In Princeton, we’re making sure we have bottled water and other supplies. It’s not clear how serious Hurricane Sandy will be. But we are grateful for the advance warning that is made possible by the National Weather Service.

Seeing as how predictions are so useful, Andrew Ferguson and I have decided to put the Obama re-elect probability in the topline. We give two probabilities, which are built on the same assumptions that went into calculating the “strike zones” in the history graph. The “Random Drift” number is a minimum (conservative) probability, and the “Bayesian Prediction” is my best shot at calculating the actual win probability. In the coming 10 days, the two numbers will converge.

I will list the assumptions again. This will make the most sense if you know a little about what we do here at the Princeton Election Consortium.

Starting from a snapshot of today

Both predictions (“random drift” and “prediction”) start from a current snapshot of polling conditions, the Meta-Analysis of State Polls which forms the core of this site. The snapshot is listed in the top line above. It is currently Obama 297 EV, Romney 241 EV, Meta-margin Obama +1.96%. This predicts what would happen in an election held today.

To calculate this snapshot, we (a) use recent polls for each state (3 polls or 7 days, whichever is greater) to calculate the probability that one candidate is ahead, (b) calculate the exact distribution of all 2^51 = 2.3 quadrillion outcomes, measured in terms of electoral votes (EV), and (c) take the median of the distribution to get an expected outcome.

In addition, we calculate the amount by which polls must swing overall to create a perfect toss-up. This quantity is just like a two-candidate margin that people are used to seeing in polls, so we call it the Meta-Margin. Both the EV estimator and Meta-Margin are extremely precise, and performed very well on Election Eve in 2004 and 2008.

Projecting into the future

Between now and Election Day, opinion may move toward Obama or toward Romney. But by how much? To turn the snapshot into a prediction, we have to estimate how much movement may occur. There are two ways to do so. I have explained these before (“The Presidential predictor sharpens,” September 29). Here is how they fit into what’s listed above.

Random drift. Using past races, I have estimated how much the Meta-Margin is likely to fluctuates over time. In this “random drift” model, I assume that opinion is equally likely to move in either direction. (Nerds: at N days before the election, the drift has a standard deviation of 0.4% * sqrt(N).) If the Meta-Margin stays above zero, then Obama wins. Today, the probability of an Obama win is 89%.

Bayesian prediction. Here I make an additional assumption, that the final outcome is likely to be drawn from the values that the Meta-Margin has explored this year. This is equivalent to the idea that the Meta-Margin is more likely to move towards its average (Obama +3.1+/-1.3%) than away from it. This has been the case in past elections. In statistics this is called a “Bayesian prior,” as in prior assumption. Today, including that prior gives a win probability of 97%.

The prior is also used to calculate the red and yellow “strike zones” in the history graph.

In my view, the prediction is the correct probability. But if the prior seems like an unwarranted assumption to you, then use the Random Drift probability instead. This is a more conservative estimate. Anyway, over the coming days these probabilities will converge to the same value.