The Numerai Meta-Model: Stake Concentration and Effective N

How Numerai's stake-weighted meta-model works, who controls it, and why the effective number of independent models has fallen from ~175 to ~50.

Every week, Numerai combines predictions from thousands of staked models into a single stake-weighted signal. This meta-model is the actual input to the hedge fund's trading system, so the structure of participation matters as much as the quality of any individual model.

Who controls the meta-model? How concentrated is that control? And is the crowd getting more or less diverse over time? The Models page tracks these metrics round by round, and the picture below is not reassuring.

What the Meta-Model Actually Is

The meta-model is a stake-weighted average of all staked predictions. Stake 200 NMR and your predictions carry 20x the weight of someone who staked 10 NMR. Participants who stake more put more capital at risk, so the system trusts their predictions proportionally.

The result is a prediction vector Numerai uses to rank stocks and build a portfolio. The fund trades real capital on it, which makes every staker a partial portfolio manager.

That raises the obvious question: if a few large stakers dominate, is the meta-model a crowd signal or just a handful of whales?

Stake Concentration: Who Controls the Signal?

The stake concentration chart tracks the share of total stake held by the top 1, 5, 10, and 25 models round by round.

Stake concentration over time: top 25 models hold ~55-60% of total stake, top 10 hold ~35-40%, top 5 hold ~25%, top 1 holds ~15% in recent rounds.
Stake concentration over time: top 25 models hold ~55-60% of total stake, top 10 hold ~35-40%, top 5 hold ~25%, top 1 holds ~15% in recent rounds.

In recent rounds the top 25 models hold 55-60% of total stake, the top 10 hold 35-40%, and the single largest staker alone controls about 15%. A small cohort has outsized influence over the meta-model.

Concentration is not inherently bad. If the largest stakers are the best predictors, weighting by stake does exactly what it should — it routes influence toward higher-conviction signals. The problem arises when the top models are correlated with each other. If the top 10 all run similar strategies, the meta-model loses diversity even with thousands of nominal contributors. The Diversification Paradox explores that failure mode directly.

Effective N: The True Number of Independent Models

The Herfindahl-Hirschman Index (HHI) is a standard measure of concentration. Square each participant's share of the total and sum the squares. The reciprocal, 1/HHI, gives the "effective number" of equal-sized participants that would produce the same concentration. If every staked model held the same NMR, effective N would equal the total model count.

Effective number of Numerai models (1/HHI) over time alongside total staked model count: effective N peaked near 175 around round 300, has declined to roughly 50 in recent rounds even as total staked models climbed above 4,000.
Effective number of Numerai models (1/HHI) over time alongside total staked model count: effective N peaked near 175 around round 300, has declined to roughly 50 in recent rounds even as total staked models climbed above 4,000.

The picture is stark. Effective N peaked near 175 around round 300-400 and has trended steadily downward since, landing near 50 in recent rounds. Over the same stretch, the total number of staked models has climbed above 4,000. Nominal participation tripled while effective participation fell by two-thirds.

That gap between nominal and effective participation is the single most important structural metric for the meta-model. The stake-weighted signal behaves as if it were built from roughly 50 equally weighted models, not 4,000. A declining effective N means the meta-model is becoming more fragile and more dependent on fewer participants — which is exactly what the data shows.

Top-10 Turnover: Is the Leaderboard Sticky?

Concentration measures how much influence the top models have. Turnover measures whether they are the same models every round. Each round, the top-10 stakers include some number of new entrants and some number of returners from the previous round.

Top-10 model turnover per round, split into retained and new entrants.
Top-10 model turnover per round, split into retained and new entrants.

In practice the top 10 is extremely sticky. From round 400 onward, most rounds see zero new entrants, with an occasional round swapping in one — and very rarely two — fresh models. The core group of large stakers is almost entirely persistent week to week. That is what you would expect from a staking system: strong performers accumulate NMR and reinforce their position, while poor performers bleed stake through burns. Burns are capped at 25% per round, so it takes several bad rounds to meaningfully dent a large position. The longer-term attrition story is the subject of Model Survival, and the age dimension appears in Stake-Weighted Age.

The meta-model ends up with both stability — the core signal does not swing wildly — and slow adaptability. Whether that balance is right depends on how fast market regimes change relative to the burn rate.

Stake Distribution: What Does the Typical Staker Look Like?

Zoom out from the top of the leaderboard and the full distribution of stake sizes tells its own story.

Histogram of stake sizes per model on a log scale: largest peak near 0.01 NMR with ~460 models, a secondary peak at 1 NMR with ~300 models, and a long right tail extending past 10,000 NMR.
Histogram of stake sizes per model on a log scale: largest peak near 0.01 NMR with ~460 models, a secondary peak at 1 NMR with ~300 models, and a long right tail extending past 10,000 NMR.

The shape is a long left tail of tiny stakers and a thin right tail of whales. The largest bin sits at 0.01 NMR with roughly 460 models — barely more than a placeholder stake. A second peak shows up near 1 NMR with about 300 models. The right tail extends past 10,000 NMR, with only a handful of models in each of the top bins.

The meta-model effectively ignores most of these participants. A model staking 5 NMR in a system where the top model stakes over 10,000 NMR contributes well under 0.1% of the weight. For those small stakers the tournament is a scoring and learning environment, not a source of real influence over Numerai's trades.

Small stakers still matter as a talent pipeline. Today's 1-NMR staker could become tomorrow's top-10 model if their strategy proves out and they scale up. The breadth of the small-staker base is a leading indicator of future meta-model diversity.

Is the Meta-Model Getting Better?

By the clearest structural measure — effective N — the answer is no. The meta-model draws on fewer independent signals today than it did several hundred rounds ago, even as nominal participation has grown. Concentration in the top cohort is also creeping up.

A few patterns are worth watching round to round on nmrdash:

  • Effective N trending down while total staked models stay flat or grow means new entrants are staking small amounts and not meaningfully diversifying the signal.
  • Top-10 turnover dropping means the same models are entrenched, for better or worse.
  • Top-5 stake concentration climbing above 30% is a warning sign for fragility.

Numerai's scoring system does push against concentration. MMC (Meta-Model Contribution) rewards uniqueness — models correlated with the existing meta-model earn lower MMC scores and lower payouts, so they accumulate stake more slowly. The incentive is real but slow. With burns capped at 25% per round, it takes many bad rounds to meaningfully reduce a large staker's influence, and the data suggests incoming diversity is not keeping pace with entrenchment.

The meta-model's quality depends on the structural diversity of the entire participant base, not just on the best individual models. Concentration, effective N, turnover, and the stake distribution say more about its health than any single performance metric. Explore the live versions of these charts on the Models page.