gauravraos wrote:

62% of baseball fans believe their favorite team will win the World Series within the next five years. But, of course, only one team can win the World Series each year, so, in a league with 30 teams, at most 5, or 16.7%, will actually win. Clearly, many of these fans’ championship expectations for their favorite teams will go unmet.

In evaluating the argument, it would be most useful to determine which of the following?

A. Whether baseball will drastically change the number of teams that qualify for the playoffs during the next five years.

B. How many teams are good enough to be considered championship contenders in an average year.

C. Whether a single team is likely win the World Series multiple times during the next five years.

D. Whether each team has roughly the same number of fans.

E. How many current fans will continue to follow their teams if their championship expectations are not met.

OFFICIAL EXPLANATION

Given that the argument seems almost self-evidently true (62.5% is much more than 16.7%), the real question in this "useful to evaluate" problem is: "How could the conclusion about fans having unmet expectations possibly be false?"

There's a very subtle disconnect in the statistics given by this question; the numbers don't actually offer the right sort of information. Specifically, there's a different between discussing the number or percentage of teams that will win, on the one hand, and discussing the number or percentage of fans whose teams will win, on the other hand. If, for instance, nearly all fans share the same favorite baseball team, then it would be quite possible for nearly all of the fans to root for a winner even as only one of 30 teams actually wins.

A simple example with numbers: Imagine 8 fans, of whom five root for the Yankees, one roots for the Dodgers, one roots for the Braves, and one roots for the Tigers. The other 26 teams have no fans. If the Yankees win the World Series, only 1/30, or about 3%, of the baseball teams in the league won the championship. But fully 5/8, or 62.5%, of the fans got to see their favorite team win and their championship expectations met.

In the face of this disconnect, we need to know whether such an uneven distribution of fandom actually exists. If it does, then the fans' expectations could be met. If, instead, the distribution of fandom is relatively even, then indeed the argument's conclusion will hold as most of the fans will see their expectations go unmet. Thus D is correct.

Answer A is not relevant, since regardless of now many teams may qualify for the playoffs we are told that only one team can win the championship each year.

Answer B sounds nice, but the conclusion is about "championship[s]," and being a contender just isn't good enough.

Answer C doubles down on the numerical flaw. If a single team wins multiple championships, then the number of distinct championship teams over the five year span would actually comprise less than 16.7% of all of the teams, potentially leaving even more fan expectations unmet.

Answer E simply does not address the conclusion. At no point do we care how fans might react to having their expectations frustrated.

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