Hockey and Conditional Probability

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.