Love it or hate it, the BCS formula has proven its worth as a marketing tool to develop weekly interest in the top college football teams. Expanding the playoff from the current 2 teams to much over 4 teams risks reducing the BCS formula's marketing value to that of NCAA basketball's RPI. This is a very strong argument for maintaining the BCS formula for the proposed system and keeping the field of teams small. As the formula is not going anywhere anytime soon an analysis of the formula is in order.
Critique of the BCS Formula
As a formula to determine the average ranking the BCS formula is not that bad. The polls have enough samples to mitigate against outliers and the computer average mitigates against them by throwing out the highest and lowest values.
Using the points awarded instead of the rankings of the polls significantly increases the accuracy of the resulting average. One improvement that could be made is to use the raw data of the computers as well. Each computer ranking used has an underlying raw score that is analogous to the total points of the polls. By linearly scaling each so that the #2 team has a value of 0.96 and the #25 team a value of 0.04 the precision of the computer ranking average can be significantly increased.
While slight improvements may be suggested, the BCS formula's algorithm is simple and effective.
Critique of the BCS Sampling Methods
One of the primary issues with the formula is its sampling methods. It relies on two polls. The Coaches poll has long been charged with voter prejudice and partisan voting blocks among the coaches who are too focused on their own teams to really consider how the other teams rank. The Harris Poll involves voters who admittedly don't even watch all of the top 25 teams play a game.
The computers used are in the middle of the pack. Several other computer methods exist that are significantly better but are excluded because they use margin of victory. This is despite evidence that margin of victory is the best single NCAA statistic at indicating the winners of bowl games. The BCS computers are too dependent on each teams win-loss records. This is done intentionally to avoid forcing teams to run up the score, which is seen as unsportsmanlike by many.
In the end the historical bias of the voters and the dependence of the computers on each team's record are opposed. I believe they are balanced fairly well but there is plenty of room for disagreement.
Consensus implied by the gaps in the BCS standings
Massey's ranking comparison indicates the standard deviation of the rankings for teams in the top 5 runs about 2. This value increases the further down the standings one looks. Usually only the top is of national interest.
A difference in BCS standings can be multiplied by 25 to give the corresponding across the board ranking difference it represents. Assuming the voters opinions of the value of each team are normally distributed, the standard deviation of the difference would be the square root of 2 times the standard deviation of the rankings. Dividing the difference by the standard deviation of the difference produces a z-score. This can be used to estimate the probability an individual voter will agree with the results, which I will refer to as consensus.
A difference of 0.0181, the difference between Florida and Texas in the final 2008 BCS standings, represents an average ranking difference of 0.4525, less than the descritization error, and represents a consensus of 56.4%. A difference of 0.0600 represents a consensus of 70.2%. This is more agreement than the 2/3 majority needed to pass an amendment to the US constitution.
These values are only valid near the top 5. At a lower ranking the standard deviation increases so the consensus would be lower for the same difference.
Critique of how the BCS formula is applied
Another other issue with the BCS formula is how it is applied. The current system only allows for two teams, so the formula is used to decide between the #2 and #3 team regardless of their difference in the standings.
Rather than use the BCS formula to separate teams at a given ranking it would be much better to separate teams at a given gap in the standings as this would be supported by the claim that the gap indicated a strong consensus agreed with the cutoff.
Using a gap also increases the credibility of the system. It would be significantly more difficult for a few voters, or even a block of voters, to manipulate a large gap than the order of two closely ranked teams.
Conclusion
The proposed championship system keeps the number of eligible teams low enough to allow the BCS formula to maintain its value as a marketing tool and uses the formula to attain a more credible cutoff while increasing the integrity of the formula itself.
Friday, January 16
Thursday, January 15
Details, details, details...
While a new idea can be presented with ease, it is impossible to address all the issues that can possibly arise. As with any system a number of foreseeable issues can arise. I will start with the biggest logistical challenge to the system.
Wild Card Game details:
The primary purpose of the wild card game is to maintain 10-11 teams in the BCS so the pool of teams for the remaining bowls is consistent regardless of the playoff format each year calls for.
2005 is the only year since 2004 that would not have resulted in the use of a Wild Card Game. The adjustments for one team or more than 9 teams would not have been needed for any year over this time period.
The logistics of hosting this game in a traditional BCS venue are very problematic, as it would basically be a double header with a traditional BCS bowl. Cities could bid on hosting these games, with the bids representing a place in line to host the game rather than the chance of having it a specific year. This would open up college football’s championship structure to venues beyond the four traditional sites.
With the month’s notice of cancellation the process would allow it may even be possible to expand the planned half-time show into an attraction of its own. A choreographed concert could have a large appeal to those outside the target audience of a wild card game and could recoup some of the costs of reserving the venue and hiring contractors to produce the game and prepare the performers.
BCS Bowl selection:
1) Teams are placed in the Bowl Championship System by the above procedures.
2) All remaining BCS conference champion tie-ins are assigned to their respective bowls.
3) All BCS bowls losing a team to the championship system and not selected to be a semifinal would make selections from the available teams in order of the seed lost.
4-A) All remaining selections would be made in order from the BCS bowl with the most distant Bowl Championship System participation to the most recent.
4-B) If two BCS bowls participated in the Bowl Championship System in the same year the bowls involved will alternate having the first selection as the need arises starting with the bowl that had the lower seeded host team the year of participation.
When all undefeated teams have a chance at the title there would be significantly less pressures to give less established conferences a seat in a premier bowl. The BCS bowls would have more flexibility to abandon the current qualification limits with this system. Allowing the bowls to be flexible with their invitations makes the system able to adjust in a more timely fashion if it is established that the conference strengths warrant it.
If the current qualifications and at large eligibility are maintained they should be changed to apply the 2 teams per conference limit to selections made after step 2.
2007 was one Hawaii loss away from showing that it might be prudent to lift the 2 team restriction for a third team from a conference in the top 8 of the BCS standings with no second team from any conference ahead of them after all conference champions in the top 16 have been selected.
Play-in Game details:
Hosting schools for play-in games may be required to use a stadium of their choice meeting a size requirement and make a specified number of tickets available to the visiting team.
Each year the number of games their locations and potential match ups, based solely on who wins each game, would be set once the final BCS standings are available. The venue for the play in games would be the only significant logistical issue, with two weeks to resolve any issues. If the home team can’t resolve the issues they would forfeit the game.
The number of teams participating in the BCS games would be 10 or 11 for all scenarios except 8 teams. This leaves a pool of teams for the other bowls that does not change systematically from one year to the next. The case of 8 teams could be handled by taking an existing first day bowl game and making it a neutral site game for the play-in game between the #4 and #5 seeds.
Problem Cases:
One problem case is when one team is a solid number one and three teams are nearly tied for the #2 spot with no undefeated teams, as was the case in 2001. This would leave only one team eligible. Another case would be like this but with a low ranked undefeated team. This case runs the risk of a close upset in the National Championship Game and a blowout between the #2 and #3 team in a BCS Bowl, leaving doubt as to the champion.
It is hard to imagine an undefeated team ending the season by beating two top 5 teams and not being the consensus #1. Both of these cases can then be addressed with the following rule:
If the base criteria only generate one team, or create a structure where a team below #4 in the BCS ranking would not play a semifinal game, the second gap in the ranking average of 1.5 would be used.
Another problem case is if the number of teams exceeds 8, which can be addressed by this rule:
If the base criteria generates more than 8 teams, eliminate all teams that did not have the highest conference record in their conference, excluding championship games. If more than 8 teams still remain, look for a gap in the rankings among the remaining teams.
The only remaining way this championship system could fail is if 9 teams ended the regular season undefeated, an extremely unlikely event.
#1 with no tie-in:
Situations where a #1 or #2 seed has no conference tie-in needs to be addressed or all teams should have a tie in defined for this purpose. For this purpose, and independently of any automatic qualification process, the Big East could be restored to the Orange Bowl. The MWC and WAC would fit geographical with the Fiesta Bowl. C-USA, the MAC and the Sun Belt Conference would fit best with the Sugar Bowl.
Incentives to Compete, strength of the regular season.
A big reason playoffs are resisted is that they could reduce the value of the regular season. Allowing all undefeated teams runs the risk of teams reducing the strength of schedule.
The games early in the season are important to climb into the top of the standings. Late losses have demonstrated a devastating impact on a team’s position near the top. Only one team since 2004, LSU 2007, would have qualified for the championship structure with two losses. Usually enough undefeated and one loss teams abound to make a second loss be the end of the story.
The undefeated teams are in by the first criterion. The one loss teams would need to build enough consensus among the BCS components to avoid being behind the first gap in the standings. A strong out of conference schedule could go a long way to this end. For these teams the cut off actually eases the system from the need to get into the top 2 as more than 2 could get in, slightly reducing the risk of a loss.
Utah earned 4.5 million more than normal in its conference revenue sharing package for their Sugar Bowl appearance. They earned 0.8 million for their trip to Michigan. Unless a team has a 2 out of 11 chance of going undefeated in their conference a team is better off getting the guarantees payout of playing a big name team. Plus, they have an opportunity to get noticed with a win.
Going undefeated in any conference is difficult. If you are running the table regularly in a smaller conference a bigger conference will eventually pick you up, reducing your chances of going undefeated. Utah and Boise State are the only teams without an automatic qualification for their conference to finish the regular season undefeated at least twice in the last decade. Few question their out of conference scheduling practice.
Wild Card Game details:
The primary purpose of the wild card game is to maintain 10-11 teams in the BCS so the pool of teams for the remaining bowls is consistent regardless of the playoff format each year calls for.
2005 is the only year since 2004 that would not have resulted in the use of a Wild Card Game. The adjustments for one team or more than 9 teams would not have been needed for any year over this time period.
The logistics of hosting this game in a traditional BCS venue are very problematic, as it would basically be a double header with a traditional BCS bowl. Cities could bid on hosting these games, with the bids representing a place in line to host the game rather than the chance of having it a specific year. This would open up college football’s championship structure to venues beyond the four traditional sites.
With the month’s notice of cancellation the process would allow it may even be possible to expand the planned half-time show into an attraction of its own. A choreographed concert could have a large appeal to those outside the target audience of a wild card game and could recoup some of the costs of reserving the venue and hiring contractors to produce the game and prepare the performers.
BCS Bowl selection:
1) Teams are placed in the Bowl Championship System by the above procedures.
2) All remaining BCS conference champion tie-ins are assigned to their respective bowls.
3) All BCS bowls losing a team to the championship system and not selected to be a semifinal would make selections from the available teams in order of the seed lost.
4-A) All remaining selections would be made in order from the BCS bowl with the most distant Bowl Championship System participation to the most recent.
4-B) If two BCS bowls participated in the Bowl Championship System in the same year the bowls involved will alternate having the first selection as the need arises starting with the bowl that had the lower seeded host team the year of participation.
When all undefeated teams have a chance at the title there would be significantly less pressures to give less established conferences a seat in a premier bowl. The BCS bowls would have more flexibility to abandon the current qualification limits with this system. Allowing the bowls to be flexible with their invitations makes the system able to adjust in a more timely fashion if it is established that the conference strengths warrant it.
If the current qualifications and at large eligibility are maintained they should be changed to apply the 2 teams per conference limit to selections made after step 2.
2007 was one Hawaii loss away from showing that it might be prudent to lift the 2 team restriction for a third team from a conference in the top 8 of the BCS standings with no second team from any conference ahead of them after all conference champions in the top 16 have been selected.
Play-in Game details:
Hosting schools for play-in games may be required to use a stadium of their choice meeting a size requirement and make a specified number of tickets available to the visiting team.
Each year the number of games their locations and potential match ups, based solely on who wins each game, would be set once the final BCS standings are available. The venue for the play in games would be the only significant logistical issue, with two weeks to resolve any issues. If the home team can’t resolve the issues they would forfeit the game.
The number of teams participating in the BCS games would be 10 or 11 for all scenarios except 8 teams. This leaves a pool of teams for the other bowls that does not change systematically from one year to the next. The case of 8 teams could be handled by taking an existing first day bowl game and making it a neutral site game for the play-in game between the #4 and #5 seeds.
Problem Cases:
One problem case is when one team is a solid number one and three teams are nearly tied for the #2 spot with no undefeated teams, as was the case in 2001. This would leave only one team eligible. Another case would be like this but with a low ranked undefeated team. This case runs the risk of a close upset in the National Championship Game and a blowout between the #2 and #3 team in a BCS Bowl, leaving doubt as to the champion.
It is hard to imagine an undefeated team ending the season by beating two top 5 teams and not being the consensus #1. Both of these cases can then be addressed with the following rule:
If the base criteria only generate one team, or create a structure where a team below #4 in the BCS ranking would not play a semifinal game, the second gap in the ranking average of 1.5 would be used.
Another problem case is if the number of teams exceeds 8, which can be addressed by this rule:
If the base criteria generates more than 8 teams, eliminate all teams that did not have the highest conference record in their conference, excluding championship games. If more than 8 teams still remain, look for a gap in the rankings among the remaining teams.
The only remaining way this championship system could fail is if 9 teams ended the regular season undefeated, an extremely unlikely event.
#1 with no tie-in:
Situations where a #1 or #2 seed has no conference tie-in needs to be addressed or all teams should have a tie in defined for this purpose. For this purpose, and independently of any automatic qualification process, the Big East could be restored to the Orange Bowl. The MWC and WAC would fit geographical with the Fiesta Bowl. C-USA, the MAC and the Sun Belt Conference would fit best with the Sugar Bowl.
Incentives to Compete, strength of the regular season.
A big reason playoffs are resisted is that they could reduce the value of the regular season. Allowing all undefeated teams runs the risk of teams reducing the strength of schedule.
The games early in the season are important to climb into the top of the standings. Late losses have demonstrated a devastating impact on a team’s position near the top. Only one team since 2004, LSU 2007, would have qualified for the championship structure with two losses. Usually enough undefeated and one loss teams abound to make a second loss be the end of the story.
The undefeated teams are in by the first criterion. The one loss teams would need to build enough consensus among the BCS components to avoid being behind the first gap in the standings. A strong out of conference schedule could go a long way to this end. For these teams the cut off actually eases the system from the need to get into the top 2 as more than 2 could get in, slightly reducing the risk of a loss.
Utah earned 4.5 million more than normal in its conference revenue sharing package for their Sugar Bowl appearance. They earned 0.8 million for their trip to Michigan. Unless a team has a 2 out of 11 chance of going undefeated in their conference a team is better off getting the guarantees payout of playing a big name team. Plus, they have an opportunity to get noticed with a win.
Going undefeated in any conference is difficult. If you are running the table regularly in a smaller conference a bigger conference will eventually pick you up, reducing your chances of going undefeated. Utah and Boise State are the only teams without an automatic qualification for their conference to finish the regular season undefeated at least twice in the last decade. Few question their out of conference scheduling practice.
What could have been...
The current BCS formula paradigm has only been in place since 2004 so BCS standings before this do not correlate with the current values. Conference tie-ins and actual bowl selections were used to estimate what the selections of the BCS Bowls not involved in the championship system could have been.
2008:
5 teams: Oklahoma, Florida, Texas, Utah, Boise State
Utah would have hosted Boise State for the chance to play Oklahoma in the Fiesta Bowl.
Florida would have played Texas in the Wild Card Game.
The winners of these games would have met in the National Championship Game.
Rose Bowl: USC vs. Penn State
Sugar Bowl: Alabama vs. Ohio State
Orange Bowl: Virginia Tech vs. Cincinnati
2007:
3 teams: Ohio State, LSU, Hawaii
LSU and Hawaii would have played in the Wild Card Game.
The winner of this game would have played Ohio State in the National Championship Game.
Rose Bowl: USC vs. Illinois
Fiesta Bowl: West Virginia vs. Oklahoma
Sugar Bowl: Georgia vs. (ASU or Boston College)
Orange Bowl: Virginia Tech vs. Kansas
2006:
3 teams: Ohio State, Florida, Michigan, Boise State
Ohio State would have hosted Boise State in the Rose Bowl.
Florida would have played Michigan in the Wild Card Game.
The winners of these games would have met in the National Championship Game.
Fiesta Bowl: USC vs. Oklahoma
Sugar Bowl: LSU vs. Notre Dame
Orange Bowl: Wake Forest vs. Louisville
2005:
2 teams: USC, Texas
Same as the current BCS system but the bowl format has changed since 2005
USC would have played Texas in the National Championship Game.
Rose Bowl: Penn State vs. Oregon
Fiesta Bowl: Ohio State vs. Notre Dame
Sugar Bowl: Georgia vs. West Virginia
Orange Bowl: FSU vs. TCU (would have been an automatic qualifier under current rules)
2004:
5 teams: USC, Oklahoma, Auburn, Utah, Boise State
Utah would have hosted Boise State for the chance to play USC in the Rose Bowl.
Oklahoma would have played Auburn in the Wild Card Game.
The winners of these games would have met in the National Championship Game.
Fiesta Bowl: Texas vs. California
Sugar Bowl: Georgia vs. Michigan
Orange Bowl: Virginia Tech vs. Pittsburgh
Teams left out:
At least two teams who felt they deserved national championship consideration are not included. Two prominent teams are USC 2008 and Georgia 2007.
Neither of these teams won all their games. Neither of these teams garnered enough support nationally to avoid a gap forming between them and the top teams in the standings.
To loosen the rules for these teams would greatly expand the structure of the system. This would be detrimental to the health of the economy of college football.
Prior Years:
Using the paradigm that the cutoff is at an average ranking difference of 1.5 it is possible to extent the simulation backwards to the older formulas. The cutoff in these systems would be a difference in the BCS formula of 3. BCS bowls are not listed due to difficulties steming from conference realignments.
2003:
3 teams: Oklahoma, LSU, USC
LSU would have hosted USC in the Wild Card Game.
The winner of this game would have played Oklahoma in the National Championship Game
2002:
2 teams: Miami (FL), Ohio State
Miami (FL) and Ohio State would have played in the National Championship Game.
2001:
1 teams: Miami (FL)
Use the second gap in the standings.
4 teams: Miami (FL), Nebraska, Colorado, Oregon
Miami (FL) would have hosted Oregon in the Orange Bowl.
Nebraska would host Colorado in the Wild Card Game.
The winners of these games would have met in the National Championship Game.
2000:
3 teams: Oklahoma, FSU, Miami (FL)
FSU would have hosted Miami (FL) in the Wild Card Game.
The winner of that game would have played Oklahoma in the National Championship Game.
1999:
3 teams: FSU, Virginia Tech, Marshall
Virginia Tech would have hosted Marshall in the Wild Card Game.
The winner of this game would have played FSU in the National Championship Game.
1998:
3 teams: Tennessee, FSU, Tulane
FSU would have hosted Tulane in the Wild Card Game.
The winner of this game would have played Tennessee in the National Championship Game.
Championship System distribution
A year with only one team happened in 2001, expanding to 4 teams.
A year with two teams happened twice, 2002 and 2005.
A year with three teams happened 5 times, 1998, 1999, 2000, 2003, 2007.
A year with four teams happened in 2006 and once after expanding from only one team in 2001.
A year with five teams happened twice, 2004, 2008.
No years with 6 or more teams have occurred.
2008:
5 teams: Oklahoma, Florida, Texas, Utah, Boise State
Utah would have hosted Boise State for the chance to play Oklahoma in the Fiesta Bowl.
Florida would have played Texas in the Wild Card Game.
The winners of these games would have met in the National Championship Game.
Rose Bowl: USC vs. Penn State
Sugar Bowl: Alabama vs. Ohio State
Orange Bowl: Virginia Tech vs. Cincinnati
2007:
3 teams: Ohio State, LSU, Hawaii
LSU and Hawaii would have played in the Wild Card Game.
The winner of this game would have played Ohio State in the National Championship Game.
Rose Bowl: USC vs. Illinois
Fiesta Bowl: West Virginia vs. Oklahoma
Sugar Bowl: Georgia vs. (ASU or Boston College)
Orange Bowl: Virginia Tech vs. Kansas
2006:
3 teams: Ohio State, Florida, Michigan, Boise State
Ohio State would have hosted Boise State in the Rose Bowl.
Florida would have played Michigan in the Wild Card Game.
The winners of these games would have met in the National Championship Game.
Fiesta Bowl: USC vs. Oklahoma
Sugar Bowl: LSU vs. Notre Dame
Orange Bowl: Wake Forest vs. Louisville
2005:
2 teams: USC, Texas
Same as the current BCS system but the bowl format has changed since 2005
USC would have played Texas in the National Championship Game.
Rose Bowl: Penn State vs. Oregon
Fiesta Bowl: Ohio State vs. Notre Dame
Sugar Bowl: Georgia vs. West Virginia
Orange Bowl: FSU vs. TCU (would have been an automatic qualifier under current rules)
2004:
5 teams: USC, Oklahoma, Auburn, Utah, Boise State
Utah would have hosted Boise State for the chance to play USC in the Rose Bowl.
Oklahoma would have played Auburn in the Wild Card Game.
The winners of these games would have met in the National Championship Game.
Fiesta Bowl: Texas vs. California
Sugar Bowl: Georgia vs. Michigan
Orange Bowl: Virginia Tech vs. Pittsburgh
Teams left out:
At least two teams who felt they deserved national championship consideration are not included. Two prominent teams are USC 2008 and Georgia 2007.
Neither of these teams won all their games. Neither of these teams garnered enough support nationally to avoid a gap forming between them and the top teams in the standings.
To loosen the rules for these teams would greatly expand the structure of the system. This would be detrimental to the health of the economy of college football.
Prior Years:
Using the paradigm that the cutoff is at an average ranking difference of 1.5 it is possible to extent the simulation backwards to the older formulas. The cutoff in these systems would be a difference in the BCS formula of 3. BCS bowls are not listed due to difficulties steming from conference realignments.
2003:
3 teams: Oklahoma, LSU, USC
LSU would have hosted USC in the Wild Card Game.
The winner of this game would have played Oklahoma in the National Championship Game
2002:
2 teams: Miami (FL), Ohio State
Miami (FL) and Ohio State would have played in the National Championship Game.
2001:
1 teams: Miami (FL)
Use the second gap in the standings.
4 teams: Miami (FL), Nebraska, Colorado, Oregon
Miami (FL) would have hosted Oregon in the Orange Bowl.
Nebraska would host Colorado in the Wild Card Game.
The winners of these games would have met in the National Championship Game.
2000:
3 teams: Oklahoma, FSU, Miami (FL)
FSU would have hosted Miami (FL) in the Wild Card Game.
The winner of that game would have played Oklahoma in the National Championship Game.
1999:
3 teams: FSU, Virginia Tech, Marshall
Virginia Tech would have hosted Marshall in the Wild Card Game.
The winner of this game would have played FSU in the National Championship Game.
1998:
3 teams: Tennessee, FSU, Tulane
FSU would have hosted Tulane in the Wild Card Game.
The winner of this game would have played Tennessee in the National Championship Game.
Championship System distribution
A year with only one team happened in 2001, expanding to 4 teams.
A year with two teams happened twice, 2002 and 2005.
A year with three teams happened 5 times, 1998, 1999, 2000, 2003, 2007.
A year with four teams happened in 2006 and once after expanding from only one team in 2001.
A year with five teams happened twice, 2004, 2008.
No years with 6 or more teams have occurred.
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