From 1985 until 2013, the NBA Finals used a 2-3-2 format to decide the NBA Champion. That is, the first 2 games are played at one team’s arena, followed by 3 in a row at the other team’s, then the last two at the first team’s. However, this year they are changing to the 2-2-1-1-1 format, where each team plays 2 of the first four games at home, then they alternate each game for games 5-7.
So how does this change affect the series? Obviously, it doesn’t change the probability of either team winning or losing. At the end of the day there are still 4 games at one team’s home arena, and 3 at the other. You can put them in whatever order you want, you won’t change the probability either team has of winning the series.
But will the order affect the number of games the series might last? To determine this, let’s assume that the two teams that meet in the finals are equal. But because of home court advantage, let’s say whichever team is playing at home has a 60% chance of winning. We can then calculate the probability that the series goes a certain number of games.
For example, for a team to win in 4 games, they have to win 4 consecutive games. In both formats, they’ll have to win 2 at home and 2 on the road. So the probability is .6*.6*.4*.4 = 5.76%.
I used Minitab Statistical Software to calculate similar probabilities for all 70 different ways a 7-game series can end. Then I added the probabilities together by the number of games the series lasts and which team won the series. Team H is the team that gets to play 4 home games (H for home) and Team A is the one with only 3 home games (A for away).
Team A wins: 2-2-1-1-1
Team A wins 2-3-2
Team H wins 2-2-1-1-1
Team H wins 2-3-2
4 games
5.76%
5.76%
5.76%
5.76%
5 games
9.98%
14.98%
14.98%
9.98%
6 games
18.24%
13.25%
13.25%
18.24%
7 games
12.81%
12.81%
19.22%
19.22%
There is a small difference in games 5 and 6. In the 2-3-2 format, the team with home court advantage has a very small chance of ending the series in fewer than 6 games. The same is true for the team without home court advantage in a 2-2-1-1-1 format. If you only get to play 2 of the first 5 games at home, your chances of ending the series in fewer than 6 games is very small. But then, you get a big advantage of getting to play game 6 at home, if the series goes that far.
Is one format better than the other?When you get to the finals in any sport, the number of games the series goes doesn’t really matter. But it can matter before that. In the earlier playoff rounds, winning a series in fewer games gives your team more rest and fewer games for a potential injury. And we see that in the 2-3-2 format, the team with the extra home game will have to play more games on average than in the 2-2-1-1-1 series (assuming they win the series).
When a team has the extra home game in a 7-game series, it is often a reward for performing well in the regular season. Having a 2-2-1-1-1 format in the earlier rounds of the playoffs furthers that reward by giving the team a better opportunity to end the series in fewer games. Considering this is the format that is used in the NHL, NBA, and MLB, it looks like they’re getting it right. It gives what should be the better team the best chance of having a short series, but is still fair to the underdog (a 4-3 format wouldn't be very fair).
As for the NBA Finals, the change in formats won’t really have that much of an effect. The NBA Finals will look pretty much the same as they have the previous 29 years with the 2-3-2 format. So if the NBA really wants to change things, they would have to do something more drastic.
Perhaps a 9-game series?