Density-dependent Growth – an interdisciplinary look at roster building

“Anyone who thinks you can have infinite growth in a finite environment is either a madman or an economist.”

Stubbornly insisting on a single approach can lead to blind alleys. Sometimes, looking at things from a different angle and changing perspectives can reveal unexpected details and help untangle contorted situations.

While I do not have a background in the more technical aspects of basketball, I compensate by putting to good use my expertise in other fields to better understand what I am watching. The pinnacle of interdisciplinary approaches, in my mind, is Evan Zaucha’s article, “The Art and Science of ‘Feel’ in Basketball”. Evan brings his neuroscience background to the forefront of his analysis to describe what the term ‘feel’ actually means in basketball terms.

Similarly, I intend to go beyond the traditional borders of basketball analysis, mapping my knowledge of ecology onto the basketball court.

Introducing the concept of density-dependent factors

A density-dependent factor is defined as “any force that affects the size of a population of living things in response to the density of the population.”

In nature, there are positive density-dependent processes, like diseases that would spread faster among individuals who live in close proximity, and there are negative density-dependent processes. In our case, we’ll take into account mostly the latter processes.

For example, the growth rate of mammal populations is generally influenced (negatively) by the density of the individuals.

Let’s take a look at how a deer population evolves. As population density increases, the amount of available food in the sample area will decline. As food declines, the body condition of individuals worsens. The birth rate is directly proportional to the animals’ body condition: when body condition is poor, the birth rate is low.

Ultimately, high density leads to scarce food supply and poor body condition, which in turn leads to a declining growth rate of the population. You can see already where this is headed.

Another variable that affects the process is the quality of the habitat, which can influence the rate at which growth declines. Habitats rich in resources can sustain higher individual densities for longer and slow the decline in growth rate; poor habitats will have declining growth rates.

(Credits @www.msudeer.msstate.edu)

This kind of process works for plants as well: just think about a very dense group of seedlings competing for the solar light.

NBA Ecosystem

An ecosystem can be broadly defined as a community of living organisms that interact with each other and their non-living environment. While I understand it doesn’t reflect what we commonly consider an ecosystem, the NBA itself can fall within this (broad, as I said) definition.

I’ve been meditating for years on the concept of the “NBA Ecosystem”: an interconnected set of biotic and abiotic components where we can identify rules and processes that we find every day in a coral reef or a boreal forest, for example. A reality that can be studied and analyzed through an ecological lens, alongside the traditional ways we analyze sports.

If we consider the entire National Basketball Association as a complex ecosystem, every team can represent a distinct habitat with its resources, population, and relative interactions. In this context of team-habitats within the NBA ecosystem, we can adopt an ecological approach to roster building, not focusing on the pieces themselves, but analyzing them in their connections with other biotic and abiotic components.

Density-dependent Growth and roster building

NBA teams can be assessed as peculiar habitats, and players as their populations, so we can try to apply the same models we generally use in ecological studies. I often think about similar ecological concepts when looking up this or that NBA roster or reading about a certain signing. And although they were modeled for a completely different field, I do think keeping in mind how these mechanisms work can help us understand certain NBA situations and players’ outcomes.

Density-dependent processes can be a useful tool for seeing rosters from a different angle, while adapting the notions we already have. First of all, rosters can have a max of 15 regular players plus three two-way contracts; the sheer number can’t be higher or lower, besides some rare exceptions. Then, what can be considered the “density”? It depends on the number of players occupying the same niche within the team dynamics. A 10-year vet and a rookie clearly don’t occupy the same niche nor have the same role with the team. In these years of rumination on the topic, I found density-dependent growth particularly fitting for the “population” of rookies and younger players who still need to develop their game.

While in the ecological studies, “growth” represents how the number of individuals in the sample area changes (generally expressed with a rate) in a roster where the number of individuals is pretty much fixed It takes on a more abstract meaning, representing the improvements of a player’s basketball ability.

The richness of resources in the context of a team/habitat is more labile from our point of view. It would take into account the number of minutes available, the quality and quantity of the staff. Three young players competing for minutes in a rebuilding team is a starkly different situation than three players competing for a similar share of minutes on a contending team with a set rotation consistently aiming for the best possible result.

This is an interesting excerpt of an article written by Tom Orsborn for the San Antonio Express-News about Spurs’ increased attention for film studies. The case was unusual, but it gives us a nice hint about something that otherwise would usually be inaccessible: even the potential hours available to study the tape can become resources young players are “competing” for.

In summary, if we consider it a functional parallel, an NBA team represents the habitat of the young players’ population, whose basketball skills’ evolutionary trajectory depends on the number of its individuals and the richness of opportunities, staff, and facilities. A fruitful habitat for maximizing these kinds of developmental resources is not guaranteed.

Brooklyn Nets, a concerning habitat?

The opening quote of this article could also replace “an economist” with “a Brooklyn Nets fan” (except for Lucas Kaplan and other rational Nets fans). The Nets represent a great example of what I’m trying to convey, and their moves during the last offseason were the spark that made me feel the urge to write about this topic.

The Nets’ roster at the beginning of the season (via spotrac.com)

With five rookies and a handful of other players who still need development competing for the same resources, the Brooklyn Nets could soon find themselves with a “declining growth rate” caused by the density within their habitat.

Looking up the Brooklyn Nets’ current per-game assists leaders represents a mystical experience: an apparent balance that hides a reality of shortcomings. All of them occupy a similar niche; all of them compete for playtime and reps; all of them will consume coaching staff resources. Considering also the fact that this season’s rookies are looking like players who need a consistent development path to impact, it is safe to assume not all of them will succeed and probably won’t have an ideal trajectory.

To me, the bigger issue is accumulating five first-round picks in a single draft: it implicitly punts the value of these picks as they are all competing for the same scant playing time/resources. Even more concerning is that all five of the selected players are fairly low-floor. A few of them will likely bust pretty hard. – The Case for Egor Demin by Avinash Chauhan

As Avi demonstrates, the concept of “overpopulation” that can limit the development of young players is something that already stuck in the back of our heads through empirical research and observations. The parallel with the density-dependent factors offers a more standardized explanation of the dynamic.

The byproduct of this messy ecological situation is evident. The team tried to find a balance, assigning players like Ben Saraf and Nolan Traore to the Long Island Nets, where they had to sail the insidious waters of the G League. Meanwhile, Egor Dëmin has his minutes and chances, but his season has been characterized by highs and lows (although it looks like he’s figuring out some things lately).

The release of Cam Thomas at the last trade deadline can be considered a symptom of the process. In a vacuum, it represents a potential waste of assets for the team, but on the other hand, it frees up resources.

Historic examples

The past offers us plenty of examples of the processes we’re examining if we look closely enough. Most rebuilding teams go through phases of overpopulation that are probably a natural consequence of trying to have and take as many draft chances as possible. The San Antonio Spurs during their 2022-2025 rebuild represent a great example I particularly care about.

The 2023-24 Spurs roster

Players like Dominick Barlow, Sidy Cissoko, Sandro Mamukelaishvili and even Blake Wesley or Jamaree Bouyea (who, to be fair, bounced around quite a bit before finally finding his niche this season) didn’t shine or had the chance to shine in this extremely young, extremely dense roster. And all of them are finding more success elsewhere.

Cissoko had some clearly likeable qualities as a prospect, but didn’t improve much from rookie to sophomore season, and the Spurs couldn’t find space in 2024-25 when they were already trying to put together wins. In this particular situation, the process was probably sped up by how quickly the team found their cornerstone (and it likely also applies for the Thunder at the time). When a team just drafted a young phenomenon and owns several future draft picks, the clock starts ticking early for those who are on the margins of the roster.

In a similar quickly developing, hyper-competitive environment, it becomes less likely for two-way players like Barlow and Bouyea to break into the rotation. Although there were probably some signs of Dom Barlow’s trajectory, especially considering how good he was at the G League level at a young age.

In the grand scheme of things, most of this stuff becomes irrelevant when your team gets the 7’4 lottery prize, but winning on the margins gives longer windows of opportunity. Look at it the other way around: how irrelevant was it for the Philadelphia 76ers finding their current starting power forward as a result of this process (Sixers? Process? Unintended pun)?

Acknowledging this process, it becomes easier to recognize buy-low, low-risk/high-reward occasions for teams disposing of plenty of resources. Besides the aforementioned Dom Barlow opportunity, Moussa Diabate going from an end-of-the-bench piece for a competitive team to growing into a high-level rotation piece for the Hornets is a notable example. In these cases, pre-draft evaluations and the G League sample are particularly relevant to identify the ideal candidates.

Another player that could become the most recent, valid argument in favor of this thesis is Ousmane Dieng. Since he left Oklahoma City, the French forward is showing things he didn’t have the chance to display consistently in the depth of the best team in the league.

The Houston Rockets from a few seasons ago are a slightly different but no less interesting case-study: players like Usman Garuba and Josh Christopher got devoured by the rebuild meat-grinder. Cam Whitmore is enduring a similar fate, though there seems to be some more attitudinal stuff going on with him. Could his issues be fixed by devoting more off-the-court attention to these issues in a less developmentally-dense environment?

It is obviously hard for us, as outside observers, to distinguish between those who simply weren’t good enough and who didn’t get enough chances to improve and have a better developmental trajectory in this case. However, those constitute interesting data points anyway.

Natural selection and density dependence

If you endured the reading of this piece to this point and followed NBA basketball in the last few years, you probably realize one of the weaknesses of this theory (or ramblings?).

Recent NBA history shows us that relying on sheer “natural selection” putting prospects in a highly competitive environment represents a functional strategy of long-term team building. Stockpiling as many prospects as possible and just find who is able to figure things out in the league seems to work decently enough.

Just think about the reigning NBA champions, the Oklahoma City Thunder.

Aleksej Pokusevski, Theo Maledon, Darius Bazley, and many others. Many players indeed busted, and many of their assets ended up in the meat grinder, but the selective pressure also allowed them to identify many pieces that are currently part of the clear-cut best team in the league.

However, the density-dependent processes remain important because not every team starts from the same foundations, with the same number of draft opportunities or resources. “Natural selection” operates within the density-dependent processes, and acknowledging them and how they work can help maximize the outcomes.

Wrapping it up

In high school, I studied Latin for 5 years, even though I attended a scientific high school. Many criticize its teaching because it’s a dead language and doesn’t have much value outside the academic world. However, Latin isn’t taught for its utility; it’s taught as a mental exercise to stimulate the identification of connections and instill a certain “forma mentis” in students.

I realized this article represents something similar. It doesn’t presume to solve team-building issues by adopting just a couple of ecological models. But this article humbly wanted to be a useful mental exercise, something that can stimulate the research of patterns and a transverse, interdisciplinary approach in a field that sometimes is a bit too vertical, fossilized in its knowledge.