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Friday, December 31, 2010

This Season's OWA Rankings

Earlier this month I laid out the logic of the One Win Away approach to the college football post-season. Tournaments are great for giving every deserving team a chance, but tournaments can weaken the regular season by admitting undeserving teams. The One Win Away approach is the perfect balance - only deserving teams are admitted into the season-ending tournament. Deserving teams are those that, if they were to beat the top-ranked team in a head-to-head, would then be ranked higher than that team - e.g. if Oregon beat Auburn, Oregon would then be ranked higher than Auburn. Therefore, by deduction, the team that wins the OWA tournament is also the team that had the strongest overall season. With the OWA approach, the size of the field will vary from year to year depending on the number of deserving teams, but there will typically be between 2 and 6 entrants.

I also suggested that the OWA field be selected using the BPR. Below is an analysis of this year's results and the OWA participants. The left column is the BPR rating, the right column is the OWA rating - the rating if the team were to beat Auburn. To qualify, a team's OWA rating must be higher than Auburn's OWA- rating in parentheses (Auburn's rating if it were to lose an additional game). Four teams would make the field this season - Auburn, Oregon, TCU, and Stanford. We would then have a 4 team tournament, with Auburn getting Stanford and Oregon getting TCU is the semi-finals. The WAC and Big 10 one loss teams might feel a little peeved for getting left out, but even with a win over Auburn they would still have faced a much softer schedule and have the same number of losses - admitting them into the OWA field would erase that.

CFBTN in the Seattle Times

Its a little late now that the game is over, but check out Bob Condotta's piece in the Seattle Times. Definitely a different game last night than Huskies vs. Huskers I.

Wednesday, December 22, 2010

Testing Matchup Myth #2: the Rivalry

Myth #2: You can throw out the records for a rivalry game

Beck to Harline, 2006
BYU beats Utah 33-31
Most college football fans and experts seem to accept at face value the notion that the outcome of a rivalry game is more random than other games - you can throw out the records. Why might this be? First, to be rivals the programs must be on relatively equal footing. Therefore, the gap in talent on the sidelines is generally not as large as the gap in records between the two teams. For example, Auburn may have had the better rank and record going in to the 2010 Iron Bowl but no one doubted that Alabama had as much physical talent as Auburn. 

Second, the underdog in a rivalry game is not going to be intimidated. Like I said before, the two programs have a lot in common. The two teams know each other intimately. The opposing players and coaches are humans, not ubermensch in fancy uniforms. And every rivalry highlights upsets from past seasons that coaches can draw on to inspire their team.

On the other hand, rivalries seem to erase the one potential advantage underdogs have. A team can only circle so many games on its schedule. Bad teams circle games against good teams; good teams circles games against better teams. But better teams will circle a game against a bad team if that team is a rival. The underdog can pull off the upset if they are preparing for the super bowl but their opponent is just preparing for another game, but both teams should be looking forward to rivalry games. 

Hall to Collie on 4th and 18, 2007
BYU beats Utah 17-10
What do the numbers say? I've picked 36 rivalry games, games with names like the Red River Shootout and the Duel in the Desert, the Apple Cup and Egg Bowl, the Backyard Brawl, Bedlam, Clean, Old-Fashioned Hate, the Civil War, the Holy War, the Game and the Big Game. These 36 pairings have played 1052 times since 1950. I have established expected results using scores from the rest of the season - the method I have used is well-tested and the results relatively reliable.

In these rivalry games, favorites have won 73% of the time; they have won 98% of games when favored by 21 or more, 81% when favored by 7 to 21, and 54% when favored by less than 7. This last result is notable, because in all 13,800 or so games since 1950, teams favored by less than 7 points have won 60% of the time. In all, underdogs have won about 25 more games (of 1,052) than expected.

Hall to George in overtime, 2009
BYU beats Utah 26-23
On average, underdogs do about 3/4 of a point better than expected, but almost 2 points better when they are expected to lose by less than 7. To offset that, they do 1.5 points worse on average when 21 point dogs or more. I would guess this is because players find it easier to keep the motor running when blowing out a rivalry than in a typical blowout.

The two charts below show the performance of teams in rivalry games compared to all games by the odds/expected score margin. The first chart, the x-axis (moving right to left) is the odds of teams winning and the y-axis (moving up and down) is the winning percentage of teams with those odds. With all games, you see that as the odds of winning increase, the winning percentage increases in a straight line. In rivalry games the relationship isn't exactly linear. When one team is favored by a lot of points, the results are as expected (that 1.5 points worse than average for the underdog doesn't dramatically affect their odds of winning when they are 30 point dogs). But when the odds are tight, the underdogs win more games than expected and, conversely, favorites lose more games than expected. 

In the second chart, the x-axis is the expected score margin and the y-axis is the difference between the actual margin and the expected margin. Consistent with the first chart, slight underdogs outperformed expectations, but big underdogs underperformed expectations.

Can we throw out records in rivalry games? Of course not. Better teams still win the majority of the time, and heavy favorites almost always win. But when the teams are close, the results are more random than we would otherwise expect.

Tuesday, December 21, 2010

Testing Matchup Myth #1: the Rematch

Myth #1: It's hard to beat the same team twice in one season
Myth #2: You can throw out the records for a rivalry game

In this first edition of the two part series, I will be taking on myth #1.

Billy Sims and the Sooners would
get revenge and redemption
The principal idea seems to be that the winner of the first game has less to prove in round 2, is overconfident entering the game, and therefore does not prepare as well or play as hard. The game 1 loser is looking for revenge or redemption.

In modern-era college football, teams play a second time in a bowl game or conference championship game. This is important for two reasons: first, it means that the teams are relatively evenly matched; second, it means that there is a whole new set of motivational variables (e.g. if the team is happy or disappointed to be in that particular bowl game) that will dilute the importance of seeking revenge or redemption for the loser.

There is a second countervailing logic: the winner of the first game already divined a game plan that wins. The loser will need to reevaluate its game plan, and faces a degree of uncertainty that the game plan will be effective. In other words, if the two teams are otherwise evenly matched, the team that won the first game has a better chance of winning the second game precisely because it won the first game.

The Choke at Doak: 31-3 to 31-31; The 5th quarter
in the French Quarter was no better for Florida
So, let's look at the numbers. Since 1950, there have been 49 rematches in college football. (Florida State tied in game 1 in 1994 - the infamous Choke at Doak.) The average score in game 1 has been 29.5-16.4, and in game 2, 31.0-17.7. Home teams were 31-16-1 in game 1. Most game 2s were played on neutral fields; home teams were only 4-6.

Game 1 winners were 29-18 in second games (62%). Simplistically, 62% is less than 100%, so game 1 losers did better in game 2, but 62% is also more than 50%, so game 1 winners were still more likely to win game 2.

Thinking about this logically, the team that won the first game was probably the better team, and so we would expect them to win the second game more often than not. Based on their performance throughout the season, we would have expected game 1 winners to win 61% of game 2s. In reality, they won 62%. In other words, game 1 winners improved their chances of winning the rematch by 1 percentage point.

On average, game 1 winners won the rematch 26.4 to 22.5. We would have expected game 1 winners to win 26.6 to 22.0 on average. That means game 1 losers outplayed game 2 expectations by .79 points. Based on game 2 scores and a pythagorean-style win/loss adjustment, game 1 losers should have won 45% of game 2s, but they only won 38%. Game 2 losers played slightly better by the scoreboard, but they were unlucky when it came to actually winning games.

In conclusion, it is not hard to beat a team twice in the same season - winning or losing game 1 has no effect on winning or losing game 2. But it is hard to blow a team out twice in the same season. So Nebraska/Washington Part II might be closer than 55-21, but don't expect Washington to pull off the upset just because they lost the first time around.

Friday, December 17, 2010

One Win Away: The Perfect Compromise between Tournament and BCS

Should we BCS or should we Tournament? That is the question.

Beyond the Senator, the Presidents of universities and one large country, the billionaire NBA owner, the anti-trust lawsuit, the books and articles, what we really have are two competing logics. The debate is heated precisely because both sides are (mostly) right.

The BCS Supporters are Right
Tournaments, especially large tournaments, make the regular season less important. Look at it this way: when the selection show ends, the typical team in college basketball's NCAA tournament has a 1.6% chance of winning a national championship; the best team has a 20-25% chance. This means that, over the course of the tournament, the best team (if it wins) improves its chances from 25% to 100% over six games, an average of 15% per game. That best team entered the season with a 15% chance of winning the national championship based on talent alone. Over the course of a 30 game regular season it improves its chances by 10%, or about .33% per game. (With a tournament invite almost guaranteed, its chances improve as it earns a better seed). A typical team improves its chances from, say, .1% to 1.6% over 30 games, or .05% per game. I don’t think many coaches are going to motivate their guys by emphasizing that today they can win 1/300th, or 1/2000th, of a national championship. And the fans don’t get that excited about it either. They wait until March, when the games are 45 times (for the best team) or several thousand times (for a typical team) more important.*

And college basketball is not the worst case of meaningless regular season games. The best pro baseball teams have a 35% chance of taking home a World Series ring when the playoffs start and a 10% chance at the beginning of the season. That means each game, even for the best team, is worth about 1/663rd of a World Series title – and the most important thing they do in each regular season game is avoid season-ending injury. NBA regular season games are worth 1/280th of a world championship for the best team, and the best NFL team looks to earn 1/92nd of a Super Bowl in each regular season game.

In college football, the best team can earn 2.5% or 1/40th of a national championship per regular season game on average. Even if other leagues only played 12 regular season games, college football would still have the most important games. Literally, every game counts.

93-81 does not a champion make
Unimportant regular season games are a problem for a couple reasons. First, fans and players don’t care as much. Second, and more pertinent to this discussion, the championship poorly reflects a team's performance over the course of the season. That, to me, is a serious problem. The '87 Twins were actually outscored in their run to an 85-77 regular season record. They would have finished 5th in the AL East, but they won their pennant and the World Series. The definition of a champion is subjective, but if you are happy putting a ring on the '87 Twins because they won 8 of 12 games after being significantly outplayed by several teams over a 162 game season, you're crazy. I support Cinderellas, but a real Cinderella goes to work from day one, not moments before midnight.

Tournament Supporters are Right
With a 64, or 65, or 68 team tournament, everyone has a shot at winning the national championship. That regular season game may only be worth 1/2000th of a national championship, but for Auburn and Utah in 2004, Boise State in 2006 and 2009, and TCU this year, every regular season game was worthless. I would rather crown the '87 Twins than completely dismiss half of a league from consideration.

This is not a touchdown
I was there when Kellen Moore led Boise State for a last minute score and win against Virginia Tech. Boise fans felt like they were a step closer to a national championship. I was not there when Brotzman missed a couple of field goals against Nevada, but I’m sure Boise fans felt like their national title hopes took a huge step back. In reality, the two games had the same effect on Boise State’s claim on a national championship: no effect whatsoever. As far as the race for the national championship is concerned, it never happened. An undefeated Boise team would have been passed over for a spot in the title game just the same as a two loss Boise team.

So, the solution is not as simple as a single national championship game or a tournament. You can leave out the ’04 Auburns and '08 Utahs, or you can crown the ’87 Twins, ’09 Fresno States, '85 Villanovas and ’95 Rockets.Good news? I have found a way to screen out the '87 Twins while letting in the '04 Auburns.

The One Win Away Approach 
Tournament logic asserts that because team A beat team B in a tournament game, team A is a more deserving champion. But that logic ignores a season of previous results. Georgetown beat Villanova twice during the season. A few days before the NCAA tournament, Georgetown won the Big East tournament and Villanova was eliminated in the semi-finals. Villanova (25-10), Georgetown (35-3); Georgetown won 2 of 3 head-to-head matchups. Villanova wasn't the better team and it didn't have the better season, but Villanova was two points better than Georgetown for 48 minutes (.042 points/minute), so they are your national champs.

In the One Win Away approach, Villanova isn't invited to dance. An invitation is offered, instead, only to those teams that are One Win Away. One Win Away generally means that if team B beat team A, we would then say that team B had the better season. Using the One Win Away Approach, we start by inviting the #1 team in the country. We then invite only those teams that, if they were to beat the #1 team, could then claim to have had a stronger season then the team they just beat**. In a typical college football season, you would have between 3 and 6 teams that meet that criterion. We would also invite any undefeated teams. The invitees would then be organized in an 8 team tournament. If there are fewer than 8 teams with invitations, the top seeds get byes.

By inviting only One Win Away teams to our tournament, it logically follows that the team that wins the tournament is also the team that has had the strongest overall season. It is, therefore, the perfect compromise.

What would a One Win Away tournament look like? In 2004, USC, Oklahoma and Auburn would be the top 3 seeds. California, Utah and Texas would also get an invite. Louisville would probably be left to watch from the comfort of their own homes, already having 1 loss and a significantly weaker schedule than the top teams. USC and Oklahoma would get byes, Auburn would play Texas and California would play Utah. The winners would get Oklahoma and USC, respectively, in the semi-finals.

Why it works: Every team in the country has a shot. We get a tournament, and the winner of the tournament will also be the team that has had the most complete season-when team A beats team B, that really does mean it is the more deserving champion. This would make the regular season slightly less important for those two teams that control their own destiny, but it would be infinitely more important for everyone else - overall, regular season college football games would be more, not less, influential in awarding the national championship.

Why it might not work: We need some way of finding the “One Win Away” teams. This is relatively easy to find using the BPR, but rankings are, inherently, somewhat subjective – especially rankings that must account for hypothetical wins. Also, the “One Win Away” approach requires a flexible postseason which makes planning and marketing much more difficult. A lot of rich and powerful people are deeply invested financially, emotionally, and intellectual in the existing system.

The "One Win Away" approach is, at least logically, the perfect compromise between a single national championship game and a tournament. Unfortunately, I have never known the sports world to be motivated by logic.

* These are, admittedly, back of the envelope calculations, but the logic is sound and the estimates lean towards the conservative.
** This does not mean they would, themselves, become the #1 team in the country, but they would, at least, be One Win Away from the new #1.

Tuesday, December 14, 2010

The Best Possible Ranking

The Best Possible Ranking ranks teams exclusively on the teams they have faced, where they have faced them, and the number of wins and losses. Essentially, a team's record is compared against the expected records of thousands of computer simulated teams. (Click here for a more in-depth explanation).

This Guy Never Got a Heisman Invite?

Who am I?

This season, I will top 3,000 yards passing on 350 attempts. I have already accounted for 40 touchdowns, 20 passing and 20 rushing. I am 16 rushing yards short of 1,200, and no team in college football won more regular season games than my team. 

Before this season is over, I will have throw for more than 10,000 yards in my career. I have accounted for 120 total TDs while throwing only 33 interceptions on 1,238 attempts. I've rushed for 1,000 yards and thrown for 2,000 for three straight seasons, putting me in pretty elite company, and I'm closing in on 2.5 rushing miles (4,090 yards to date). And the program has dramatically improved in my 4 years, reaching new heights in my senior season.

Through it all, I've kept my nose clean. 

But if you don't know who I am, don't worry. Even my own fans don't always recognize me.

Sunday, December 5, 2010

The Best Possible Ranking

The Best Possible Ranking ranks teams exclusively on the teams they have faced, where they have faced them, and the number of wins and losses. Essentially, a team's record is compared against the expected records of thousands of computer simulated teams. (Click here for a more in-depth explanation).