Over the past couple decades, we have heard effectively the same complaint that the NBA’s Western Conference is simply too tough and that the Eastern Conference teams have it relatively easy. During the last decade, it’s the primary reason that people dismiss LeBron James’ run through seven consecutive NBA finals as a result of the “weak” Eastern conference. As free agency has gotten off to a bang with multiple high profile Eastern Conference players heading west; the question has more so become “Can the West send ten teams to the NBA playoffs instead of eight?”

In this post, we take a look at what if the NBA seeding was completed by rankings instead of their current format of conference and record. The reason I select ranking is due to the fact that the each conference plays a weighted schedule: 30 games out of conference and 52 games in conference. Furthermore, taking a rather standard algorithm and treating it as a probabilistic distribution allows us to incorporate some errors into the model, such as upsets and resting players.

We will then be able to compare conferences and actually quantify what people have been claiming for years. Therefore disproving or affirming the common exclamations about the conferences.

Before We Begin… Ranking Methodology – Colley’s Method

If you haven’t heard about Colley’s method before, I encourage you to read about it. Wes Colley wrote a fairly strong article detailing his thoughts, some of which are incorrect but not egregious. In his article, without understanding the probability theory, Colley proposed a weighted continuity correction to the Bernoulli distribution. The idea is that as teams play against each other, correlations between which teams can beat others will arise; therefore giving every team a small bit of weight based on every game’s outcome. However, Colley missed that the process is weighted (he calls it unbiased), in which we showed that the Colley method is really a biased procedure that can be gamed; if scheduled such as way

That said, since the schedules are standard across the league, I find that there should be no major outcries over using Colley’s method for this analysis.

How NCAA Does It…

Consider the Pacific, Southwest, Northwest, Atlantic, Southeast, and Central divisions as NCAA conferences. Then teams that win their division should be guaranteed entry into the NBA playoffs. There’s two main ways to go about this. One way would be to take the division records only. Another way would be to take the overall records. For completeness, we will look at both for this previous year.Once we identify the six teams guaranteed to make the playoffs, we then select the next ten top teams according to their ranking.

The final seeding for the NBA playoffs would then be the six division champions and the ten best ranked non-winning teams sorted by ranking order.

2016 – 17 NBA Season: West Over the East 246 – 204

For the 2016-17 Season, we saw that the West posted a 636-594 overall record. With each team playing 52 games against their own conference, guaranteeing a .500 record, we see that the West held a 246-204 advantage over the East.

The resulting Colley Rankings are given as

We see that the six division winners are kept within the top nine ranked teams. We also see that the top 16 teams include only eight Western Conference teams; despite the vast difference in the conference vs. conference records.

Scenario 1: NBA Playoffs According to Ranking and Overall Record

If division winners were found by overall records, then we would see the Celtics, Wizards, Cavaliers, Warriors, Spurs, and Jazz win their divisions and receive automatic bids into the playoffs. The remaining teams are then decided by the Colley’s method; and actually are not far off from the real-life methodology of the NBA. The lone difference between Colley and the NBA format is that the Miami Heat would be the final team into the playoffs instead of the Chicago Bulls. That said, the Heat only beat the Bulls by a Colley score of 0.0033.

The resulting brackets would look like this:

Under this scenario, we see that the Cleveland path to the NBA Finals would be considerably more difficult with Oklahoma City (10th) instead of Indiana (15th); San Antonio (2nd) instead of Toronto (8th), and Houston (3rd) instead of Boston (4th). However, this scenario makes it easier for Houston and Utah to reach the “Conference Finals” portion of the bracket.

Scenario 2: NBA Playoffs According to Ranking and Division Record

Now, if we went full NCAA, then the overall records only matter for seeding. Instead we would use the division records; making division games imperative for teams to win. To note, only two division champions won their division. Those teams? Golden State Warriors and San Antonio Spurs. The fact that teams can finish third in their division despite winning their division shows that divisions are relatively useless. Sorry, Cleveland Cavaliers, Utah Jazz, and Washington Wizards.

Instead, if we set division champions by division record (a la pre-2017 Ivy League rules), we would see the Golden State Warriors (14-2), San Antonio Spurs (11-5), Portland Trail Blazers (11-5), Toronto Raptors (14-2), Milwaukee Bucks (10-6), and Charlotte Hornets (10-6) make the playoffs. That’s right… the Charlotte Hornets were the best team in Southeast by division record.

Due to NCAA rules, this would place Miami on the bubble and we would see the Charlotte Hornets make the playoffs as the 16-seed to face the Golden State Warriors instead of the Miami heat.

What this NCAA Scenario (and Statistics) Shows… The East is Indeed Weaker

Through the rankings algorithm we can then start looking at the disparity between conferences. The way we examine this is through the distribution of rankings. For the 2016-17 season, we write the random variable as counts per rank:

Western: (1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0,0,1,0,0,1,1,1,1,0,0,0,1,1,0)

Eastern: (0,0,0,1,0,0,1,1,1,0,0,1,1,0,1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,1)

These vectors will be left-heavy (full of one’s on the left hand side) if the conference has more higher ranked teams; right-heavy if the conference has more lower ranked teams. From a basic nonparametric test, the Wilcoxon-Mann-Whitney test, we can test a single year to see if one conference dominates another. The test is ridiculously simple to implement:

1. For each team, count how many teams in the opposite conference they beat in their ranking. Take that number and add it to their conference’s total.
   • Golden State Warriors: 15 Eastern teams. (West at 15)
   • San Antonio Spurs: 15 Eastern Teams. (West at 30)
   • Houston Rockets: 15 Eastern Teams. (West at 45)
   • Boston Celtics: 12 Western Teams. (East at 12)
   • …
   • Western Conference: 128, Eastern Conference: 97
2. Check the counts by adding the two numbers. If they equal the two group sizes multiplied together, we are in business!
   • 128 + 97 = 225
   • 15 * 15 = 225
   • We are in business!
3. Compute the Wilcoxon Man Whitney p-value.
   • Python commands:
     • import scipy.stats as stats
     • w = [30,29,28,26,25,21,20,17,13,10,9,8,7,3,2]
     • e = [27,24,23,22,19,18,16,15,14,12,11,6,5,4,1]
     • [s,p] = stats.mannwhitneyu(w,e,alternative=’greater’)
   • p-value for this year is 0.2669; which states there is not enough evidence to support that the East is weaker.

Let’s make the claim that only the playoff teams matter. Under this scenario we only consider the rankings of the eight playoff teams in each conference. We follow the same methodology as above; but this time it’s over 8*8 = 64 values. In this case, the Western Conference has a tally of 48 versus the Eastern Conference’s 16. The resulting p-value is 0.0518. This suggests that the Western Conference’s playoff teams are significantly better than the Eastern Conference’s playoff teams.

What this proves is that while the Eastern Conference is not significantly different than the Western Conference, their collection playoff teams are far inferior to that of their Western counterparts. Does this guarantee James-led teams to storm into the NBA finals easily every year? No. Not at all. But it does suggest that a team that makes it out of the Eastern Conference may not have as good a chance of making it out of the Western Conference.

What About the Previous Years?

So let’s look at the claim that the West has been stronger than the East during LeBron James’ run of seven consecutive NBA finals. If the west is indeed better, we should see the rankings aggregate as a left-heavy vector. In fact, over the previous seven years, the Eastern Conference has only had ONE top ranked team: Miami Heat in 2012; the contract-shortened season.

Aggregating the totals, we see that the Western Conference dominates the higher rankings. Plotting these aggregated rankings; or the aggregated data vectors, we see this dominance quite clearly.

Now performing the comparison test, there are 105 possible rankings for each conference across the 7 years. This results in a test statistics that may climb as high as 11,025. From the data across 2011-2017, the Western Conference has a test statistic of 6,895. This results in a p-value of 0.0008432. This suggests that over the seven year period, the Western Conference is head and shoulders better than the eastern conference as a whole.

But what about the playoffs? Restricting to the top eight seeds for each conference, the maximum value the test statistic can take is 3136. In this case, the Western Conference scores a test statistic of 849; resulting in a p-value of 0.00001409. This indicates that once again the West is head-and-shoulders better than the Eastern Conference.

What this technically means is, LeBron Haters, you have evidence to claim that making it out of the East is easy compared to the West. Unfortunately, you have no merit to denounce the NBA Finals wins.

Final Notes…

A comment made on Twitter after the first two days of Free Agency today was “Can the West send 10 teams to the NBA Playoffs?”  If we operated under NCAA rules, here’s how the previous seven years would have panned out…

• 2017: 8 west, 8 East – Warriors Champions
• 2016: 7 West, 9 East – Cavaliers Champions
• 2015: 10 West, 6 East – Warriors Champions
• 2014: 10 West, 6 East – Spurs Champions
• 2013: 10 West, 6 East – Heat Champions
• 2012: 9 West, 7 East – Heat Champions
• 2011: 10 West, 6 East – Mavericks Champions

We see that the West should have 8-10 teams in the Playoffs almost every year and this is not by overall record; but rather distributional rankings based on head-to-head interactions! Twice have teams from the weaker conference won the NBA Finals: Miami Heat.

So the real question is this… with the West already supposing to have 8-10 teams in the playoffs prior to this summer’s free agency bonanza… will the West dominate the East even that much more and make the case to put in 10-12 teams?

What do you think?

If you want a copy of the Colley Matrix code and the associated data, please feel free to shoot me an e-mail at jjacobs1@umbc.edu or follow me on Twitter: squared2020.