What would a "Fair" college football playoff be?

Here we are, at the end of another college football (CFB, for short) FBS (formerly NCAA Division 1A) season.  Alabama routed Notre Dame to win the BCS National Championship (NC) for the 3rd time in 4 years.  All that settles the issue for this year of 2012, right?  Weeeeelllll ... no, not completely.  There's still a lot of debating going on about whether the teams participating in the NC game were the best teams.  Texas A&M beat Alabama head-to-head in Tuscaloosa (but lost to Florida and Louisiana State).  Notre Dame was undefeated but looked really overmatched in losing to Alabama.  Might another team have been a better matchup against Alabama?  And so on ... and on ... and on ...

All this brings up the topic of a BCS CFB playoff again.  The BCS will go to a 4-team playoff format in 2014 - but it still won't settle all the debates.  Presumably, the still-imperfect ranking system used by the BCS will decide which four teams are included in the 2-round tournament, thereby inevitably leaving deserving teams on the outside looking in, which happens every year, even without a playoff.  If they go to a 16-team playoff, or pattern the FBS playoff on the FCS playoff algorithm or the NFL system, or any other structure whatsoever, you still will have potentially deserving teams left out.

The goal many seem to have is that the "best" team win the championship (especially if it's their team!).  But how is the determination of the "best" team to be done?  Yes, subjective ranking systems, or pseudo-objective computerized systems (that use subjectively developed algorithms) are far less satisfactory than "settling" the issue on the playing field.  One team wins, the other loses.  How difficult can it be?

Well, game outcomes are the result of nonlinear processes that ultimately are unpredictable.  Seemingly minor things like a gust of wind that makes the winning field goal attempt good (or bad), a ball tipped in the secondary just happens to be intercepted (or not), a ball touches a receiving team player on a kickoff and is recovered by the kicking team (or not), and so on.  Football involves "matchups" of players on offense against players on defense.  In some cases, a good player at a position either plays poorly or plays extraordinarily well against the particular player he faces, and that turns out to be a key to the outcome.  And there are many more things that can happen in CFB.  The ball bounces to favor one team over the other, a bad referee call somehow is upheld even after review, the weather conditions favor one team over another, and injuries to key players.  All these things and more play a role in game outcomes between evenly-matched teams.

There's an often-heard argument after a close game goes against a particular team - "Well, if they played the game 10 times, my team would win 6 of them (or whatever number)!"  This is an interesting hypothetical - but does it make any sense at all?  In science, we try to do experiments on large samples of data in order to have some confidence in the numbers we generate.  Let's make it 100 games to be played between each team, instead of just 10.  That would give us considerably more confidence in the winning/losing percentage numbers.  In 2012, there were 120 FBS teams.  They each play 12 games, for a total of 12x120 = 1440 games per season (not counting bowl games).  If each team played every other team in the FBS 100 times, that would make 120x119x100 = 1,428,000 games!  Now that would be a decent sample size - roughly a thousand times more games than we now have in a regular season!  Every true CFB fan would love it, right?

Realistically, it's impossible to play that many games even if the season went on continuously all year!  Note that if two teams play 100 games, there still would be some team pairings that could come out tied, 50 games each, so perhaps we should make that 101 games (for a total of 1,442,289 games).  Even if somehow all those games could be played in a single season, there are more problems.  With each team playing 11,900 games, the chance for injuries to key players becomes a near-certainty.  To be entirely fair, an injury resulting in any player being unable to continue at 100% would mean that game would have to replayed, after giving the injured player(s) time to heal up to 100% fitness again (basically impossible, of course).  Any bad call (including those upheld after replay) would mean the game had to be replayed.  Any "bounce" favoring one team over another - replay the game!  Any departure from fair weather - replay the game!  All games, naturally, would have to be played at completely neutral sites with equal numbers of fans on the stadium for each team in the venue.

By this point, we're talking about taking many years to finish even a single season, and since age affects different people differently, it's likely that unfair advantages would develop from the aging process (including injury healing times).  Of course, with this many games, players would develop more experience in one season than they now get in an entire CFB career.  Different players gain differently from experience, so more unfair advantages would crop up.  By the way, with this many games, the playing fields would suffer tremendously, so time for the recovery of the playing surfaces would have to be allowed - the playing surface might give one team an unfair advantage, after all.  All venues would have to be equal in terms of swirling winds, playing surface, fan seating, etc.

I think it's likely reasonable to conclude that any absolutely fair, objective effort to determine the "best" team, even on the playing field, is not possible.  The whole notion of the "best" team is only an abstract speculation that can't be tested in any completely fair and objective way, on the field or off.  As shown on a regular basis in the NFL, the "best" team (however difficult that might be to define) doesn't always win the Super Bowl, unless you define "best" only by the outcomes of the playoff games.  If the FBS goes to a playoff system, the same will be true for them.  In fact, there will little difference between CFB and the NFL at that point, except for player salaries.  Not everyone will be happy with this choice of direction for CFB, despite the crowning of an unambiguous champion at the end of every CFB season.

UPDATE:  The choosing of the "Final Four" for this season (2014/15) absolutely confirms my prediction that even a playoff system can never satisfy everyone.  The BCS formula was flawed, but so will be any playoff system.  Teams left out always will be howling in protest.  And the winner of a playoff will not always be the hypothetical "best" team in many minds.