Contests, both political and sporting, brings polls and probabilities to mind, and these, often enough, need to be deconstructed a little. Let me start with a topical example from presidential politics.
George Bush Versus Candidate X
There have been several polls in recent months indicating that, were the presidential election to be held early, President Bush would lose to a generic Democrat in a close race. This is an interesting fact on the surface, but becomes somewhat paradoxical when these same polls also show Bush beating each of the primary Democratic contenders by a slight margin.
One way in which this can occur is for each one of the viable Democratic contenders to have a different and distinctive policy or personality trait that alienates 5-10 percent of likely voters. When asked whether they would prefer Bush or a generic representative of their party, Democratic voters reasonably assume that the generic representative will not have the offending policy or personality trait, and so the generic Democrat gets their vote.
Related to this is the fact that the title "Democratic Nominee for President" has a certain weight that many of the actual candidates suffering from low name recognition lack. Incredibly, polls show that a majority of Americans can't name a single Democrat (other than Wesley Clark) running for the nomination.
Among those who can identify some of the candidates a small, but non-negligible percentage idealize the generic Democrat, yet disdain Kerry, Dean, and every specific candidate. One conclusion hard to resist is that poll questions about generic Democrats are almost useless.
The old comedian Henny Youngman had it right. His signature joke has somebody asking him, "How's your wife?" He replies, "Compared to what?" (In our presumably less sexist era, "How's your husband or significant other?" may be substituted.)
Other bits of political news also sound like jokes. Last month many news sources reported, "Bush told his senior aides Tuesday that he 'didn't want to see any stories' quoting unnamed administration officials in the media anymore, and that if he did, there would be consequences, said a senior administration official who asked that his name not be used."
This reminds me a little of the old joke about the pollster who asked people, "To what do you attribute the ignorance and apathy of people?" The most common response was, "I don't know and I don't care."
Baseball: Too Many Seven-Game Series?
Subject to its share of statistical oddities, baseball often arouses more interest than politics. This year the focus has been on the curses said to afflict the Chicago Cubs and Boston Red Sox, both of whom lost the 7th game of their respective playoffs in — for fans of the teams, at least — a particularly heartbreaking way. Of course, losses have to be extensive to carry much statistical weight so it should go without saying that a relatively few vividly remembered anecdotes over the years do not constitute evidence for much of anything.
A more interesting question mathematically was raised recently by the newsletter, Inside Science, published by the American Institute of Physics. Among the best-of-seven World Series (first team to win 4 games wins) of the past 50 years, have there been more that went the full seven games than probability theory would have predicted?
In the period from 1952 to 2002, 24 of the 50 Series (or 48 percent) went the full seven games and the likelihood of this many or more 7-game Series is a small and statistically significant 1 percent. Most of these Series occurred in the period 1952 to 1977. If, however, the analysis is extended back to include all World Series, 35 of the 94 (or 37 percent) went the full seven games, higher than expected, but not statistically significant.
So what is the probability of the Series going seven games? Assuming the teams are equally matched, the probability the Series will go seven games is 31.25 percent. (If you want to know why, see the calculation in the sidebar below.) If the teams aren't equally matched the probability of going seven games is less.
There's not much room for curses and the like in these statistics, merely, it seems, a slight predilection to go a full seven games. Some have conjectured that the team behind after five games is more likely to pull out all stops to win the do-or-die 6th game.
I'll end with one small link between my two topics. If we pitted the American League champion New York Yankees (Bush) against, say, the National League All-Star Team (generic Democrat), the All-Stars might very well be favored against the Yankees, even if the Yankees were favored against every particular NL team.
Professor of mathematics at Temple University and adjunct professor of journalism at Columbia University, John Allen Paulos is the author of several best-selling books, including Innumeracy, and the just released A Mathematician Plays the Stock Market. His Who’s Counting? column on ABCNEWS.com appears the first weekend of every month.