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How are the odds in FiveThirtyEight's political election forecasts calculated?

For example, Bernie is predicted to win the majority of votes with odds of "1 in 2 (46%)" as of 2/23/2020. This is neither 1/(2+1) (about 33%) or 1/2 (50%).

Two days later, his odds are "2 in 5 (43%)". Again, this is not actually 2/5 (40%).

Where do these odds come from and why don't they match the percentage?

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    "1 in 2" is an approximation of 46%. – Joe C Feb 23 at 19:27
  • What does "1 in 2" mean? – Tim Feb 23 at 19:28
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    "1 in 2" means (approximately) 50%. – Joe C Feb 23 at 19:29
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    This appears to be referring to journalistic decision of 538.com and others. Expressing as percentages gives an unrealistic level of precision (46%, and not 45 or 47!) and puts too much emphasis on "the prediction" and not the probability. To counteract this 538 and others have been expressing chances as "1 in 2" to mean "about 50%" 46% is roughly 1 in 2. It could also be roughly 3 in 7 or exactly 23 in 50, but since 46% is only an estimate, the fractions are kept as simple as possible. However this is just one journalist's algorithm. There is no particular rule. – James K Feb 23 at 20:26
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    @dandavis - The percentages are very precise in the sense that they are the (probably rounded) results from running their model n number of times and in 46 out of every 100 runs, Bernie wins. But they're also imprecise because the model has a margin of error in its assumptions and output. So they're the exact results of a series of guesses, and thus shouldn't be interpreted as exact predictions. But they're not made up. – Bobson Feb 26 at 0:03
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Expressing as percentages gives an unrealistic level of precision (46%, and not 45 or 47!) and puts too much emphasis on "the prediction" and not the probability.

There is a particular potential confusion when making probabilistic predictions of election results. A reader can confuse "40% probability of winning" with "winning 40% of the popular vote". These are vastly different, but seem to have the same headline number. This was seen in the 2016 election

To counteract this, 538 and others have been expressing chances as "1 in 2" to mean "about 50%". 46% is roughly 1 in 2. It could also be roughly 3 in 7 or exactly 23 in 50, but since 46% is only an estimate of the candidates probability of winning, the fractions are kept as simple as possible. However this is just one journalist's algorithm.

538 has a mathematical model of voting. It takes as inputs the results of polling, and background information like state demographics. It output a number representing the probability of each candidate winning the election. It then rounds this number in two ways, firstly to a whole percentage, and secondly to a fraction with a small numerator and denominator. The web site then uses the fraction as the headline figure.

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