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How Not to Be Fooled by Odds
Credit…Tomi Um
By David Leonhardt
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Now that The Upshot puts odds of a Republican takeover of the Senate at 74 percent, we
realize that many people will assume we’re predicting a Republican victory. We’re not.
There really is a difference between saying something will almost certainly happen and
saying that it is more likely to happen than not.
We know many people don’t buy that, so let me explain. Maybe more important than
any explanation, we have also come up with a list of outcomes that happen about 26
percent of the time — the flip side of 74 percent — which gives a sense for how common
26 percent still is. The list is below.
It’s an unavoidable truth that the world is an uncertain place. Probabilities help us make
sense of that uncertainty. When a situation involves knowable odds and repeated trials,
human beings often feel comfortable with probabilities. If I tell you that the odds
of rolling an eight or lower with two dice are about 74 percent — 72.2 percent to be
precise — you get it. You don’t think that I’m predicting you will roll an eight or lower.
You won’t call me wrong if you roll an 11. You understand that I am saying you will roll
nine or higher less than 50 percent of the time but more than never.
The situation becomes more complicated when the odds are less knowable and the event
in question is not an easily repeatable one, as is the case with an election. An election
brings all kinds of uncertainties. Is the polling in sparsely populated Alaska accurate?
Will Kansans sour on an independent candidate after an initial flirtation with him?
Will a late-breaking development hurt a candidate?
Not only are campaigns uncertain but we also can’t rerun them, as we can roll a pair of
dice multiple times and see with our own eyes that 26 percent doesn’t equal 0 and
doesn’t equal 50 percent. When an election is over, there is only one outcome, and it can
come to seem inevitable — or at least come to seem as if everyone should have known
the outcome all along. If only a few things had broken differently in 1960, for example,
Richard Nixon might have won and John F. Kennedy might be remembered as an
inexperienced loser.
Our forecast is as much a product of history as it is of math. We’ve looked at decades’
worth of election results and compared them with the current polls and other data. The
combination indicates that the Republicans are in a strong position but not an
invulnerable one. When candidates have a two- or three-point lead at this stage, as some
do, history suggests they usually win. Put all that information together, and the
Republicans have roughly a three-in-four chance of winning enough races to take the
Senate.
Though we might wish otherwise, we can’t make uncertainty disappear. Traditionally, a
lot of analysis and coverage of elections has made a version of this mistake. It’s been too
quick to call a race a “tossup” even when one candidate had a clear, if still modest,
advantage. To say that one candidate was ahead felt too much like making a prediction
that could later look bad. Calling most campaigns a tossup or a close call was easier and
safer.
But when you do take that approach, you’re not adding much useful information to the
discussion. The only way to give useful probabilities — the kind that scientists, business
executives and successful investors like Warren Buffett use in their worlds — is to give
probabilities that will sometimes seem wrong. To be more specific, a prediction that puts
a 74 percent chance on an outcome should be “wrong” about 26 percent of the time.
Here’s that list of situations that occur about 26 percent of the time (specifically,
between 25 and 30 percent of the time). Not all of these are true probabilities; some are
just frequencies. But they all give a sense for what 26 percent means.
■ The odds of rolling a 9, 10, 11 or 12 with two dice
■ The chances that a blackjack casino dealer busts
■ The percentage of calendar years since World War II that the Standard & Poor’s 500
has declined
■ The share of days in which it rains in Kansas City (as it did Monday, postponing a
baseball playoff game)
■ The frequency with which a 25-year-old woman is shorter than 5 feet 3 inches
■ The frequency with which a 25-year-old man is 5-11 or taller
■ The odds that a National Football League defense prevents a first down on third-andone.
■ The percentage of full-time graduate students in electrical engineering in this country
who are American citizens
■ The percentage of mothers with children under 18 who stay home with their children
■ The share of Americans who live in California, Texas or New York
■ The percentage of subway cars on the C line with dirty seats or floors, according to the
Straphangers Campaign
If the odds of a Republican victory — in our Senate model and others — remain in the
neighborhood of 74 percent, it won’t be right if the Republicans win any more than it
will be wrong if the Democrats keep control. These models should instead be judged
over multiple elections and years: When they say 74 percent, have they made you
smarter about the state of a campaign?
Amanda Cox and Josh Katz contributed reporting.
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How to Avoid Being Duped by Odds
Tomi Um is credited.
David Leonhardt’s
• October 15, 2014: 2024 – Essay Writing Service | Write My Essay For Me Without Delay
43 o
We now have a 74% chance of a Republican takeover of the Senate, according to The Upshot.
Understand that many people will believe we are predicting a Republican victory. We aren’t.
There is a big difference between saying something will almost certainly happen and saying it will almost certainly happen.
stating that it is more likely than not to occur
We know that many people do not believe that, so allow me to explain. Perhaps more importantly than
any explanation, we have also come up with a list of outcomes that happen about 26
percent of the time — the flip side of 74 percent — which gives a sense for how common
26 percent still is. The list
