My apologies for asking this question because I know its been asked and answered before but I can’t find the thread.
The question is, all things being equal, what are the chances of any given team in MLB making the postseason playoffs, given that the American League has 3 divisions, two with 5 teams and 1 with 4 teams, that the three division winners each make the playoffs, and that a wild card team, being the remaining team with the best overall record, also makes the playoffs. The National League has a similar setup, but with two divisions of 5 teams each and one division of 6 teams, and with a wild card team too.
Based on the way you’ve structured the question, it looks as if the answer is straightforward:
Probability of an AL team qualifying for postseason play = 4/14 = 0.286
Probability of an NL team qualifying for postseason play = 4/16 = 0.25
But I’m guessing you were looking for something a bit less obvious than that.
Xema, I hate to say it, but you’re wrong. I don’t know what the right answer is, but your answer is incorrect.
A team in the American League East (which has 5 teams) has a 1 in 5 chance of winning the division, and also chance to win the wild card. A team in the AL West, which has 4 teams, has a 1 in 4 chance to win the division plus the same chance to win the wild card that every other team in the league has.
What I can’t figure out is the interrelationship between the wild card and winning the division, because a team cannot win both chances in the same year.
Not even that. MLB plays unbalanced schedules, with a team facing divisional opponents more often than others, and different interleague opponents too. A team in a weaker division, or with a weaker interleague schedule, has a better chance.
The overall chance that a team makes the playoffs is the ratio of the number of teams that make it divided by the total number of teams. So, if you’re looking for an overall average chance by league–then yes, it is that simple.
Now, if you want an average chance by division, it probably can’t be calculated from mathematical basic principles–a team from a smaller division obviously has a slight advantage (they’re competing against fewer teams for the division pennant), but a team with weaker divisional competition will also have an advantage. If you want to ignore that, and just focus on the division size, then it would just be the sum of their a priori chance of winning their division (1/4 or 1/5) and the product of the chance of their not winning the division (3/4 or 4/5) with the chance of their being the best of the group of non-division-winners (a priori 1/11 or 1/13).
For American League teams, this means a 31.82% chance of making the playoffs in the 4-team division, and 27.27% chance in one of the 5-team divisions. This averages over the fourteen teams to 28.57%, or 4/14, as expected.
The question has no real world meaning. All things are not equal. You can’t rationally argue that the Washington Senators before this season had a 27% chance of making the playoffs (or even more ludicrously, a 27.27% chance).
A team’s record is a reflection of its talent, so probability doesn’t apply. Some teams have more talent than others, and that totally wrecks probability. It’s like saying a coin has a 50-50 chance on being heads, when a one-pound weight it attached to one side.
You can’t speak of this sort of thing in probabilities (at least, not in the real world; I don’t know about Mathmagicland).
Well, since the Washington Senators have been out of business since they moved to Texas in the early 1970s, of course they currently have no chance at all. The Nationals can’t even spell their own name right on their own uniforms, so they don’t stand much of a chance either and were mathematically eliminated about Memorial Day 2009.
Even so, to say that we can’t compute “all things being equal” numbers in baseball is just silly.
We can certainly compute them, but they don’t mean much. We’ll know more about next season in March, but I’d give the Yankees much better odds than 27.27% to make the playoffs in 2010, and the Royals worse odds than 27.27%.
How about this: For a team in the AL East or Central, it’s (1/5) + (4/5)(1/11) = 3/11 = .2727
For the AL West, it’s (1/4) + (3/4)(1/11) = 7/22 = .3182
Either they win their division, or they don’t win their division but they’re the best of the 11 non-division-winners.
At least, if you calculate the probabilities this way, they add up to 4 for the 14 teams in the league (as they should if 4 teams make the playoffs).
I do await the day we get two more teams (tho it may be awhile, if no promising markets are currently available) and we get both leagues back up to equality.
They’re totally useless as predictors, yes. As a baseline for measurement of a team’s historical success, I think it has some value. For instance, the Yankees have made the postseason 14 of the past 20 seasons (including this one), for a recent 70% success rate. Given the prior probability of making the playoffs in their division, expected playoff appearances would be 5.5; so they’re just over three standard deviations above expected performance, which would happen less than one time in a thousand by chance. We can therefore conclude that the Bronx Bombers ain’t just lucky–they’re cheating good. OK, we thought we knew that already–but this is solid statistical evidence, bub!
And on that note, we can go to four four-team divisions and get rid of the wild card, go back to something closer to a balanced schedule, and - in a perfect world - do away with interleague play.