (R_i + R_j), where this factor represents a game in which team i beat team j. In order to build home field advantage into the model, we need one additional parameter. Let's call it h. Think of it as a multiplier that affect the home team's rating.

Let's look at the same simple "season" we looked at last time:

A beat B
B beat C
C beat A
A beat C

In the basic model, we chose ratings A, B, and C so as to maximize:

P = A/(A+B) * B/(B+C) * C/(A+C) * A/(A+C)

Now let's assume that the home teams in those games were A, C, C, and A. If h is a multiplier that alters the home team's rating, then A's probability of winning that first game isn't A/(A+B), it's hA/(hA+B). And so the quantity to be maximized is:

P = hA/(hA+B) * B/(B+hC) * hC/(A+hC) * hA/(hA+C)

Now instead of having three dials (A, B, and C) to twiddle, we have four dials: A, B, C, and h. But it's the same game: set them all so as to maximize P. Here are the home-field-included rankings through week 14:


TM Rating Record
======================
sdg 5.600 11- 2- 0
ind 4.326 10- 3- 0
chi 4.141 11- 2- 0
bal 3.769 10- 3- 0
nwe 2.451 9- 4- 0
nor 1.688 9- 4- 0
cin 1.678 8- 5- 0
jax 1.545 8- 5- 0
dal 1.322 8- 5- 0
den 1.278 7- 6- 0
nyj 1.216 7- 6- 0
nyg 1.197 7- 6- 0
ten 1.078 6- 7- 0
buf 0.981 6- 7- 0
kan 0.861 7- 6- 0
phi 0.775 7- 6- 0
atl 0.720 7- 6- 0
sea 0.719 8- 5- 0
mia 0.688 6- 7- 0
pit 0.679 6- 7- 0
car 0.550 6- 7- 0
min 0.474 6- 7- 0
cle 0.405 4- 9- 0
gnb 0.404 5- 8- 0
hou 0.364 4- 9- 0
was 0.324 4- 9- 0
stl 0.292 5- 8- 0
sfo 0.273 5- 8- 0
tam 0.247 3-10- 0
ari 0.180 4- 9- 0
oak 0.114 2-11- 0
det 0.088 2-11- 0

HFA = 1.556

If you take two averagish teams, say the Bills and Titans, and plug in the numbers, you get a 63% probability of Tennessee beating Buffalo in Nashville and a 59% probability of the Bills winning that same matchup in Buffalo. If, on the other hand, you have two mismatched teams like the Colts and Lions, then homefield means very little and you get 99% Colts in Indy and 97% Colts in Detroit.

How to incorporate margin of victory into a maximum likelihood model

Several months ago I told you about what I call the very simple rating system. That was a rating system that included only points scored and points allowed (and schedule). It doesn't directly consider wins and losses at all. However, by tinkering just a bit, you can turn it into a system that does consider wins and losses. In fact, you can turn it into a system that only considers wins and losses (and schedule). In doing so, you lose the theoretical elegance of the method, but you might get a system that "works" better. And most of the time that's what you want.

The situation here is similar. Maximum likelihood is a method that only considers wins and losses and doesn't consider margin of victory at all. But with a little tweaking you can turn it into a system that does exactly the opposite or you can set it somewhere in between. Just as is the case with the simple rating system, tweaking the system in this way strips it of some of its abstract beauty. But if it turns it into a tool that is better for the purpose you have in mind, then that's OK.

To incorporate margin of victory, all you have to do is (conceptually) pretend the game is 100 games and then decide based on the final score how you want to divvy up those hundred games between the two teams. Or, to put it another way, you want to award each team some percentage of a win and some percentage of a loss.

The easiest way to do it is to award the entire game to the winner. That's just the basic margin-not-included system we've been talking about.

The other extreme would be to award something like

(1/2) * ( 1 + (WinnerPoints - LoserPoints)/(WinnerPoints + LoserPoints) )

to the winner. So for example a 17-10 win would be worth about .63 wins, while a 37-30 win would be worth about .55 and a 37-10 win would be worth .79. A shutout would always be worth one full win. Using this system, the NFL ratings through week 14 look like this:


TM Rating Record
======================
chi 1.940 11- 2- 0
jax 1.777 8- 5- 0
sdg 1.589 11- 2- 0
bal 1.551 10- 3- 0
dal 1.420 8- 5- 0
cin 1.370 8- 5- 0
nwe 1.360 9- 4- 0
nyg 1.348 7- 6- 0
ind 1.305 10- 3- 0
nor 1.231 9- 4- 0
den 1.211 7- 6- 0
mia 1.074 6- 7- 0
phi 1.071 7- 6- 0
buf 1.057 6- 7- 0
ten 0.946 6- 7- 0
kan 0.937 7- 6- 0
pit 0.924 6- 7- 0
car 0.918 6- 7- 0
atl 0.898 7- 6- 0
nyj 0.861 7- 6- 0
sea 0.854 8- 5- 0
hou 0.848 4- 9- 0
min 0.801 6- 7- 0
was 0.738 4- 9- 0
cle 0.699 4- 9- 0
stl 0.639 5- 8- 0
ari 0.617 4- 9- 0
sfo 0.616 5- 8- 0
det 0.604 2-11- 0
gnb 0.589 5- 8- 0
oak 0.521 2-11- 0
tam 0.483 3-10- 0

HFA = 1.158

The "predictions" now look much more intuitive. Colts over Lions, instead of being a 95+% walkover for the Colts is now seen as a 71% chance of a Colts' win in Indy and a 65% chance of a Colts win in Detroit.

It makes sense that this change in the algorithm would result in much more conservative (and more realistic) predictions of future games. By treating a win as only a partial win, we're allowing the algorithm to use information that our brains are already using when we make a quick top-of-the-head guess. For instance, when the Colts beat Buffalo 17-16 in week 10, it goes down in the standings as one win for the Colts and one loss for the Bills, and the basic maximum likelihood model likewise counts it as a 100% win for the Colts. But the modified model instead sees it as a close game that really could have gone either way but that the Colts happened to win.

The model above treats that Colts win as a 52% win for Indy and a 48% win for Buffalo. Some people might think that goes a bit too far, that winning should count for something extra beyond the point margin. Those folks might use a split like this to the winner:

.6 + .4 * ( (WinnerPoints - LoserPoints)/(WinnerPoints + LoserPoints) )

This guarantees winners at least 60% of the win. Not surprisingly, it will have the effect of making the rankings look more like the standings (but still not as much as the original margin-not-included model):


TM Rating Record
======================
chi 2.169 11- 2- 0
sdg 1.905 11- 2- 0
bal 1.795 10- 3- 0
jax 1.755 8- 5- 0
ind 1.600 10- 3- 0
nwe 1.508 9- 4- 0
cin 1.424 8- 5- 0
dal 1.418 8- 5- 0
nyg 1.329 7- 6- 0
nor 1.323 9- 4- 0
den 1.229 7- 6- 0
buf 1.054 6- 7- 0
phi 1.039 7- 6- 0
mia 1.011 6- 7- 0
ten 0.983 6- 7- 0
kan 0.938 7- 6- 0
nyj 0.919 7- 6- 0
pit 0.897 6- 7- 0
atl 0.883 7- 6- 0
car 0.858 6- 7- 0
sea 0.850 8- 5- 0
hou 0.753 4- 9- 0
min 0.748 6- 7- 0
was 0.656 4- 9- 0
cle 0.649 4- 9- 0
stl 0.576 5- 8- 0
gnb 0.564 5- 8- 0
sfo 0.557 5- 8- 0
ari 0.516 4- 9- 0
det 0.461 2-11- 0
tam 0.441 3-10- 0
oak 0.431 2-11- 0

HFA = 1.204

9 Comments | Posted in BCS, Statgeekery

Maximum likelihood, part II

Posted by Doug on December 15, 2006

For reference, here is maximum likelihood, part I. This post won't make much sense unless you've read that one.

Remember that I likened the method of maximum likelihood to trying to twist a bunch of dials (one for each team) so that a particular quantity is as big as possible. If you're looking at a season of 1A college football, you've got 119 dials, the thing you're trying to maximize has about 800 parts to it, and each of the dials directly controls about 12 of those parts.

Suppose you're twiddling with the Florida dial. In that mess of 800 factors, you see (R_flo / (R_flo + R_vandy)). Turning up the Florida dial increases that piece. So turn it up. Likewise, cranking the Florida dial increases the (R_flo / (R_flo + R_arkansas)) bit, so you turn it up some more. But then you notice there's a (R_auburn / (R_auburn + R_flo)) piece in there. Turning up the Florida dial decreases this part. You could counteract that by turning up the Auburn dial, but you know you're going to have to pay a price for that eventually because of the (R_georgia / (R_auburn + R_georgia)) piece, among others.

The point is, there is a place which is "just right" for the Florida dial. They won a lot of games, many of them against good teams (this creates big denominators), so you want to turn their dial up. But you can't turn it up too much, or else it will turn down that Auburn/Florida piece, to the detriment of the entire product.

Now consider Ohio State's dial. Turn it up. Now turn it up some more. Now turn it up some more. Keep turning it up and, because the Buckeyes never lost a game, you'll never run into any problem. There's nothing stopping you from turning Ohio State's dial up to infinity. You can always make that product bigger by turning Ohio State's dial up. Their rating has to be infinite.

That's OK, you say. Ohio State was undefeated and should be ranked first, right? Right, but then note that the same thinking applies to Boise State. They must, in a sense, necessarily be tied with Ohio State with an infinite rating. Is that what we want? Maybe, and maybe not, but I'm pretty sure most people don't want a system that mandates that undefeated teams always rank at the top no matter what.

But the plot thickens. Michigan's only loss was to Ohio State. So the only way it hurts you to turn up Michigan's dial is because of this term: (R_osu / (R_osu + R_mich)). But if Ohio State's ranking is infinite, then you can turn up Michigan's dial without penalty. And since they won all the rest of their games, turning up the Michigan dial helps increase the product. So Michigan, it turns out, needs an infinite rating as well, though not quite as big of an infinite rating as Ohio State's [yes, I'm getting sloppy with the infinities here --- my goal is to give an impression of the way things work, not to be mathematically precise].

Now who else needs an infinite rating? Wisconsin, whose only loss was to Michigan. Once Michigan's dial is jacked up to a gazillion, it doesn't hurt you much to jack Wisconsin's up to a few million.

Rather than start talking about the technicalities of this infinity business, let's just summarize with this: the method of maximum likelihood, in its purest form, mandates that, no matter what the schedules look like, the top ranked teams must be those that have never lost, or have only lost to teams that have never lost, or have only lost to teams that have only lost to teams that have never lost, or ....

In many situations --- basketball, baseball, NFL --- this isn't generally a problem. For college football, it's a huge problem. It's certainly defensible to have Michigan ranked ahead of Florida. But even setting aside Boise State, I don't know too many people who think Wisconsin should be ranked ahead of Florida. Further, if you wanted to rank all 706 college football teams, then any undefeated Division III or NAIA team would have to rank ahead of Florida too.

In my opinion, maximum likelihood is one of the best rating systems around: it has a sound theoretical basis, is relatively easy to understand, and produces what most people consider to be sensible results in most cases. But all models break in some situations and this one unfortunately happens to break right when and where it's needed most: at the top of the standings of a typical college football season.

But there are some ways to fix it.

One way is simply to count a win as a 99% win and 1% loss. How do you do that? Well, the easiest way to think about it is to pretend that every game is 100 games, 99 of which were won by the winner and one of which was won by the loser. Now Ohio State isn't 12-0; they're 1188-12. But the point is that they are now in the denominator of a few terms for which they are not also in the numerator. So their rating won't be infinite. If you do this with the pre-bowl 2006 college football data, you knock Wisconsin down to #9.

This practicality, however, is gained at the expense of elegance. In particular, why 99%? Why not count a win as 94% of a win, or 63%, or 99.99%? The higher that number is, the more your rating system will depend on wins and losses. The lower it is, the more it will depend on strength of schedule. As soon as it gets below 94%, for example, Florida starts to rank ahead of Ohio State. [Astute observers will at this point suggest varying that percentage according to the margin of victory: a 1-point win could count as 60% of a win, for example, while a 28-point win could count as 99% of a win. This indeed can be done --- and I'll do it in a future post --- but for now I'm playing by BCS rules: only Ws and Ls.]

An arbitrary parameter just jars my sensibilities. It might "work" (depending on what you mean by "work"), but it ruins the nice clean description of this method. I have seen a couple of academic papers that employ more complicated fixes, but they also have a parameter and no objective basis for determining what that parameter ought to be.

What I prefer is the simple fix proposed by David Mease. He simply introduces a dummy team and gives every team a win and a loss against that dummy team. Problem solved; now no team is undefeated and no team will have an infinite rating. If you find this a cludgy or arbitrary solution that ruins the theoretical beauty of the method, then you can read Mease's paper, where he explains how the introduction of the dummy team can serve as a set of Bayesian priors. If you're into that kind of thing.

Mease's ratings are among my favorites and, if I were running the BCS, they'd be a part of it. Now back to Peter Wolfe, whose ratings are included in the BCS and who uses something he describes as a maximum likelihood method. He does not specify exactly how he fixes the infinite rating problem. I keep meaning to email and ask him, but for some reason I only remember to do so every year around early December, and I figure he's probably got enough emails to deal with in early December.

I have tried putting in a dummy team. I've tried counting wins as P percent wins for various values of P. But I can't replicate the order of Wolfe's rankings. That might have to do with the fact that Wolfe ranks all 706 college football teams, whereas I'm only ranking the D1 teams (with an additional "generic 1AA team" included to soak up the games against 1AA teams.). Or he might have some elegant fix that I'm not aware of. Maybe in February or March I'll remember to email him and ask.

6 Comments | Posted in BCS, Statgeekery

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