### June 2011

### Mr. Huntsman: A Case Study in the Difference Between Polls and Prediction Markets

DavidMRothschild on June 08, 2011 @ 3:50PM

This morning Nate Silver, writing in his blog in the New York Times, notes the disconnect between a few recent polls and Intrade's prediction market in regard to the likelihood of Mr. Huntsman ultimately gaining the Republican nomination for President. He is concerned that Republicans are giving Mr. Huntsman the highest "unacceptability" ratings of any major Republican vying for the 2012 Presidential nomination; 51% of Republicans state that he is unacceptable in recent polls. Yet, despite these unacceptability ratings, Mr. Huntsman is being given 13.3% likelihood of the Republican nomination by the prediction markets, placing him in a strong third place (the fourth place contender, Ms. Palin, is at just 6.7%).

As Mr. Silver notes, Mr. Huntsman is unknown to most Republicans and, if they know anything, they are likely to only know that he was an ambassador for President Obama. I will quote the comment on the New York Times article written by "David from NJ" (who, despite the description, is not me!): "The press on Huntsman has characterized him as a moderate and his role as ambassador to China puts him in the Obama camp. The net is he falls in the same group as Romney and Pawlenty, with possibly less well known knowledge about his positions than either."

The first reason that prediction markets (Intrade and Betfair are very close on these numbers) differ from the polls is that prediction markets take into consideration what the Republican voters will learn between now and their primary elections, while polls do not. Knowledgeable prediction market users are expecting voters to eventually learn what "David from NJ"already knows: that Mr. Huntsman is not in the Obama camp, but a standard Republican. The prediction markets are predicting that those unacceptability numbers will disappear in the next few months.

The second reason that prediction markets differ from the polls is that the prediction market users assume that Mr. Huntsman, in expectation, matches up the best against Mr. Obama in a general election. Mr. Obama has a 62.7% likelihood of winning the general election, but that number is related strongly to the likelihood of meeting his different potential Republican challengers. He is more likely to beat some challengers than others.

Mr. Romney has a 30.0% likelihood of winning the nomination and an 11.7% likelihood of winning the general election. When thinking about "electability" what I think about is the likelihood of winning the general election assuming the candidate wins the nomination. For Mr. Romney, that likelihood is 39.0% or 11.7/30.0; Mr. Romneyâ€˜s electability is similar to Mr. Pawlenty (33.5%) and Ms. Palin (37.9%). All three of these fall in the middle range, making them about as likely to win a general election as the average Republican challenger against Mr. Obama. Ms. Bachman, who is a very extreme candidate, has an electability of just 27.6%. If she won the nomination, Mr. Obama's likelihood of wining the general election would shoot up to nearly 75%.

Mr. Huntsman has a 48.5% likelihood of winning the Presidential election,contingent on winning the Republican nomination. Thus, the second reason that the prediction markets think Mr. Huntsman is so likely to win the Republican nomination, despite his initial weak polling numbers, is that he is the most viable candidate for the Republicans in the general election. He is the only candidate that the markets think could turn the general election into a dogfight.

As of today, the championship series in both basketball and hockey stand at 2 games to 1 game. PredictWise has determined that the Heat (up 2-1) are 75.9% likely to win the NBA championship and the Canucks (up 2-1) are 74.6% likely to win the Stanley Cup. For the sake of this article, I will say both currently leading teams are about 75% likely to win their respective titles.

There are ten possible scenarios of wins (W) and losses (L) that can occur when a team has a 2-1 advantage in a best of seven series. In six scenarios they win the title (WW, WLW, WLLW, LWW, LWLW, LLWW) and in four scenarios they lose the title (WLLL, LWLL, LLWL, LLL). The probability that they win the title is sum of the probabilities of the first six scenarios. If I assume that any given game is 50% for both teams (i.e., the teams are both equally likely to win any given game), the first six scenarios add up to 68.8% probability that the leading team will ultimately win the title. Thus, the market (and consequently PredictWise) does not believe that each game is independent and does not believe that both teams have a 50% likelihood of winning any game.

The market may be assuming that the leading team has a greater than 50% chance of winning any future game. If that is the case, to give the leading team a 75% probability of victory, the market needs to assume that they have 55% likelihood of winning any given game.

The market may be assuming that there is a home arena advantage, where both series have two games left at each team's home arena. If that is the case, to give the leading team a 75% probability of victory, the market needs to assume that the home team has a 75% probability of winning any given game. The leading team just needs to win its two home games, while the team that is down 2-1 needs to win at least one game on the road.

The final thing to consider is whether or not streaks affect a team's chances of winning. If the leading team wins game 4, on the road, and takes a 3-1 lead, does that make them even more likely to win game 5? If the team that is down 2-1 wins the next two games to take a 3-2 lead, does the other team become demoralized?

Enough with the theory, both leading teams are on the road for game 4. The Mavericks and Bruins, both down 2-1, are approximately 55% favorites to win the game in their home arena. Thus, there is clearly a home advantage, but not to the extreme necessary to cover the 75% probability of the leading team winning the title. Thus, there must be some element of a greater likelihood of victory being assigned to the teams currently in the lead and a non-independence of the different games, where if they win game 4, they increase the likelihood of winning game 5 against a demoralized opponent. In short,the answer is somewhere between these three simplified explanations.