NBA Playoff Plinko

June 15, 2010

With the Los Angeles Lakers down 2-3 in the NBA finals and hosting the Boston Celtics in Los Angeles, it is fun to speculate about what might happen in tonight's Game 6. There are several reasons to speculate that the Celtics are the likely victors tonight. For one thing, the Lakers have miserable history against the Celtics in the Finals. For another, our previous analysis suggests that, even though the Celtics (50-32) have a worse record than the Lakers (57-25), the Celtics have a 57% chance of winning Game 6.

Fig. 1: NBA Playoff Plinko. The team with the better record at the end of the season (the "better team") is awarded home field advantage and hosts Games 1, 2, 5, and 7 (light grey shading) whereas the worse team hosts Games 3, 4, and 6 (dark grey shading). Circles represent the record after each round of the playoffs and the size and "redness" of the circle represent the number of times such a record has been observed in the NBA playoffs since 1984 (mouseover for value). Click on a circle to see the probability of the better and worse team winning under these circumstances. Line thickness and opacity quantify the probability of each team winning; moves to the right indicate that the better team won whereas moves to the left indicate that the better team lost (mouseover for value; click to select).

The aim of this blog post is to determine whether it is even reasonable to extrapolate our Playoff Plinko analysis from the NHL playoffs to the NBA playoffs. To address this issue, I generated a Playoff Plinko diagram (Fig. 1) for the NBA playoffs from all seven-game playoff series since the 1984-85 season, all of which are played in the 2-2-1-1-1 format. Note that this excludes the first round of from 1984-2003, when the first round only had five games.

Just like the NHL playoffs, the better team in the NBA playoffs has a huge advantage of winning at home (over 75% for the NBA) and playing at home for the worse team only mitigates the skill of the better team.

One considerable difference between the NBA playoffs and the NHL playoffs is that the NBA playoffs are more lopsided than the NHL playoffs. Before a playoff series even starts in the NBA, you would expect the better team to win 77% of the time whereas you would expect the better team to win 63% of the time in the NBA.

In spite of its lopsidedness, another interesting difference between the NBA and the NHL is that the elimination effect during Game 6 really only benefits the worse team. The better team only has a 52% chance of winning Game 6 when they are leading the series 3-2 whereas the worse team has a 70% chance of winning Game 6 when they are leading the series 2-3. In practical terms, this means that the Celtics have a 76% chance of winning the NBA Finals (click on the "2-3" circle in Fig. 1 to see for yourself).

contributors to this post

headshot of Dean Malmgren
headshot of Mike Stringer