Written by: Carlo Duffy

With the rise of mediocre NBA teams prioritizing draft position more highly than present success, basketball fans may wonder if such teams have become worse. And with the Golden State Warriors’ recent titles and their current, star-studded “Core Four,” fans may also wonder if the elite teams have become more elite. Thus one question emerges: have teams become increasingly great or increasingly bad? This question is about *parity* over time.

Another interesting question emerges from looking at the best teams: has success been concentrated among a few teams? Have there been only a handful of truly great teams, or a wide range of good teams? This question is about *competition* over time.

To answer these questions, it makes sense to treat the NBA as an economy. I am not the first to do this. Our colleagues at the Harvard Sports Analysis Collective (HSAC) have written several articles about parity in the NBA, among other sports leagues. Using NBA teams’ preseason odds, Kurt Bullard concluded that the NBA betting market is so unequal, that compared to the inequalities of countries’ economies, it would be “the world’s most unequal economy” **[1]**. In another article, Andrew Puopolo compared the betting markets for several major sports leagues—MLB, NFL, NBA, NHL, EPL, and La Liga—from 2009 to 2016, and found that, of the four North American sports leagues, the NBA had the most unequal betting market **[2]**.

Both articles look at teams’ perceived odds of winning the championship. Their findings make sense. Favorable odds are usually given to the team that ends up being the champion. Minimal odds are usually given to teams that may outperform expectations, but have no chance of winning it all. Such odds are also given to simply mediocre teams.

But looking at this does not tell the whole story about parity and competition. These articles do not account for teams that, despite unlikely chances of success in the playoffs, are quite good in the regular season. Such teams have talent, after all.

That is why I am interested in looking at the NBA regular season’s parity and competition over time. Previous articles have looked at parity. In his basketball blog, Nick Neuteufel looked at parity in the regular season over time from 2001 to 2014, and observed Gini coefficients (economic measurements of parity) roughly between 0.14 and 0.20 **[3]**. With an average of these Gini coefficients, one could claim that, based on Central Intelligence Agency’s World Factbook of countries’ Gini coefficients, the NBA would be the world’s second most equal economy behind only Jersey’s **[4]**. That finding is a huge departure from the Harvard articles’ conclusions, but is understandable. Using regular season wins is a better way to examine teams that have talent but cannot win in the playoffs.

But Neuteufel restricts his analysis to the 21^{st} century. Since Basketball Reference provides a yearly regular season win totals from 1946 to 2017 for active and defunct franchises **[5]**, I can examine parity over a wider time period.

Specifically, for each regular season I can look at the Gini coefficient:

where x_{i} is the number of regular season wins for an individual team, and n is the number of teams (here: 30) **[6]**. In words, the Gini coefficient takes the sum of all possible differences between teams’ regular season wins, and divides this by 60 (2 times 30) times the sum of all teams’ regular season wins. This turns out to be a value between 0 and 1, where 0 means absolute parity and 1 means absolute disparity.

To my knowledge, no one has looked the NBA regular season’s competition over time using the Herfindahl–Hirschman Index, which economists use to capture to what extent a market—a subset of an economy—is dominated by its most successful firms. So using the same data, I can also look at this.

For each regular season I look at the normalized HHI:

where H (the unnormalized HHI) is

(s_{i} represents an individual team’s number of wins, divided by the total number of wins for all teams), and N is the number of teams **[7]**. Often the unnormalized HHI is used to measure concentration **[8]**, but I use the normalized form to account for the increasing number of teams in the NBA over time. Like the Gini coefficient, the HHI also turns out to be a value between 0 and 1, where 0 means complete presence of competition and 1 means complete absence of competition.

For this analysis, I use R’s **ineq** package in R to obtain Gini coefficients (just as Neuteufel did) and normalized HHIs for every NBA regular season from 1946 to 2017. I then use R’s **tidyverse** collection of packages to visualize the data.

As a sanity check, I first looked at the relationship between the Gini coefficients and normalized HHIs for every season. I expected to see a positive association: for every additional increase in the Gini coefficient, on average the normalized HHI should increase. Why would this make sense? Disparity and competition are not exactly the same, but pretty interconnected. In the NBA, more disparity means quite a few teams are extremely good (imagine peak Golden State) and quite a few teams are extremely bad (imagine the 76ers during "The Process"). If no team were just average—making the Gini coefficient high—the extremely good teams would control a large share of success. In economic terms, this would translate to little-to-no competition and thus a high normalized HHI.

The data confirms this.

Figure 1 shows exactly the interpretation in my prediction. There is a pretty strong positive, linear association (r = 0.475) between the Gini coefficient and normalized HHI. For further evidence I fit the data using a simple linear model and obtained:

**Predicted H* = -0.004 + 0.053G**.

Since 0.053, the estimate for the slope, is statistically significant (p = 2.47*10^{-5}), I can conclude that *G* and *H** are indeed positively correlated.

I am now ready to answer the following question: over time, how have parity and competition changed in the NBA regular season?

Let’s first look at the Gini coefficient over time.

The highest Gini coefficient, 0.233, occurred during the 1972-73 season, while the lowest, 0.061, occurred during the 1956-57 season. Over time, disparity has not really increased or decreased. Massive swings in the 1950s and 1970s stand out among all the fluctuations. For the most part, the Gini coefficient seems to hover around 0.17. My range of values falls way below Andrew Puopolo’s range using NBA preseason title odds for seasons from 2009 to 2016. Puopolo found Gini coefficients spanning roughly from 0.6 to 0.8. This aligns pretty well with what Neuteufel found from 2001 to 2014: the NBA regular season shows really high parity.

I then wondered if my plot of the normalized HHI over time goes with this story.

The highest normalized HHI, 0.018, occurred during the 1959-60 season, while the lowest, 0.001, occurred during the 1956-57 season. It looks like the general trend can be split into two parts: pre-1980 and post-1980. Before 1980, the normalized HHI, despite extreme volatility, appears to tend to decrease over time. But after 1980, it appears to remain around 0.025 with comparatively less fluctuation. Overall, though, the range of values is extremely low. The U.S. Department of Justice states that markets, subsets of an economy, are “moderately concentrated” if the HHI is between 0.15 and 0.25, or “highly concentrated” if the HHI is greater than 0.25 [5]. So the NBA would be considered minimally concentrated: the best teams do *not* make up a rather large share of success. It’s as close as you can get to perfect competition.

To summarize, I extended Neuteufel’s analysis of parity in the NBA regular season from 2001 to 2014. I calculated the NBA’s yearly Gini coefficients and normalized HHIs from 1946 to 2017. From the low values for both economic measures, I found that the regular season has been very equal—contrary to, but in tandem with, very high disparity in the preseason title odds—and very competitive. Following this analysis, one area for future research could be parity *within* teams. Here, parity means the extent to which a team’s talent is distributed. On one extreme, a team could rely solely on a single superstar while the rest follow; on the other, a team could consist of equally-contributing solid players. A paper presented at Chicago Booth’s 2013 Sports Symposium has looked at this. The paper calculates teams’ Gini coefficients using player PERs among other metrics, and finds that “teams with higher Ginis tend to do better overall, but disproportionately better in playoffs” **[9]**. But the paper only uses NBA data from the 1991–1992 to 2011–2012 seasons **[9]**. That is understandable since, compared to the NBA’s history, the PER is relatively new. But it would be interesting to find a way to analyze teams’ parities over a larger time period.

**References**

[1] http://harvardsportsanalysis.org/2016/10/distribution-of-nba-title-odds-would-be-worlds-most-unequal-economy/

[2] http://harvardsportsanalysis.org/2016/12/which-sports-league-has-the-most-parity/

[3] https://sportsandillumination.wordpress.com/2014/06/07/nba-wins-in-the-21st-century/

[4] Note: The CIA multiplies countries’ Gini coefficients by 100, so the range of possible values becomes from 0 to 100: https://www.cia.gov/library/publications/the-world-factbook/rankorder/2172rank.html

[5] https://www.basketball-reference.com/leagues/NBA_wins.html

[6] https://en.wikipedia.org/wiki/Gini_coefficient

[7] https://en.wikipedia.org/wiki/Herfindahl_index

[8] The U.S. Department of Justice uses the HHI to determine the most concentrated markets (Note: Scaling differs between my HHI and the DOJ’s. To get the DOJ’s equivalent of my HHI, multiply mine by 10,000): https://www.justice.gov/atr/herfindahl-hirschman-index

[9] https://medium.com/@mau.zachrisson/the-sports-gini-evaluating-whether-stars-matter-more-in-the-playoffs-9779f86b8cbb