Numerai Meta-Model: Stake Concentration and Effective N

Numerai's stake-weighted meta-model now has an equal-weight-equivalent participant count near 50, down from a peak near 175, even as total staked models passed 4,000.

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

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 numbers round by round, and the structural trend is toward concentration.

What the Meta-Model Actually Is

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

The result is a prediction vector Numerai uses to rank stocks and build a portfolio. Real capital trades on it, which makes every staker a partial portfolio manager. If a handful of large stakers dominate the weighting, the meta-model behaves less like a broad crowd average and more like a concentrated committee.

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 controls about 15% on its own. A small cohort has outsized influence over the meta-model.

Concentration is not inherently bad. If the largest stakers are also the best predictors, weighting by stake routes influence toward higher-conviction signals — exactly what the system is designed to do. The problem shows up when the top models correlate with each other. If the top 10 run similar strategies, the meta-model loses diversity regardless of how many thousands of nominal contributors sit behind them. The Diversification Paradox walks through that failure mode.

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.

Effective N peaked near 175 around rounds 300-400 and has trended down ever since, landing near 50 in recent rounds. Over the same stretch, total staked models climbed past 4,000. Nominal participation tripled while effective participation fell by two-thirds.

That gap is one of the clearest structural metrics for the meta-model. The stake-weighted signal has the same concentration as a portfolio built from roughly 50 equally weighted models, not 4,000. A declining effective N means the meta-model is more dependent on fewer participants, even if the nominal crowd is large.

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 staker turnover per round, split into retained models and new entrants, showing most recent rounds retaining almost the full prior top 10.
Top-10 staker turnover per round, split into retained models and new entrants, showing most recent rounds retaining almost the full prior top 10.

The top 10 is extremely sticky. From round 400 onward, most rounds see zero new entrants, with an occasional round swapping in one fresh model and very rarely two. The core group of large stakers is almost entirely persistent week to week. That is exactly what a staking system produces: strong performers accumulate NMR and reinforce their position, 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. Model Survival covers the longer-term attrition picture, and Stake-Weighted Age tracks the age dimension.

The meta-model ends up stable — the core signal doesn't swing wildly — but slow to adapt. 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 very large accounts. 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 small stakers the tournament is a scoring and learning environment, not a real source of influence over Numerai's trades.

They still matter as a talent pipeline. A 1 NMR staker can become a future top-10 model if the strategy proves out and the position scales up, and the breadth of the small-staker base is a leading indicator of future meta-model diversity.

Is the Meta-Model More Broadly Distributed?

By the clearest structural measure -- effective N -- the answer is no. The meta-model draws on a more concentrated recent stake base than it did several hundred rounds ago, even as nominal participation has grown, and concentration in the top cohort keeps 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 back 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 reduce a large staker's influence, and the data suggests incoming stake diversity is not keeping pace with entrenchment.

The meta-model's resilience depends on the structural diversity of the whole participant base, not just the best individual models. Concentration, effective N, turnover, and the stake distribution say more about that resilience than any single performance metric. Quality still has to be judged through realized fund and tournament outcomes; these charts measure who has influence and how broad that influence really is. Live versions of these charts are on the Models page, with round-by-round detail in the Rounds and Trends sections.