Audience Attractor

Abstract

This playground models the viewership of personality-driven media as a stochastic dynamical system with sticky basins of attraction. Streamers, talk-radio hosts, podcasters, and political commentators do not grow along a smooth curve; their audiences sit in bands. Habit, parasocial attachment, social proof, platform memory, and community lock-in create floors. Niche capacity, format constraints, and identity lock-in create ceilings. The result is a landscape of metastable audience regimes separated by barriers that only sufficiently large shocks can cross.

Background

The intuition that started the project: once a streamer reaches a certain viewership band, neither falls easily below it nor easily rises above it unless something external changes. The sharpest version of that intuition is not "viewership has a minimum" but "viewership has stable attractor regimes."

Three lines of work support this reading.

Cumulative advantage. Salganik, Dodds and Watts (2006) ran an artificial cultural market with 14,341 participants and showed that social influence increased both inequality and unpredictability: popularity itself changed future popularity. Independent Twitch popularity work (over 10,058 users, 55,000 streams, 50,000 clips) finds power-law-like distributions consistent with cumulative advantage, although not proof of any single mechanism.

Superstar economics. Rosen's superstar model (1981) argues that small differences can produce very large outcome differences when distribution technology lets top performers serve huge markets. Personality-driven media inherit that asymmetry, with a twist: intimacy and community are partly anti-scalable, so the same identity that built the floor can prevent escape into a larger basin.

Loyalty decomposition. A 2026 livestream-loyalty preprint decomposes audience loyalty into stability, competition resistance, post-peak retention, and a floor ratio across 2.94 million minute-level observations from 18 channels over 3.3 years. These four components are close to the model's structural terms.

Model description

State variable: V_t = C_t + A_t, total viewers in period t, decomposed into a slow-moving core and a fast-moving casual pool.

Core dynamics:

C_{t+1} = retention(habit, retentionShock) * C_t + conversion(parasocial, quality) * A_t

Habit retention multiplies the core stock down by a factor close to one each period. Parasocial conversion moves a small fraction of casuals into the core. A schedule-collapse scenario multiplies the retention term by 0.52.

Casual dynamics:

A_{t+1} = platform(V_t) + noise + shock - nicheDrag

where platform(V_t) is the saturating cumulative-advantage term

platform(V_t) = discoverability * 8 * (V_t + 1)^(0.24 + cumulative * 0.03) * (1 - V_t / capacity)

The cumulative-advantage exponent makes large audiences acquire faster, but the capacity term cuts that off as the niche fills. The niche-drag term penalises operation beyond 72 percent of capacity and is amplified by saturation and identity lock-in.

Shocks are seeded so the simulation is deterministic given the parameters and the scenario. Each scenario adds one or two timed events: a collaboration window for breakout, a capacity lift for the format pivot, a negative-drift band for a trust shock, a retention multiplier for a schedule collapse.

The six scenarios

The playground exposes six named runs designed to span the four regime tiers.

Baseline sticky band. No major events. Floor and ceiling do all the work. The cleanest demonstration of a single stable attractor.

Breakout campaign. A collaboration window from roughly 20 percent to 45 percent of the run doubles discoverability. The test is whether the trajectory holds the new band after the window closes.

Format pivot. Capacity rises by 65 percent at the 35 percent mark and quality lifts by about a point. Identity lock-in competes with the new ceiling.

Trust shock. A negative-drift band runs from about 30 percent to 42 percent. The core's habit retention is unchanged, so the question is whether the floor holds.

Schedule collapse. Habit retention is multiplied by 0.52 from the 25 percent mark onward. Isolates the role of routine.

Slow decay. No events. Low discoverability, modest quality, but strong habit. The falsification target for the floor: does the basin hold without acquisition?

Results

Stable basins exist. The baseline scenario reaches a single dominant dwell band that captures more than half the run. The trajectory wobbles inside it and rarely leaves.

Transitions are visible. Breakout and pivot configurations move the system into a higher dwell band that persists after the event window closes. The signature in the landscape view is a ball that has rolled into the upper well.

Floors fail when habit goes. Schedule collapse drops the trajectory below the inherited floor and keeps it there. Habit retention is the decisive term, not raw shock magnitude.

Trust shocks recover. A pure controversy can crash peak viewership without destroying the basin: the core holds, and the trajectory reapproaches its band as the shock window closes.

Wandering is the falsifier. Drop habit, identity lock-in, and saturation to near zero and the trajectory ceases to dwell. There is no dominant band, only a noisy walk on the log-scale. The attractor metaphor stops doing work for that configuration.

Limitations

The model has no calendar time, no seasonality, no production-cost or burnout dynamics, and no creator effort variable. The two-pool decomposition is a deliberate compression: real audiences cluster into more than two behavioural strata. The simulation runs with a single seed, so reported dwell shares describe one path rather than a distribution. The classification of regimes into four tiers is a legibility choice, not a claim that audience phenomenology cleanly bins into four bins.

The model is comparative, not predictive. The calibration table compares simulated final viewers against reader-assigned expected values from the cited literature; close agreement means the model's shape is consistent with that reading, not that it has been fit to any specific creator's history.

References

• Salganik, M. J., Dodds, P. S. and Watts, D. J. Experimental Study of Inequality and Unpredictability in an Artificial Cultural Market. Science (2006).
• Rosen, S. The Economics of Superstars. American Economic Review (1981).
• Bourdieu, P. Distinction: A Social Critique of the Judgement of Taste (1979).
• Lobato, R. Streaming and the Politics of Default (2024).
• Braithwaite, J. Crime, Shame and Reintegration (1989).
• Twitch popularity power-law analyses (2022).
• 2026 arXiv preprint on livestream loyalty decomposition.