One shortcoming here is that, in the AL scenario, you're not taking into account the effect that a close-to one week layoff would have on the Yankees.

A wholly different view is this: playoffs will not definitively settle "who is best" questions, so we should regard them as simply being a chance to see baseball played at its current best level--in effect, a series of exhibition games, but with ample tangible and intangible rewards available to provide motivation.

Back in the day, a good part of the charm and attraction of the World Series was that it was the first and only time that the two teams could meet: that greatly augmented fan interest by providing season-long fodder for "who's really best", because that couldn't be tested, directly or indirectly, till the Series.

If we today had "real baseball" as our goal, rather than financial returns from the post-season, we would establish four 7-team leagues (nominally structured as one pleases, say AL E & W and NL E & W) and a two-level playoff structure, with no interleague play. Yes, not every city gets to host every team--what does that signify in an age in which television viewership greatly exceeds physical attendance? A side benefit is that every game would be directly meaningful to the league championship, and the winner in each league more likely to be the best team in that league.

Nothing like that is ever going to happen, because virtually the sole desideratum today is money, but it's fun to contemplate.

I don't think the playoff system is really meant to determine, in a serious way, who the best team is. It's purpose is really to generate revenue while providing a dramatic conclusion to the regular season. The owners would never even consider the kind of reform you're talking about, because they don't WANT the best team to win the WS on anything like a consistent basis. That would make it predictable and therefore a less compelling piece of entertainment.

Even though the three-stage playoffs format is here to say, I do think purists have a legitimate gripe about how difficult this format makes it for the best team to actually win the WS. But I think there is a simple solution that would at least somewhat address this concern: Each year, at the beginning of the playoffs, there should be a trophy awarded to the NL and AL teams who "win" the regular season. Each league would have its own trophy, named for an historical luminary associated with that league. The trophy presentation would be a part of the opening ceremonies of whatever divisional playoff series the winner was participating in.

The award would entitle the team to display a banner like the ones used to denote division championships, pennants, and WSs. Thus, finishing with the best RS record would be recognized as an achievement on a par with these other achievements.

To get the ball rolling, I would further propose awarding the trophy retroactively going back to the first year of the current playoff format.

I agree with the above two comments, the purpose of the playoffs seems to have more to do with keeping fans happy, and generating additional revenue, with a tournament featuring the best or most high profile teams, instead of determining "the best" team. If we look at it this way, its important that the teams in the playoffs are actually the teams that the fans want to see in the playoffs. For this reason keeping traditions alive (not monkeying with a accepted system too much), representing different regions, and keeping the integrity of the leagues (though not the divisions) becomes important. I would add that I like pennant races and would like a playoff structure that featured that.

The Yankees can hire the Washington Generals to keep them in top shape during the week then.

What are those regressed winning percentages? Isn't an observed winning percentage an unbiased estimator of the population value? Or are you imposing a prior that all teams are .500? In general, a Bayesian approach might be helpful here....

Eric,
Yes, those are regressed assuming a distribution of true talent with mean .500 and SD .06. So that's the prior. The SD was calculated by subtracting the expected variance from the actual variance in WPCTs over a number of seasons. So you are correct, the Bayesian-style approach is used when I said I regressed each team's WPCT. Tango's got a lot on this at his Book blog if you want to read up more....

Others - Keep in mind that this system doesn't prove who's best. It simply gives teams a chance to win in proportion to the probability that they are the best. I think that the more those numbers deviate, the more unfair the sport's playoff structure "feels". I think that's true of any sport or any setup, be it MLB, beer league softball, a kids' ping-pong tournament, etc.

I think the whole point of the playoffs is to randomize the winner. I think American owners are afraid that if the champion is too predictable before the season, ala European football then the fans will lose interest. Hence the fact that lower seeded teams have too much of a chance in the playoffs is not a bug, it's a feature

I think you missed what are really the two main reasons for playoffs.

The original reason for playoffs was to determine which team was best when the teams did not play each other in the regular season. The World Series prior to inter-league play is a prime example. Since the American League champion never played any National League teams during the season, there was no way to know whether they were
better than the National League without going head to head in the post-season. This also applies, to a lesser extent, to the present day situation in which teams play more games against teams in their own division than against teams not in their division.

The second reason for playoffs is money, plain and
simple. Adding more teams to the post-season increases broadcast and ticket revenue. More playoff spots mean that more teams get to play meaningful games late in the season. More playoff games means more commercial time can be sold.

The college basketball playoffs just expanded to 68 teams even though none of the additional slots will go to teams that have even a 2% chance of making it to the final game. To me it is obvious that the new slots were only added to increase revenue and not because there are truly deserving teams who got left out under the 65 team setup.

But no matter how you set up a playoff system, you can never be sure that the best team will win.
If the 2010 MLB playoffs were repeated 100 times there's a good chance that all 8 of the participating teams would win the World Series at least once. The teams are all good and in a short series, anything can happen.

One final thought regarding the futility of playoffs is the question of what is meant by a "team". Is it the team as it was constituted in April? Or is it the team that took the field in July? Or is it the team that played in September? Imagine if the Cardinals make the playoffs but Albert Pujols and Matt Holliday break their wrists on the last day of the season and can't play in the post-season. Obviously the "team" that St Louis puts on the field for the playoffs is not the same team that was so good from April to September.

As fans, we love to debate which teams are the best, but the reality is that teams are in a constant state of flux. The team that is best today might be mediocre tommorrow as a result of a couple of injuries to key players.

Just a thought here: How about realizing that no matter how you manage it, awarding a championship is unfair? Let's supose that one team won 150 games one year, and is 99.9% sure of being the best team in baseball. No one would argue with that. However, it's still not fair because some of the 18 players on that team are not, in fact, among the best 18 players in baseball. In fact, there is a pretty good chance that even with that scenario, the best player in baseball is not on that team.

So, should we now divvy up the championship between players? Or should we recognize that championships are one, just one, way of enjoying a season. It seems to me that baseball and college football are the 2 sports which most appreciate the good that goes with a season that does not involve championships. Why devise a complicated way of making championships the be all end all in these sports? Why not simply devise other ways, such as in baseball individual awards and recognition, and in college football the bowl system, to ensure that teams not winning championships also have a little fun?

If you want to get closer to the true percentages, why not just give teams a run handicap? Give the Yankees a 1-0 lead to start off the games, for example.

Many people have rightly pointed out that the point of the playoffs isn't really to "determine the best team". Look at this another way...perhaps (as I see it) the point of the regular season is to determine who deserves to be in the playoffs (and thereby have a right to play for the championship)?

Even if you decide the playoffs are for determining "the best team", using regular season results to handicap thins seems to be the unfair thing to me. The regular season is affected by a lot of factors, especially things like injuries...what if there is a team that is twice as talented as the next closest team, but suffers many injuries (but gets healthy in time for the playoffs), I don't want to see this team handicapped. Teams already benefit from having a better record in the regular season, due to confidence near season's end that the playoffs will be earned, and because the team will be able to set its rotation and rest players.

Despite the fact that the 2009 Yankees had the best regular season record AND won the World Series, I'm still not convinced that they were the "best" (i.e. most talented?) team. However, they were a team with a lot of good health, a great level of base talent, and much of that talent performed to or above expectations. They also took advantage of their home ballpark and won many games in lucky fashion, then used the benefits of the strong regular season (including rest and the ability to choose the days they would play, which let them use a three-man rotation for the playoffs).

The 2009 Yankees deserved and earned their championship, but it didn't definitively prove anything about a "best team". Why would you ever want to reward what could be nothing more than good luck with a playoff advantage?

Another thought I had on this, though I think it applies more to some other sports such as football, is that such a system would effectively eliminate the highly successful teams that just "coast" at the end of the season - every game really does matter now, even after "clinching" first place in a league.

Much of the variability in baseball lies in the fact that baseball is more truly an individual sport than a team one. Other than infield groundouts or outfield assists, there is not much to be said for one player's performance being based on another.

Another example is with pitching. The 1995 Braves had Maddux, Glavine, and Smoltz, who had a combined 47-16 record that year. But every 4th day, you would get Steve Avery, who with a 7-13 mark was quite obviously not up to par. However, when you enter the playoff scenarios, suddenly this 1995 team became significantly better, as only those three starters were required, and Avery resorted to bullpen duty. Perhaps there is some meat to be found in analyzing the 'probably superior' teams and their chances of winning in the playoffs, based on this new 3-man rotation.

What if there was no such thing as a monolithic "best team in baseball"? What if team quality -- team "true skill" -- changes on a monthly, daily, or even hourly basis? What if the best team yesterday is not the best team tomorrow, or the best team at this exact moment is never the best team again for the rest of the season, but reached a level for however brief a time that will not be matched by any other team?