Friday, September 28, 2018

Published 10:45 PM by with 0 comment

How Do I Convert An Election Poll Into A Win Probability

You normally see polls as something like 51% candidate A, 47% candidate B, and 2% other. How do you estimate a win probability from that?

Basic Idea


Real predictions like those on upshot or 538 use complicated models with a lot of factors (turnout likelihood, funding for each campaign, etc.). However, you can get a rough estimate of win probability simply from poll numbers. The basic algorithm is:
  1. get values for each candidate + number of people surveyed in the poll
  2. calculate difference in support for each candidate and standard deviation of that difference
  3. find out what % of the normal distribution from the two numbers given above is less than 0 for the underdog and greater than 0 for the favorite

Step 1

This has to be given to you and it generally is for polls. For this example, assume that the poll surveyed 519 people and found that 52% support candidate A and 48% support candidate B.

Step 2

The difference in support is just the difference in the numbers given. In this case, that's 52% - 48%, or 4%. The standard deviation is a bit harder to find. The following equation works for it:
p1 = candidate A's support
p2 = candidate B's support
n = number of respondents


Plugging in our numbers, we get 4.4%.

Step 3

Converting this to a normal distribution requires software. I made a google sheet that you can use to try out numbers. For our numbers, candidate B has a ~18% chance of winning. The probability distribution for results looks something like this:


For fun, here are a few others:
  • 1000 voters say 52% to 48% means candidate B has a ~10% chance of winning
  • 519 voters say 55% to 45% means candidate B has a ~1% chance of winning
  • 52 voters say 55% to 45% means candidate B has a ~23% chance of winning


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