## NCAA Tournament: Kentucky still dominating odds going into Sweet Sixteen (Originally posted on Yahoo!'s "The Signal" Blog)

Once again, we're taking a break from politics to discuss the most pressing upcoming contest in America: March Madness. Kentucky heads into the Sweet Sixteen in the same place it was a week ago, the overwhelming favorite to win the championship at a 29.9 percent likelihood of victory. Mitt Romney is slightly more likely to win the Presidency than Kentucky is to win the NCAA crown, but let's be fair: Kentucky has four rounds left, while Romney only has two.

## Up 2-1 in the Series &#8230;

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.

## 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 …

## 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.