With the recent announcement that the NBA is changing the format of playoffs by seeding the playoffs based solely on records, we take a look at the complexity and reasoning for dividing out the 30 NBA teams into 6 divisions. For Major League Baseball and the National Football League, divisions serve a major role in scheduling.

An MLB team plays their division opponents 18 times each, accounting for 72 of their 162 games; 44.4% of their games are division opponents. Non-division opponents within the same league are given two to three series each, leading to approximately 6-8 games; accounting for another roughly 70 games. This leaves the remaining 18-24 games to be “Inter-League” games.

An NFL team plays their division opponents 2 times each, accounting for 6 of their 16 games; 37.5% of their games are division opponents. Each NFL team plays an entire division within conference, as well as an entire division out of conference, accounting for 8 more games. The final two games are teams who finished with the same rank within their respective division, within the same conference. The divisions entirely dictate the schedules.

In the NBA, this is not quite the case. Let us consider the 51 – 31 Portland Trailblazers from the 2014 – 2015 NBA season. Due to their Northwest Division championship, Portland guaranteed fourth place in the conference seedings for the Western Conference playoffs. With respect to the conference, Portland finished in sixth place; 16 games behind Golden State, 5 games behind the Los Angeles Clippers and Houston Rockets, and 4 games behind the San Antonio Spurs and Memphis Grizzlies. In the NFL and MLB, an argument can be made that the records don’t adequately reflect the unbalanced schedule. However, in the NBA, the schedule is not unbalanced.

Portland’s schedule saw every team from their division: Oklahoma City, Denver, Utah, and Minnesota, play 4 times each. This leads to a total of 16 games within division, or 19.5% of their total schedule. Similarly, Portland played the Pacific Division’s Lakers, Clippers, and Suns 4 times apiece while playing the Kings and Warriors 3 times each. Similarly, Portland played against the Southwest Division’s Spurs, Mavericks, and Grizzlies 4 times apiece while playing the Rockets and Pelicans 3 times each. This led to a relatively balanced schedule of 52 in-conference games.

The remaining 30 games, and the reason why some teams are only played three times instead of four in within conference, are split across the 15 out of conference teams, resulting in 2 games apiece. As it is seen, divisions are meaningless in the NBA when compared to the MLB and NFL with regards to scheduling and playoff seeding.

So what makes the divisions meaningful? A simple answer is bragging rights. Therefore, the divisions should be optimal relative to locality. If a team is competing for second or third in their respective division, then it makes sense that those teams as close to each other locally as possible so that the fans can have access to the games. We find this phenomenon relatively consistent in other sports: Chicago Bears fans travel four hours north to root against the Green Bay Packers. Yankees and Red Sox fans have a habit of invading each others’ spaces; as well as the spaces of the Baltimore Orioles on a consistent basis. In this effort, we take a look at re-aligning the divisions that make the most sense by optimally shrinking the travel time between division opponents.

Taking a look at the current NBA divisions, we see that there are non-overlapping sets of divisions. This is not true for the NFL or MLB. The downside to this is that we can never expect a “subway series” for an NBA championship. The question is, is this the best partitioning of the NBA teams into six divisions?

To give an answer to this question, we utilize an algorithm called k-means clustering. A simple form of this algorithm is to select the number of clusters, or in this case divisions, and identify the six optimal coordinates such that the points closest to each of these coordinates form a cluster. To measure closeness, we can use the standard square-error distance or absolute error distance. The goal is to minimize the distances from each of the six points to each point within their respective cluster; as well as minimize the distance across all clusters. This algorithm is fast for this application and completes in under one second. However, the obtained result is not the divisions we expect.

Here we see that there are indeed six divisions. However three divisions have six teams, one division has four teams, and another division has three teams. This poses a scheduling nightmare and gives the revised Mountain Division of Utah, Phoenix, and Denver a much easier path to earning a division title than their non-division counterparts.

To rectify this, we impose a constraint by forcing each division to have five teams. This is a much more difficult algorithm to compute as we now must place a penalty on the original k-means clustering algorithm by penalizing distance measurements if they have more or less than the prescribed five teams. By doing this, we obtain a slightly different alignment of divisions.

We see a mix of the clustering algorithm and the original NBA divisions. For instance, the Southeast and Atlantic Divisions are kept in tact. Indiana is siphoned off from the Central Division and places into the South Division. Their replacement is Minneapolis. The Pacific Division returns to their glory 1980’s days with the California teams and Portland. Seattle and Phoenix aren’t part of the old Pacific Division as they are now a part of the Mountain Division.

While we have identified the smallest regions that partition the NBA teams into conferences, we see no change in actual travel schedules of the teams. We also find no significant impact of divisions other than bragging rights. Ideally, we would split the conferences back into two divisions as in years past and include two more teams into the NBA. Ideal locations would be Kansas City and Seattle.

Whatever the divisions may be, the fact of the matter is that removing incentives for winning a respective division should not warrant a higher seed in the playoffs. Winning a division should justify a guaranteed spot in the playoffs, just not a high seed. With the slight step from removing the top three playoff spots for division champions to guaranteed top four spot for division champions, the writing for this move has been on the wall for nearly a decade.

As a final numbers display, in 2008 we witnessed the Los Angeles Dodgers make the playoffs due to winning the National League West with an 84-78 record; best for eighth place in the National League. They were instead granted third seed for the playoffs while four other teams with better records from their own league/conference watched from home. This type of environment is possible with multiple small divisions with a large dependency of scheduling on those games. In the case of the NBA, this has never happened in the three division format. The closest we came was the 2005-2006 Miami Heat with a 44-38 record, still nine games better than the first team out of the playoffs.

The NBA made a good move with the playoff format change. It will be interesting to see more appropriate match-ups at every round of the playoffs.