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.