Odds or Probability?
What are the odds you know the difference between odds and probability? While not the same, the two words often are conflated in lay discussions and, perhaps, most ironically, in a recent New York Times article, How Not to Be Fooled by Odds. Numerous times, the article used the word “odds” when it should have used the word “probability.” For example, the very first line states, “The Upshot puts odds of a Republican takeover of the Senate at 74 percent.”
To quickly illustrate the difference between the two terms, the odds in favor of heads in a standard coin flip is one to one (in mathematical notation, 1:1). The probability of heads is 50 percent. The Times should have said either
- “The Upshot puts the probability of a Republican takeover of the Senate at 74 percent;” or
- “The Upshot puts the odds of a Republican takeover of the Senate at about 3 to 1.
The Ask Dr. Math forum has several entries on odds versus probability. Summarizing, one way to conceptualize (non-technically) the probability of an event is the number of ways that an event can occur divided by the total number of possible outcomes. The probability of heads in a fair coin flip is 1/2 (50 percent). The probability of drawing a red card from a standard deck of cards is 26/52 (50 percent). The probability of drawing a club from that deck is 13/52 (25 percent). And so on.
The odds for an event is the ratio of the number of ways the event can occur to the number of ways it does not occur. For example, using the same events as above, the odds for:
- the coin flipping heads is 1:1 (said “1 to 1”)
- drawing a red card from a standard deck of cards is 1:1; and
- drawing a club from that deck is 1:3.
Probabilities should also be stated in the range zero to 100 percent (or the decimal or fractional equivalent). Odds are typically expressed as two integers.
Understanding the distinction between odds and probability is not just convenient for gambling or card-playing or writing New York Times stories. Odds are used to express essential information about health benefits and risks. The odds ratio, for example, is an important way of communicating information about the relative benefits of one health intervention over another. Another way of communicating such information is through relative risk. In many common situations, these numbers are quite different, and the difference matters.
A highly simplified example illustrates this: Suppose that 18 out of 20 patients (90 percent probability, odds of 9:1) in an experiment lost weight while using diet A, while 16 out of 20 (80 percent, odds of 4:1) lost weight using diet B. The relative risk of losing weight by choosing diet A over diet B is 1.125, while the odds ratio is about 2.25.
The reasons a medical article might choose one method of reporting over the other are complex, but the message here is that sorting that out starts by being clear about the difference between probability and odds. As for your own writing, when in doubt, use probability rather than odds. Both concepts are often difficult for readers to grasp, but odds are usually harder.