Just as in our heliocentric solar system many small planets orbit a much larger sun, heliocentric NBA offenses feature several role players orbiting around one (or two) stars. Think four shooters zipping around the court while Luka Doncic isolates or Trae Young determining the fate of almost every Hawks’ possession.
A lot of the discussion about heliocentrism has focused on how heliocentric teams are becoming more common and even more reliant on top players. I want to do something a bit different from this great work and develop a one-number metric to determine how heliocentric a team is.
How can we measure how heliocentric a team is? One approach is just to look at how much usage the team’s top player has. That work pretty well for a lot of cases, but doesn’t distinguish a team like the 2020 Rockets where almost all their offense runs through two players from a more egalitarian team that has one standout star, like the 2021 Jazz. As Tatooine demonstrates, not every planet orbits around just one sun; I want a metric that identifies that the 2020 Rockets were very heliocentric (they just happened to have two suns instead of one) and gives us a number to measure exactly how heliocentric each team is.
The Heliocentric Hoopers Index does just that.
How to measure how Heliocentric a team is
The Herfindahl-Hirschman Index (wisely abbreviated as HHI) is a tool in economics used to measure how concentrated a market is — essentially, how much is the market dominated by a small number of firms? A higher score means a small number of organizations control most of the market, and a maximum score of 10,000 means one firm has a complete monopoly. Smaller numbers indicate a more competitive environment, where many small firms each have a fairly equal share of the market.
Bigger HHI means more monopolistic. Smaller HHI means more evenly distributed.
This means the HHI is the perfect sort of tool for measuring how heliocentric NBA teams are — how much they rely on one (or two or three) players to generate their offense. Teams that are most reliant on the smallest numbers of players will have higher scores than spread out the job of creating offense among more of their players.
How the Herfindahl-Hirschman Index works
One of the HHI’s greatest features is its simplicity. Say we have four companies that sell basketballs in Seattle, each with a different percent of total basketball sales in the city (their market share):
- Rainy Balls: 35% of market share
- Cloudy Hoop Supplies: 30% of market share
- Sunny Sporting Goods: 10% of market share
- Salty Sonics Sports: 25% of market share
The HHI would be 352 + 302 + 102 + 252 = 2,850.
So we just take the percents, square them, then add them up. If Rainy Balls and Cloudy Hoop Supplies merged to become one firm with 65% of the market share, then the HHI will go up to indicate that the market is more concentrated.
The HHI is now 652 + 102 + 252 = 4,950.
So now we just need the basketball equivalent of market share for each player on each team. Thankfully this already exists in the form of usage statistics (in fact, there are several different versions of this statistic). We’ll be taking the usage stats for each player from BasketballReference for now.(Basketball Reference’s Usage has the major flaw of not counting assists, but it works very naturally for an HHI calculation, so I’ll use it for now and consider this a proof of concept for measuring basketball “heliocentricity” to be improved on later.)
The Heliocentric Hoopers Index (HHI)
Usage% measures the percentage of a team’s possessions a player ends. A player can end a possession by taking a field goal, shooting free throws, or committing a turnover.
We want to measure how much of a team’s total offense each player is responsible for, regardless of whether they’re on the court. We don’t want ball dominant 10th men who have 35% usage in 5 minutes per game to mess with our results. So I calculate an estimate of a team’s total reliance on a player by multiplying the player’s usage% by the fraction of his team’s total minutes that he played.
Player’s “Market Share” = (% of Team’s minutes played) * (Usage%)
We can put these “Market Shares” in the HHI calculation to get an HHI for each team. The higher the team’s HHI, the more heliocentric that team was, according to the Heliocentric Hoopers Index.
Now let’s look at what the Heliocentric Hoopers Index tells us about each team in the 2021-22 season.
The Most Heliocentric NBA Teams of the 21-22 Season
Chicago might not be the first team people think of when they think of heliocentric teams, but DeRozan had the second highest contribution to his team’s HHI, behind only Trae Young, and Chicago’s other stars, LaVine and Vucevic, both had relatively high contributions to the Bulls’ HHI with 289 and 225, respectively.
| Player | HHI Contribution |
| Trae Young | 536 |
| DeMar DeRozan | 489 |
| Jayson Tatum | 485 |
| Luka Doncic | 474 |
| Joel Embiid | 465 |
| Nikola Jokic | 398 |
| Giannis Antetokounmpo | 379 |
| Devin Booker | 362 |
| Donovan Mitchell | 357 |
| Julius Randle | 341 |
Atlanta and Dallas, two of the more notoriously heliocentric teams, ranked lower than you might expect (6th and 12th, respectively) for a couple of reasons: injuries at points in the season, meaning more of their offense came from lesser-use players than
Are Heliocentric Offenses Better?
Putting the ball in the hands of your best offensive player(s) as often as possible is a pretty intuitive strategy. Does taking this approach lead to a better offense?
Teams with higher Heliocentric Hoopers Index value tend to also have better offensive ratings, but the effect is relatively small (R2 =. 30).
The correlation between HHI and offensive ratings could be driven less by Heliocentrism being the ideal way to structure an NBA offense in general and more by the fact that there are a few things that can hurt a team’s HHI and their Offensive Rating.
Teams with low heliocentrism and low offensive ratings mostly fit into one of three categories:
- Young, tanking teams who are trying to give a lot of players opportunities to develop and show their potential at the expense of winning (Think OKC, Detroit, Orlando, Houston, and Portland.)
- Teams who experienced a lot of injuries throughout the season, especially to key players, meaning they had to rely more on players further down their depth chart. (The Clippers, Cavs, Heat, and, again, the Blazers saw their offensive ratings and HHIs both drop due to injuries.)
- Teams with major roster turnover in the season that never quite figured things out. (Sadly, the Kings and Pacers are the standout example of struggling teams that shook things up only to continue to struggle.)
These three types of teams — the young tankers, the injury sufferers, and the desperate flailers — occupy the low HHI, low Offensive Rating quadrant.
The only teams with a below average HHI (less than 935) and an above average Offensive Rating (greater than 111.4) were Brooklyn (who had a ridiculously offense-focused roster), Miami (whose resilience to injuries was one of the major stories of the season), San Antonio (who was led by the GOAT coach), and Indiana (remarkably).