Roster Geometry and Resilience: Salary-Weighted Lineup Connectivity Predicts Playoff Stability

By Luke Blommesteyn, Yuvraj Sharma, and Lucian Lavric • Accepted to Carnegie Mellon Sports Analytics Conference

This is a web adaptation of the paper. Lighter commentary, same methods and same results.

The question

A common belief about NBA rosters is that a team built around a few expensive stars is fragile. Lose one of them and the offense has nothing to fall back on, while a team with its salary spread across the rotation keeps going. We wanted to know whether that holds up in the data or is just hindsight. Does the shape of a roster, meaning how salary is spread across the players who actually share the court, carry information about playoff survival that payroll and net rating miss? We built each team-season as a salary-weighted lineup network, stress-tested it by removing stars and connectors, and checked whether the geometry predicts how far a team goes.

The answer is a little, and consistently. Topology lifts Macro-F1 a couple of points over a strength-only control. That is a small effect, but it reproduces and it points the same way each time: when the money is spread across lineups that actually play together, the roster holds up better.

Abstract

We test whether the network geometry of NBA rosters, namely how salary resources are distributed across players who actually share the court, predicts playoff stability. Prior work links payroll level to outcomes or analyzes in-game pass networks. It rarely ties salary allocation to lineup connectivity or evaluates resilience to disruptions. We model each team-season as a salary-weighted, shared-possession network: nodes are players with size proportional to salary share, and edges capture co-presence intensity. We compute topology features (salary dispersion, salary assortativity, community structure, centralization, edge concentration) and define a Roster Resilience Score via robustness simulations that remove stars, role players, or community connectors, then score predicted drop from a model trained on intact networks.

Using public data from Basketball-Reference and Cleaning the Glass for 2020-21 through 2024-25 (149 team-seasons), we ask whether topology improves prediction of ordinal playoff advancement beyond a strength control. With salary-true features and leave-one-season-out cross validation, the full topology model raises Macro‑F1 from 29.0% to 31.3%. We release a reproducible pipeline covering data build, modeling, and figures.

Introduction

NBA front offices build rosters under a cap and a pile of other constraints. Payroll level correlates with success, but two gaps remain. First, salary dispersion usually gets studied without any regard for who plays with whom. Second, network studies tend to focus on ball movement rather than roster structure under cap realities. So we propose a roster-level network view that weights players by salary share and connects only the ones who actually share possessions. That makes it possible to study geometry, things like centralization, modularity and assortativity, and to test resilience when you lose a player.

What we wanted to find out

RQ1. Do salary-network topology features add anything beyond a traditional team-strength control when you predict playoff advancement?

RQ2. Which specific patterns, like negative assortativity, decentralisation, or concentrated edges, show up in the rosters that stay resilient?

RQ3. Does weighting co-presence by high-leverage possessions improve that explanatory power, compared with just counting shared possessions?

Contributions

We propose a roster network formulation that combines salary topology with who actually shares the floor. On top of that graph we define the Roster Resilience Score, which we generate by systematically removing different player archetypes and measuring the predicted drop. We evaluate the predictive lift with season-wise cross-validation, and we document every decision so the study reads like a preregistered run. We also ship a reproducible pipeline in the public repo: data build, modelling scripts, figures, and all the configuration.

Who this is for

If you work in analytics. These features can be added to models you already run. They’re built from public salary and lineup data, so you can recreate them in a notebook, plug them into your playoff simulators, and see how much topology adds on top of adjusted net rating or luck-adjusted efficiency.

If you coach, run a front office, or just watch a lot of basketball. Where the expensive players sit in the rotation matters along with how many you have. Rosters that avoid one high-salary hub, and keep several links between groups of players, hold up better when an injury, foul trouble or a matchup change hits. The rest of this turns that intuition into numbers you can test.

Related Work

Salary and performance studies look at aggregate spend. Basketball network analyses capture interaction patterns, but not salary topology. And network robustness research shows that structured node removal reveals where a system is vulnerable. We combine those three ideas by linking salary topology to lineup connectivity and stress testing the roster graphs, using public sources throughout.

Data

We study NBA team-seasons from 2020-21 through 2024-25, for a total of 149 team-seasons.

Lineups and possessions

We use lineup and four-factor tables from Cleaning the Glass. Positions and possessions reconstruct on-court units. We compute co-presence counts for each pair of teammates and aggregate lineup Off and Def points per possession to a team-season strength proxy.

Salaries

We obtain player and team salary tables from Basketball-Reference and normalize to within-team salary shares.

Labels

We assemble playoff advancement labels from Basketball-Reference postseason brackets.

Data pipeline

1. Parse lineups into possession-weighted on-court units.
2. Merge salaries and normalize to team share per player.
3. Compute co-presence counts \(c_{ij}\) and player possessions \(n_i\).
4. Build graph \(G=(V,E,w)\) with \(w_{ij}=c_{ij}/\max(n_i,n_j)\) and threshold low-minutes nodes.
5. Compute topology features: salary dispersion, salary assortativity, community structure, centralization, and edge concentration.
6. Aggregate lineup Off and Def PPP to team NR and attach playoff labels.
7. Export leave-one-season-out splits and freeze seeds and hyperparameters.

Five seasons, public sources only, deterministic builds. You can reproduce every aggregate yourself.

Methods

The whole method in one sentence: weight players by salary share, connect only the ones who actually share the floor, then test how fragile that shape is.

Network construction

Let \(V\) be players with at least 300 possessions. For players \(i\) and \(j\), define the bounded co-presence intensity

$$ w_{ij} = \frac{\text{shared\ poss}_{ij}}{\max(\text{poss}_i,\text{poss}_j)} \in [0,1]. $$

Node size \(s_i\) is the player’s salary share. A leverage-weighted variant \(\tilde{w}_{ij}\), which up-weights close or late contexts, is straightforward to add once leverage flags are integrated.

Topology features

• Salary dispersion: Gini and top-\(k\) share for \(k\in\{1,2,3\}\).
• Salary assortativity: weighted Pearson correlation of salary shares across edges \((i,j)\) using weights \(w_{ij}\).
• Community structure: modularity \(Q\) and the coefficient of variation of community sizes.
• Centralization: Freeman degree centralization with edge weights.
• Edge concentration: fraction of total \(w\) captured by the top five and top ten edges.

In words: the features ask whether the money is spread out, whether stars share the floor with role players, whether the roster splits into cliques, and whether a few pairings absorb most of the possessions.

Performance proxy for stress tests

We fit a standardized ridge regression that maps intact topology features to team NR,

$$ \widehat{\mathrm{NR}} = f_\theta(x),\qquad f_\theta \in \{\text{Ridge}\}. $$

This proxy exists only to score stress-test perturbations consistently.

Robustness simulations and RRS

We remove, in turn, the highest-degree node, a mid-salary node, and the highest-betweenness node. After each removal we recompute features and score with \(f_\theta\). Let \(\Delta_s\) be the drop relative to intact,

$$ \mathrm{RRS} = 1 - \mathbb{E}_s\!\left[\frac{\Delta_s}{\left|\widehat{\mathrm{NR}}^{\,\text{intact}}\right|+\varepsilon}\right],\quad \varepsilon=10^{-3}. $$

We use winsorization in sensitivity checks when \(\widehat{\mathrm{NR}}^{\text{intact}}\) is near zero.

RRS is a stress test. Pull a star, then a role player, then a connector. If the predicted strength barely drops, the roster is resilient.

Predictive modeling of playoff advancement

We predict ordinal playoff rounds \(y\in\{0,1,2,3,4\}\), where 0 indicates missed playoffs and 4 indicates champion. We fit a multinomial logit as a robust ordinal surrogate with season-wise standardization. We evaluate with leave-one-season-out cross validation and report Macro-F1, Accuracy, and mean absolute error of expected round.

Ablations. (A) Strength control only, so just NR. (B) Control plus salary dispersion. (C) Control plus connectivity features, including salary assortativity. (D) Full topology. We add one feature group at a time so we can tell which block is responsible for any lift.

Pre-registered analysis plan

Before training we fixed the feature list and thresholds, the cross-validation splits, the ablation order and metrics, and a small hyperparameter grid for ridge and multinomial logit.

Results

Three things came out. Connectivity lifts Macro-F1 roughly 2 to 3 points over a strength-only control. Negative salary assortativity, meaning salaries mixed across connected lineups, lines up with resilience. And lower edge concentration means fewer single points of failure.

Incremental predictive value

Look at the Macro-F1 column. Salary dispersion on its own hurts. The lift only appears once the connectivity features are added.

Resilience and topology based on RRS

When RRS is available, its association with degree centralization is weak, while salary assortativity is negatively related to RRS. That suggests mixing salaries across connected lineups is what lines up with robustness to simulated disruptions. This surprised us. Running possessions through one hub was not what hurt resilience. Clustering the expensive players together was.

Could this just be chance?

For each team-season we hold the lineup graph fixed, randomly permute salary shares across the nodes, and compute a z-score of the observed assortativity against that permutation distribution. This shows what “random” looks like on the same network. Real teams mix salaries more than random, and the teams with more negative z-scores tend to reach later rounds.

Assortativity deciles for a managerial view

Sorting team-seasons into deciles by observed salary assortativity shows that the lower-assortativity deciles, the ones with more cross-salary mixing, advance further on average.

Case studies of network geometry

Here are two anonymized team-seasons with a similar expected playoff round from the ordinal model, but very different topology. One is star-centered with high edge concentration. The other is more distributed, with balanced communities. The star-centered roster depends on its hub. The distributed one keeps several playmaking links, so no single removal disconnects it, and it has the higher resilience score.

Model diagnostics

What could be wrong with this

Salary data. Name resolution can miss two-way or ten-day players. We report match rates and rerun the analysis with both strict and lenient filters.

Leverage. Edges currently reflect possession counts, not clutch weighting. A close-and-late variant is on the roadmap as an ablation.

Confounding. Minutes, role and salary all correlate tightly. We include net rating (NR) as a strength control and publish the ablations.

Measurement. Co-presence abstracts away play types, and community detection is coarse. Future work could add tracking data to enrich what an edge means.

Generalisation. Five seasons and 149 team-seasons is a limited scope. We lean on regularisation and season-wise cross-validation to keep the claims modest.

RRS scaling. When \(|\widehat{\mathrm{NR}}^{\text{intact}}|\) gets close to zero, the normalisation can exaggerate resilience. We winsorise in sensitivity checks to stabilise the metric.

Ethics and transparency

All the data came from public sources: Basketball-Reference and Cleaning the Glass. We comply with the providers' terms of use, and we release code, seeds and environment files so readers can reproduce the results from publicly accessible exports.

Reproducibility statement

We provide the data-processing scripts for lineup graphs and salary merges, pinned environment files, a Makefile that regenerates every table and figure, and documented loaders for the Basketball-Reference and Cleaning the Glass exports.

Conclusion

We link salary-weighted roster topology to lineup connectivity, and show that connectivity adds information beyond team strength. Across five seasons, topology features, especially salary assortativity and edge concentration, improve ordinal playoff prediction over a strength-only control. A permutation test confirms the observed negative assortativity isn’t just a byproduct of roster size or lineup coverage, and the playoff-round outcomes support the same pattern. For practice, front offices can stagger high salaries across lineups and reduce edge concentration, which improves robustness without raising total payroll. Future work should bring in leverage-weighted edges, expand to more seasons and leagues, and add richer controls like injuries and rest.

References

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5. Basketball-Reference.com, “NBA statistics and history,” basketball-reference.com, accessed 2025.
6. Cleaning the Glass, “NBA lineup and four-factor statistics,” cleaningtheglass.com, accessed 2025.