If Romney wins South Carolina, he’s 95% likely to win Florida and Nevada too

On the day of the Iowa caucuses last week, the prediction markets Intrade and Betfair gave Mitt Romney a 44 percent chance of winning the South Carolina primary. After barely winning Iowa and handily winning New Hampshire, Romney's chances in the Palmetto State now stand close to 70 percent.
But Romney's rise does not necessarily reflect growing affection among conservatives in South Carolina, or any major shift in opinion away from Gingrich or Santorum, who have both fared well there at various points. Romney is winning mainly because, well, Romney is winning. If he does win in South Carolina, his odds of a clean sweep of the first five states--Florida and Nevada come next--will rise as high as 95 percent, according to the markets.

At The Signal, we sometimes draw analogies between politics and football, and here is a great example of how the two sports differ. When the 13-0 Green Bay Packers lost to 5-8 Kansas City, as they did in week 15 this year, the Packers' odds of winning the following week barely dropped, if at all. Barring injuries or other longterm factors, any two football games are, for the most part, independent, like two rolls of a roulette wheel.
In politics, however the outcome of a vote in one state depends very much on the outcome in other states. Traders on prediction markets know about this tendency, and reflect it in the prices they set for political contracts on the exchange.

Candidates chances of winning South Carolina Republican primary, January 1-12, 2012
As of this writing, Intrade lists Romney with a 70 percent chance of winning South Carolina. Meanwhile, another contract on Intrade assesses his chance of going undefeated all the way through Nevada as not much less than that: 67 percent. What does it mean? It means that if Romney hangs on to win the Palmetto State, the market says he has a whopping 95 percent chance of grabbing the most delegates in Florida and Nevada too.
Notice that this estimate is much higher than what you would get if the three states were truly independent. In that case, Romney's fate in South Carolina wouldn't matter for Florida and Nevada, and his likelihood of winning both of the latter two states would be about 82 percent, not 95 percent. (For those who are fuzzy on probability math, we get the hypothetical 82 percent by multiplying his individual odds in Florida and Nevada together: 0.89 times 0.92. We get 95 by dividing Romney's chance of winning all three states by his chance of winning South Carolina alone: 0.67/0.7.)
In the last 24 hours, Romney's odds of capturing South Carolina have dropped from 80 percent to 70 percent, perhaps as attack ads take their toll. (Like football, injuries do matter to the odds!) What seems to be clear is that, were it not for those two wins already under his belt, he'd be faring far worse.