Tuesday, September 15, 2009

Mundane Comments on the Playoff Structure

Believe it or not, this is a post filled with opinions. The underlying assumption is that if you are not interested in my opinion, you will not read, and so I’m not going to go around and apologize for giving my opinion in what follows.

The current MLB playoff system is bizarre from a certain standpoint, as the number of teams vary from division to division, even within the same league. It is apparent that teams from different divisions do not have equal likelihoods of making the playoffs (and therefore winning the pennant or the World Series) due to this structure, even if one assumes that all teams are equally likely to win each game.

In fact, if you grant me another assumption, that there is no home field advantage (I would add a balanced schedule, but since we have assumed that all teams are equal, we really don’t care--your opponents are .500 even if you play the Dodgers in all 162 games) in the playoffs, it is relatively simple to calculate the chances of a team from each division reaching certain goals.

Using the AL East as the example, there are five teams in the division; each team therefore has a 1/5 chance of winning the division title. 4/5 of the time, they will not win the division and thus will be in competition for the wildcard. There are fourteen teams in the American League, three of which will win division titles, so they are competing against eleven teams for the wildcard, and are expected to win with probability 1/11. The probability of making the playoffs is straightforward:

P(Playoffs|AL East) = (1/5) + (4/5)*(1/11) = 7/22

Since we have assumed equality amongst team and no home field advantage in the playoffs, the probability of winning the pennant is simply:

P(Pennant|AL East) = P(Playoffs|AL East)*(1/4) = (7/22)*(1/4) = 7/88

And the probability of winning the World Series is just as simple:

P(World Series|AL East) = P(Pennant|AL East)*(1/2) = (7/88)*(1/2) = 7/176

The probabilities for the other divisions can be figured similarly, and converting to four place decimals (overkill, I know, but I feel bad about killing all the nice fractions), this is what you get:

I realize that I am not telling you anything you couldn’t figure out for yourself.

One thing to note here is that the difference between playing in the AL and the NL is not too much of an issue as long as the divisions are of equal size. An AL East team can expect an extra playoff appearance every 89 years and another world title every 714 years compared to its NL East counterpart. This isn’t really worth worrying about IMO, and since the AL was at a similar disadvantage between 1977 and 1992, it only seems fair in a way.

The real issue lies in the divisions of different sizes, not the fact that the leagues are different sizes. An AL West team can expect to make the playoffs 32 times in a century, while an AL East or Central team will make the playoffs 27 times. Of course, there are so many other factors at play (after all, teams are not perfectly balanced as we have assumed) that you may not find this particularly troublesome.

The gap between the two extreme divisions, the AL West and the NL Central, is pretty extreme. Nine extra playoff trips and one extra world title per century seems inherently problematic for my money.

It would be nice if you could balance the two issues (more teams in the division making a division win less likely, more teams in the league making a wildcard less likely) by putting the larger division in the smaller league, but of course it is only because the league is larger that a division must be larger.

Assuming that expansion to thirty-two teams is inevitable (and I believe it is, although any guess on the timeframe would be me blowing smoke), and that the two league structure will endure (no need to start a civil war here), what should the divisions look like when it happens? As a side note, it certainly appears as if there will be no expansion prior to 2015, which will make the period from 1998-whenever the longest period of non-expansion in the expansion era (surpassing 1977-1993).

What I would suggest is two eight-team divisions in each league, with the wildcards being the two non-winners with the best record. In fact, I would like to see such a structure right now, with the difference being that the AL divisions would each have seven teams. Larger divisions are my preference as they increase the probability of the best teams making the playoffs.

However, the entirety of American pro sports history shows a trend towards smaller divisions over time. I did not check thoroughly, but I do not believe that any of the four major leagues have ever reduced the number of divisions. Certainly baseball has not, going from no division to two divisions in 1969 to three divisions in 1994. Football has gone from two to three to four, and hopefully will serve as a cautionary tale for baseball.

After all, in the NFL, it is relatively common for 8-8 teams to win one of the four-team divisions; in 2008, the Cardinals and the Chargers both pulled this off, and while it was unusual to have two such cases in one season, individual occurrences are not particularly uncommon.

For the NFL, the issue of having two good teams in one of the divisions while a mediocre team wins another division is blunted by the presence of two wildcards. But still, something just feels wrong about having the 11-5 Patriots on the outside looking in while the Chargers are in. Any divisional format will occasionally result in teams with better records being left out, but the tiny divisions increase the odds.

For baseball, unless the playoffs were expanded, you don’t have a lot of choices. You can have:

1) 4 4-team divisions, no wildcard
2) the NL model of 2 5-team divisions plus a 6-team division, 1 wildcard
3) 2 8-team divisions, two wildcards
4) one big league

While this is certainly a matter of personal taste, option four is the clear winner to me, while option three is the most attractive that would have a prayer of being implemented.

As an aside, I find the phenomenon of increasing numbers of divisions as time has marched on somewhat puzzling. Travel times and expenses should have made smaller divisions and unbalanced schedules most appealing early in the history of leagues, not now. The universality and as of yet unrelenting nature of the trend could be explained in a few ways. The most generous explanation is that fans like the excitement generated by more, smaller divisions, and the leagues are just giving their customers what they want. I find this preference odd, as an 8-8 team winning a four-team division does not seem any more exciting to me than a 9-7 team beating out another 9-7 team for a wildcard spot. But it may well be there the cachet that goes with winning a division as opposed to winning a wildcard justifies the system economically.

It may be so, but the reasoning behind it is completely foreign to me. In the small division race, you have to beat out just three other teams. In the wildcard race, you have to beat out thirteen other teams (admitted they are all teams with lesser records than at least one other team in the league and possibly as many as three). Still, I’m not impressed by being a division champion if all that entails is beating out three other teams.


  1. excuse my English, I write from Venezuela. I also have a baseball blog. I would like to know what web page i can get the win shares of each player ... THANKS

    Diego Alvarez

  2. How about four leagues, 8 teams each? The NL classic 8, the AL classic 8, the 8 NL expansion teams, and the 8 AL expansion teams. 154 games, then a four-team playoff tournament. Bam. Simple as pie. This has the added benefit of the Astros and Diamondbacks of the world no longer being in the shadow of the big boys (Yankees, Cardinals, etc.) and actually being able to develop some history and rivals with one another. Plus it rewards regular season success, and I think we all agree it's harder to be the best team over a long season than other a few short playoff series.

    Granted that's pretty radical (although a little known fact is that the idea of expanding with a third league rather than new teams in each league was considered in the late 50s). My second choice is your 2-division/8 teams per structure but really I think having 8 playoff teams is overkill considering that it allows mediocre teams to make it in and it is one of many factors causing the World Series to run into November these days. Plus I think the wildcard ruins the authenticity of playoff races these days, but that's a whole different subject.

  3. Diego: Unfortunately, I don't believe that anyone is currently publishing Win Shares for free on the internet. They used to be on The Hardball Times (hardballtimes.com), but they no longer do. Bill James' website (billjamesonline.net) has Win Shares for key players, but it is a pay site.

    Su ingles es muy bueno, pero mi espanol es muy mal... :-)

    Daniel, I don't think that's a BAD idea, but I think fans are too used to seeing a variety of different opponents to go back to playing the same 7 teams all year.

    What you could do, maybe, is pair two of the leagues together each year. Say there was a NL, AL, Federal, and Continental League. One year the NL plays interleague against the AL while the FL plays the CL. In the second year, the NL plays the FL and the AL plays the CL, and in the third year the NL plays the CL and the AL plays the FL. That way, you would get more diversity in opponents, but intra-league competition would not be any more diluted than it is today.

    I'm not crazy about the first playoff round either, but that genie is out of the bottle and it ain't going back in. There's just too much $ to be made (and I believe that you and I hold a minority viewpoint among fans--most fans like the expanded playoffs).

  4. p,

    That's an interesting idea, that whole rotating interleague play thing. I really like it. That way teams in the same league still play the same schedule so it's a fair competition, unlike the current system where the Mets get six games against the Yankees and the Rangers get six against the Astros. It would definitely help sell the idea to the average fan. Good call.

    But you know, the thing about the average fan is I'm not so sure they know what they want. They say they like the expanded playoffs. But they also complain about too many meaningless games and about how long the season is. If there were fewer playoff teams, games would matter more late into the season. You can't really have it both ways and I think fans would appreciate more drama late in the season at the expense of a few playoff teams. Just some thoughts.

    At the very least if the People In Charge must have their first round of the playoffs they ought to make it seven games. Five games is really really really short. (And I'm not bitter about my Cubs being swept two years in a row or anything haha.)


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