May 2012

Hockey and Conditional Probability

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Update 5/27 at 2 PM ET: With the Devils capturing the Eastern Confernece on Friday the markets bore out my assumptions. The Kings were 53.1 percent likely to win against the Eastern Confernece champion when it was 25 percent likely to the Rangers and 75 percent likely to be the Devils. Now that the opponent is 100 percent likely to the Devils they are 58.9 percent likely to win the Stanley Cup. Had the Rangers prevailed they would have fallen to about 42 percent likely to win ...

Game 6 of the Eastern Conference finals is tonight, Friday May 25, between the New Jersey Devils and the New York Rangers. The Devils lead the best of seven series 3 game to 2 and are in a strong position to play the Los Angeles Kings for the Stanley Cup. Currently, the likelihood of winning the Stanley Cup is the Los Angeles Kings 53.1 percent, Devils 31.7 percent, and Ranger 15.2 percent.

The Kings are most likely to win the Cup because they have one less round to win. They are already in the finals with 100 percent where the Devils and Rangers face uncertainty in regard to their place in the finals.

The Devils need to win one of the next two games to get into the finals. They are approximately 75 percent likely to achieve that. Thus, the Rangers, who need to win both of the next two games, are 25 percent likely to make the finals. I am assuming the teams are about 50 percent likely to win any individual game and the game are independent (i.e., a loss tonight does not make it more likely the Rangers win Game 7). In reality, the Devils are slightly more than 50 percent to win tonight and the Rangers would be slightly more than 50 percent to win game 7, if necessary.

Based on the current odds, if the Devils are 75 percent to make it to the finals, then they are just 42 percent to beat the Kings when they get there. They are 31.7 percent to win the finals, with a 75 percent likelihood of playing in the finals, thus, 31.7 / 0.75 = 42 percent.

If the Rangers are 25 percent to make it to the finals, then they are 61 percent to beat the Kings when they get there. They are 15.2 percent to win the finals, with just 25 percent likelihood of playing in the finals, thus, 15.2 / 0.25 = 61 percent.

If the markets are perfectly efficient, a Devils win tonight should push the Kings up to 57 or 58 percent from their current 53, as they would have a 100 percent likelihood of facing the Devils. If the Rangers win tonight the Kings should drop to about 47 or 48 percent as they will be a little more than 50 percent to face the Rangers in the finals. If the markets are extremely efficient, you can see them move in real-time as the game progresses.

In the interest of full disclosure my ancestral home is New Jersey and I am proud Devils fan.

David Rothschild is an economist with MSR-NYC. He has a Ph.D. in applied economics from the Wharton School of Business at the University of Pennsylvania. Follow him on Twitter @DavMicRot.

The purpose of the census, as outlined in the Constitution, is ostensibly to allot House of Representatives members. But it also provides an essential snapshot of the population. In modern society, however, the demographics of the country change far too rapidly to capture adequately in a decennial survey. That’s why the Census Bureau also conducts an annual poll of a large sample of the population, known as the American Community Survey, to fill in the gaps in the data. Now, the House of Representatives is threatening to cut this essential product on the basis that it violates one’s privacy.

Eliminating the ACS would be devastating to the economy. Just as political operators use polling data to guide the deployment of resources, governments and businesses use the data to decide how to invest on a much larger scale. A business involving transportation may need to measure a sample of commuters by distances and types of vehicles. A business involving construction may need to determine the sample of homeowners and renters by years of occupancy, and how they shifted over the last few years. Businesses of all sizes rely on its data to make investment decisions, meaning the United States recovers every penny invested in the survey in many times over in economic growth.

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When Barack Obama announced his support for gay marriage on May 9, most commentators immediately turned to how this would affect his chances in the 2012 campaign. Now that a few days have elapsed, we can say with confidence that the effect was negligible.

The following chart illustrates the most accurate and real-time forecasts, derived from prediction market data, two days before and after the announcement.

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There are many ways to keep score on whether Barack Obama or Mitt Romney has better odds of winning the general election, which is almost exactly six months away. Here at The Signal, we are fervent evangelists of the political prediction markets, where people place real money on the line to bet on the winner. These markets proved to be more prescient than polls in the Republican primary.

Many journalists prefer to stick to reporting on raw daily polls. While these surveys offer valuable information, it is dangerous to read too much into the daily fluctuations, especially this far in advance. Currently, Rasmussen has Romney leading Obama 49 to 44, while Rueters/Ipsos has Obama leading Romney 49 to 42. This disagreement is due to several common sources of error that occur on any poll. Averaging several polls to get an aggregate figure, as RealClearPolitics does, helps ameliorate these errors.

Upcoming work by Bob Erikson of Columbia and Chris Wlezien of Temple, recently presented at the Midwest Political Science Association conference, demonstrates a second problem with following the daily polls too closely. The researchers looked through past presidential elections, aggregated the national polls, and created the most effective forecast based on that data. They found that, even when properly aggregated and averaged, national polls do not have predictive power at this point in the cycle.

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