Up 2-1 in the Series …

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.

 

Explaining the Favorite-Longshot Bias in Prediction Markets

To illustrate the favorite-longshot bias, assume that, six months before an election, an investor believes the Democratic candidate has a 95% chance of winning. There are several reasons why this investor would not pay a full $0.95 for a contract that pays off $1 if the Democratic candidate wins. First, there is an opportunity cost of the bet being held for upwards of 6 months, because there is limited liquidity in many markets. The investor's money is tied up in this market, when it could be out doing something else: sitting in a bank, providing capital for a startup, being used to consume something, etc. The cost is literally the opportunity to be doing other things with the money while it held up in the market. Secondly, there are transaction costs of around $0.015 per $1 invested, thus the investor will actually bid up to whatever she determines is the optimal price minus the transaction cost that will be lost when the bet is processed. Finally, if there are two bets that are equal in expectation, the investor gains more utility from betting on a longshot. It is not clear to researchers whether investors are risk loving (i.e., they gain utility from doing risky things) or beset by misconceptions or Prospect Theory (i.e., they overvalue small probabilities and undervalue high probabilities), but it is accepted in the academic literature that they are not risk neutral.

All this brings me to the subject of Intrade's market for the Democratic Nominee for President of the United States in 2012. Currently, Mr. Obama is trading at a bid of $0.910 per $1 and an offer of $0.937 per $1 for a price of $0.924 per $1. If this seems too low to you, let's examine why you might be correct.

(I should note that the rules of the market specifically state that the contract is voided if any nominee in the market passes away, so that is not an issue.) Let us consider our three remaining causes of the favorite-longshot bias:

First, the market will not settle until September of 2012 (i.e.,15 to 16 months from now). This means that any money tied up in this market is lost for a consider amount of time. Thus, there is a large liquidity cost.

Second, Intrade has just switched to a flat fee model, while there are still transaction costs, they are much lower for Intrade than for any other market, so this is not a big factor in the low price.

Third, people get more utility out of holding (and dreaming about) the longshot Mrs. Clinton to be the nominee, with a bid at $0.030 and an ask at $0.040 per $1, than the favorite Mr. Obama, so they are willing to bid more than is realistically likely in order to own the contract. Again, I am not sure if it is the utility of dreaming about/holding onto longshots, or is it because people are miscalculating long odds. Yet, if an investor deemed an investment in Obama and Clinton equal in their likely payout, they are going to gain more utility from the Clinton investment.

While the direct translation of these prices would say that Mr. Obama has 92.4% likelihood of the nomination and Mrs. Clinton a 3.5% likelihood of the nomination, my calculations would place it closer to 99% and 0.2%. Which one seems more realistic to you?

 

Huckabee and Trump Depart the Race

Within the past week, both Mike Huckabee and Donald Trump announced that they would not seek the Presidency in 2012. The prediction markets had plenty to say about these candidates both before and after they dropped out of the running. Both men's likelihood of winning the Republican nomination peaked at nearly 9%, but the markets show that the end of their campaigns came about under very different circumstances. Below is a chart of Mike Huckabee's likelihood of winning the Republican nomination, where the red line marks the moment when he made the announcement he was not running during his weekly Fox News TV show. One day before his on-air announcement, when rumors of an impending announcement on his campaign began to spread, this market tanked rather quickly. The market was reasonably quick to recognize that he was going to drop out of the race. However, it appears as though the market began to second-guess itself over the following 24 hours – perhaps due to conflicting rumors – and by the time of his announcement, the Huckabee contract regained about 1/3 of the value lost during the previous day.

Donald Trump's likelihood of winning the Republican nomination peaked just before President Obama released his long-form birth certificate on April 27, and began its precipitous decline just as Obama announced the death of Osama Bin Laden on May 1. The final drop on May 17 coincided with his announcement that he will renew his job as a television personality, rather than run for President. While Huckabee was an extremely viable candidate prior to his announcement, Trump had already been trending towards irrelevancy, even before his announcement.

I regret that we had not been tracking Jon Huntsman's chances until very recently, but the other two candidates who clearly benefited the most probability of victory with the Huckabee announcement were Mitt Romney and Tim Pawlenty. As I note in the first chart there are really two separate noteworthy events in Huckabee's withdrawal from the race. The first occured when rumors of an impending announcement were circulating and the second occurred a day later when his decision was announced. The first reaction of the market was to assume that Romney was going to really benefit from Huckabee's departure. After the rumors began, going into the formal announcement (where the red line is located), Romney had absorbed almost all of the Huckabee's total loss. Yet Romney gained little from the formal announcement while Pawlenty, who had already fallen back down to his pre-rumor level, got a nice boost from the actual announcement. One thing is clear from this analysis: the market is undecided on who benefited from the Huckabee announcement.

Death of Osama on 2012 Election

A key question in political circles over the last few days has been the effect of the death of Osama Bin Laden by the U.S. armed forces on the outcomes of the 2012 election. Indubitably, the event is beneficial to the Democratic party and President Obama in particular. Polls conducted in the days following the event gave Mr. Obama at 9 percentage point increase in approval. There are a few points to consider on the prediction market's reaction to the event.

First, it definitely increased President Obama's probability of victory in 2012. On average his probability of victory has gone from around 60% to around 63%. Second, both Intrade and BetFair, the two leading markets, took a surprising amount of time "digesting" the information. Today, seven days after the event, they are still moving sharply. Prior to Mr. Obama's press conference announcing the death of Osama, the probability is relatively flat for weeks, but after the event there is a distinct trend in both markets that is still visible. Third, the two markets ultimately disagreed on the trajectory of the "digesting". Betfair is digesting the news by moving even further in favor of an Obama victory and Intrade, from an almost identical position, is moving back toward the pre-Osama death probability of victory. I am not going to discuss here the true underlying value of Osama's death, beyond the values provided by the markets, but I can state that in a few days arbitrage will bring these two markets together and we can have a clearer picture of what the markets feel is the underlying value of Osama's death on the 2012 Presidential election.

There appears to minimal effect on the House. The probability of the Democratic party regaining the House remained flat through the last two weeks.

Prediction Markets Working Well on Republican Nomination

Three recent polls have come out in regard to the Republican Presidential Nomination. These polls by CNN, Fox, and NBC have Donald Trump in first, third, and second respectively. Further, they have Mitt Romney in fourth, second, and first respectively.

Imagine that there is three types of information about the current field of Republican candidates: first is known to the average Republican voter, second is known to political informed people, and third is unknown. An example of the first type of information for Trump is that he is a popular TV personality and for Romney that he is a former governor of Massachusetts. An example of the second type of information for Trump is that his business affairs and personal life are very rocky and for Romney that he was an extremely successful businessman. The third type of information is all of those things that will happen between now and Election Day, for which is unknown.

In short, differences between poll-based and prediction market-based forecast of who will ultimately win the Republican nomination hinge heavily on the second type of information: information that political informed people in the prediction market know and the average Republican voter does not know now, but will know on Election Day. In this situation, that type of information is generally neutral or positive for Romney, Tim Pawlenty, and Mitch Daniels, but negative for Trump. That is why although Trump is trending second in the polls of today, the self-selected politically informed people who gamble in the prediction markets have Trump as the fourth most likely person to get the Republican nomination. They are betting that the public will learn what they know about Trump and then become less likely to vote for him, relative to the other candidates.

Volatility in Baseball Probabilities

Let me pose a question that address in further as this blog progresses: What is the appropriate level of volatility in an efficient forecast? Here is the forecast of the World Series winner for the three most probable teams: Phillies, Yankees, and Red Sox, based on BetFair prices. The probabilities cover the first week and a half of the season. Useful volatility represents new and meaningful information, un-useful volatility is just random movement. While the starting pitching has been a little less than amazing, the Phillies (7-2) are basically achieving at expectation and their probability remains essentially flat. Having to make the playoffs and then win three rounds, it is essentially impossible for them to move much beyond 25% this early in the season, even if they win every game. The Yankees (5-4), just dropped 2 of 3 from the Red Sox (2-7), but remain slightly up and the Red Sox slightly down from the start of the season. Does it seem reasonable that the Red Sex have a 13% of winning the World Series? Does going 0-6 in a 162 game season mean they are 25% less likely to win or does it provide minimal new information? The Yankees are clearly moving upward in because of the probability of making the playoffs the AL East winner increases their chances of doing well in the playoffs, but is that putting too much weight on the first step? These are questions I will address in later posts …

Government Shutdown

 

The table is now not as useful as a chart of the evening. The deal was struck at 10:30 PM and the probability derived from Intrade's prices moved just as the deal was being announced. That being said, it was generally moving in that direction as some information was dispersed. At 10:30 PM HuffingtonPost and others were still giving very neutral headlines, while Intrade was in its steady march downward towards no shutdown.

 

Watch this number as we approach midnight! It is currently at 55% with 6 hours to go …

NBA Playoffs

My local NBA team has left us, so I do not follow basketball as closely as I did in the past, but it is hard not be interested this year. The Heat are a huge news story and the playoffs will generate a buzz not felt in years. Below is the chart of how of the price of $1 contract on the Heat winning the NBA championship and, for comparison, the Lakers are on the chart as well. The first thing to notice is how dramatically high the price was for the Heat in the early part of the season and how far it has fallen. The second thing to notice is that it has actually fallen well below the Lakers as the season nears its end.

Below is a second chart, that shows the next three most probable teams. First, look at the two West teams, notice how they mirror each other (the Mavs, not shown, have held steady at a very consistent $0.04 to $0.05). Second, compare the Celtics and the Heat early in the season and the Bulls and the Heat late in the season and you can see that the two teams mirrored each other for parts of the season, while the third team was relatively stable.Yet, despite the that mirroring, the sum of West teams (Lakers, Spurs, Mavs, and Thunder) has been moving slowly upward and the East teams (Heat, Bulls, Celtics, and Magic) has been moving slowly downward.

What this all means is that the market is now assuming that winning the championship, once your team gets there, is basically a toss-up, while midseason the East champion was much more likely to win the finals. Still, the main driver of the indivdual team prices are a reflection of their relative strength within the conference … right now the Lakers are looking so strong, not because they are necessarily any better than the Heat, but they have a much easier path the NBA finals.

Libya and Gaddafi

The dotted line you see here represents the exact point in time that the UN passed its resolution for a no-fly zone over Libya. The interesting thing about this line is that the price for a contract on Gaddafi not being in power past the end of the year reached a local peak as it passed, not after. The reason is that Intrade did a good job here incorporating the information about the UN and the actual passage became a fete-de-complete. More important, the price has been impressively stable even as events swirl back and forth on the ground in Libya. The contract is for the end of the year and I take the stability as a sign of a mature and liquid market, where Intrade had, in the past, had issues with dramatic volatility in similar situations … Finally, what most people really care about, I would translate the current price (at 1:00 PM EST on Thursday, March 31) into a probablity of 85% that Gaddafi does not make it into the New Year as the ruler of Libya.

Mrs. Palin's Political Trouble from Saturday's Massacre

Immediately in the aftermath of Saturday's assassination attempt on Congresswoman Gifford, that resulted in the death of six people including a federal judge and a nine year old girl, the media began speculating on the political fallout to Sarah Palin's 2012 Presidential aspirations. In March she had put out an advertisement with a target on Congresswoman Gifford and then told asked that her followers "Don't Retreat, Instead – RELOAD!" Thus, after the massacre people began to discuss her contribution to both the specific target and the general heated atmosphere in politics; regardless of her complicity, and thus far there is no direct evidence the assassin followed Mrs. Palin, talk of it has political consequences. As several blogs have already noted, the market for her 2012 Republican nomination responded immediately … on Intrade. She lost over 1/3 of her probability in the immediate aftermath of the massacre. Yet, the movement a different market, Betfair, was much smaller, as it was already trading lower for Mrs. Palin; Betfair has consistently had less confidence in Mrs. Palin's viability as the Republican nominee. The chart is below: