Payout Gini: Is Numerai Becoming Winner-Take-All?

Numerai payout inequality rose from a Gini of 0.85 to 0.97, but it tracks stake concentration rather than amplifying it. The system is unequal, not rigged.

Every tournament has a concentration question: as stake piles up in fewer hands, do payouts follow the same distribution, or does the formula amplify the gap? The Gini coefficient -- the standard inequality metric from economics -- gives a direct answer. A Gini of 0 means perfect equality; a Gini of 1 means one model captures everything.

This post computes the payout Gini for every weekly Numerai Classic round, compares it to stake inequality, and tests whether the tournament is becoming winner-take-all. For background on how payouts work, see The Payout Factor. For aggregate NMR flows, see Round Economics.

Payout Inequality Over Time

For each round, take all models with nonzero payouts (positive or negative), compute the Gini coefficient of absolute payouts, and plot it over time.

Payout Gini coefficient per round from round 200 to round 1200, rising from about 0.85 to 0.97 with a 20-round rolling average
Payout Gini coefficient per round from round 200 to round 1200, rising from about 0.85 to 0.97 with a 20-round rolling average

The payout Gini started near 0.85 around round 200, climbed steadily through round 600, and has sat in a tight 0.95--0.97 band ever since. That is high, comparable to global wealth inequality, but the trajectory matters more than the level. The Gini stopped rising around round 600 and has been flat for over 600 rounds.

The initial climb from 0.85 to 0.95 coincides with a surge in participation and stake concentration. More models entering at small stakes mechanically pushes the Gini upward even if the payout formula is neutral. The plateau suggests an equilibrium: stake distribution stabilized, and payout distribution followed.

Does the System Amplify Concentration?

The key question: does payout inequality exceed stake inequality? If the payout Gini sits consistently above the stake Gini, the tournament formula amplifies concentration. If it tracks below, the formula dampens it.

Dual-line chart showing payout Gini and stake Gini over time, both near 0.95-0.97, with payout Gini slightly higher throughout
Dual-line chart showing payout Gini and stake Gini over time, both near 0.95-0.97, with payout Gini slightly higher throughout

The two lines track each other closely. Payout Gini sits slightly above stake Gini across most rounds. The red-shaded region shows where the system amplifies concentration; the gap is narrow, typically 1--3 percentage points. Stake inequality explains most of payout inequality.

This fits the mechanics. Payout equals stake times score times the payout factor. If scores are roughly similar across models, as metric convergence suggests, then payout inequality mirrors stake inequality with small amplification from score variance. Large stakers do not earn higher percentage returns. They earn more absolute NMR because they stake more. The same pattern shows up in the payout ROI by stake tier chart.

Who Captures the Payouts?

Breaking positive payouts into cohorts shows where NMR actually flows.

Stacked area chart of payout share by cohort -- top 1 percent in red, top 1-5 percent in amber, top 5-10 percent in blue, bottom 90 percent in teal
Stacked area chart of payout share by cohort -- top 1 percent in red, top 1-5 percent in amber, top 5-10 percent in blue, bottom 90 percent in teal

The top 1% of earning models captures roughly 10--15% of total positive payouts in recent rounds. The top 10% combined takes 30--40%. The bottom 90% still receives the majority -- concentrated, but not winner-take-all in the strict sense.

The top-1% share has held steady since round 600. Earlier rounds show more volatility because fewer models participated, so one high earner could swing the percentage. As hundreds more models entered, cohort shares smoothed out. The pattern matches the stake concentration data: the top 10 models hold a significant share of total stake, but that share is not growing.

Lorenz Curves Across Three Eras

A Lorenz curve plots cumulative payout share against cumulative model share. The further a curve bows from the 45-degree equality line, the more unequal the distribution.

Three Lorenz curves for rounds 309, 599, and 1099, showing increasing bow from the equality line across eras with Gini values of 0.92, 0.97, and 0.96
Three Lorenz curves for rounds 309, 599, and 1099, showing increasing bow from the equality line across eras with Gini values of 0.92, 0.97, and 0.96

Round 309 (early era, Gini 0.92) sits well below the equality line but visibly closer to it than later rounds. Round 599 (mid era, Gini 0.97) and round 1,099 (recent era, Gini 0.96) are nearly identical -- both strongly bowed, with the bottom 60--70% of models accounting for only a thin slice of total payouts.

The convergence between the mid and recent eras is the key finding. Payout inequality is not still growing. It stabilized at a high level around round 500--600, when participation and stake distributions settled into their current shape, and has held there since.

What This Means for Small Stakers

A Gini of 0.97 sounds alarming, but several structural factors work in small stakers' favor:

  • Payouts scale linearly with stake. A model with 10x the stake earns roughly 10x the payout for the same score, not 100x. Percentage returns are similar across tiers, as staking profitability data shows.
  • Count disparity drives the Gini, not systematic extraction. Thousands of models stake tiny amounts. A few hundred stake large amounts. That alone produces a high Gini even if the system treats everyone proportionally.
  • Score-based payouts reward model quality. Unlike pure capital markets where returns scale with position size, Numerai payouts depend on prediction accuracy. A small staker with a strong model earns a higher percentage return than a large staker with a weak one.
  • The payout factor compresses everything. At a payout factor near 0.10, both earnings and burns are small fractions of stake. Absolute inequality in NMR terms is far lower than when the factor was 1.0 in early rounds.

The tournament is not becoming more winner-take-all. It became concentrated early as stake distribution settled, and has held steady since. Payout inequality tracks stake inequality with only marginal amplification. For small stakers, the binding constraint is model quality -- the same constraint that applies to everyone.