The DeFi herding statistic that mostly counts different wallets

Imagine 100 consecutive trade pairs. If 98 pairs come from different wallets, the cross-wallet bucket can own most of the total autocorrelation even when each cross-wallet pair is only weakly aligned. A large bucket share is not the same claim as strong pairwise herding.

Bai and Kan expose that denominator problem in on-chain markets. Their correction is a ratio called kappa (κ): cross-account sign correlation divided by same-account sign correlation. The distinction reverses the casual reading of small Uniswap swaps and reveals a different mechanism—accounts racing to the same centralized-exchange price—where κ really is high.

A trade sign is +1 for a buy and −1 for a sell. Persistent order flow means nearby signs tend to agree. For a chosen lag, let p be the fraction of pairs from the same account. Let ρ_same and ρ_diff be the average products of demeaned signs for same- and different-account pairs. Their ratio κ = ρ_diff/ρ_same measures behaviour pair by pair. The traditional herding share h measures contribution to the total after weighting by how often each pair type occurs.

def herding_share(p_same, kappa):
    cross_weight = (1 - p_same) * kappa
    return cross_weight / (p_same + cross_weight)

def kappa_from_share(p_same, share):
    return (share * p_same) / ((1 - p_same) * (1 - share))

The site runs the tested TypeScript implementation; Python and C++ are line-for-line translations. The equation makes the confound visible. Whenp shrinks, the cross-account bucket receives almost all pair weight, so h rises even if κ does not change.

Feeding the reported 65% share and 2.5% same-wallet rate backward through the equation gives κ ≈ 0.048. That is close to the paper's 0.05 after allowing for rounded table inputs. On the order book, a similar 61% share accompanies κ = 0.76—a fundamentally different market even though h looks familiar.

On the EVM order book, pairs no more than ten blocks apart contribute 90–96% of cross-account covariance. Same-block orders cannot imitate fills that neither account has observed yet. The authors instead test a common-signal explanation: a cross-fitted gradient-boosted model predicts each order sign using only recent Binance returns, signed volume, and volatility.

The main filter removes 84% of cross-account covariance. Delaying every input by half a second barely moves that result—83%—which weakens the concern that its latest 100 ms grid cell leaks post-block Binance data. Cross-fitting by clock-hour parity prevents the filter from absorbing its own in-sample noise into the residual statistic.

A basis point is one hundredth of a percent. A negative markout means the liquidity provider sold before the reference price rose or bought before it fell. Orders aligned with the filter's predicted sign receive steadily worse markouts, connecting the statistical race to adverse selection rather than merely to classification accuracy.

Reproduce the decomposition before training anything: report p, κ, and h together across venues, lags, and size thresholds. Then fit a shallow XGBoost-style model with strict time-blocked cross-fitting, and compare it with a transparentlogistic-regression filter. If the inferred common component survives delayed inputs and alternative leading venues, test whether it predicts markouts out of sample.

The general lesson travels beyond crypto. Whenever a headline contribution share combines a group's frequency with its conditional effect, publish both parts. Otherwise a population with more entities can look more coordinated even when its pairs are less correlated.