How Much Screening Buys a Second? Speed, Selection, and the Maker's Spread

Дата публикации: 15-10-2026 13:04:19

We study the spread a liquidity provider needs to break even against counterparties that can exploit a stale quote, and we place two defenses on a single scale: repricing sooner and screening informed flow. A break-even condition pins down the exact screening rate at which a slower maker matches a faster unscreened venue: the selection that buys back the extra staleness. The result requires only an integrable price innovation and therefore holds under jumps, atoms and infinite variance. We take the model to four USDC-WETH pools benchmarked against Binance ETH-USDT from June to August 2026.
TLDR
The one-second benchmark innovation is sharply non-Gaussian: 73% of seconds show no price change, and the excess kurtosis is 154;
Cutting cadence from twelve seconds to one sheds 84.5% of the expected shock, so a twelve-second maker must screen at least 84.5% of informed flow to match a one-second venue, far above the 71.1% that a Gaussian model implies;
The conclusion does not depend on pinning toxicity down: over the informed shares admitted by the tightest netting bound, the threshold stays between 84.5% and 85.2%. Matching one-second execution from a twelve-second slot is worth screening out roughly six in seven informed orders;
In trending markets, the stale pool is picked off at execution: with-trend fills obtain an effective spread 11.1 bps lower than against-trend fills, with the same sign in all four pools;
Missed proposer slots show the discrepancy a stale pool must absorb growing with elapsed staleness at an elasticity of 0.45, close to the diffusion rate of one-half;
Predictable drift is a centering problem: it widens a spot-centered quote, but its cost vanishes once the quote is recentered on the expected reference.
1. Why does staleness matter for liquidity providers?
An LP who posts a firm two-sided quote has written an option on the asset. Traders who know where the price is heading exercise it against the maker, while everyone else trades by chance. The maker recovers what the informed take from the spread it charges the rest. The competitive spread is the width at which the two balance: losses to better-informed counterparties are repaid by earnings from everyone else.
Automated market makers, or AMMs, make this option unusually stark. A constant-function pool quotes a deterministic price off its reserves and refreshes only when someone trades against it. Between trades, the quote is stale, and on a chain that settles in discrete blocks, it can stay stale for the whole block, roughly twelve seconds on the network we study. With no last look and no way to pull a posted quote, an arbitrageur watching a faster venue picks the pool off the moment the external price clears fees.
A maker has two defenses: shorten the time its quote is exposed, or screen the flow and decline the orders most likely to be informed. Which defense is available depends on the venue. A permissionless pool must fill every order that clears its invariant, so its only lever is exposure; a proprietary or curated maker can do both. Our question is how much a second of reduced staleness is worth against a unit of screening, and when one substitutes for the other.
Three following features organize the paper:
The threshold is scale-free. Under a driftless diffusion it depends only on the ratio of the two horizons and the informed share \theta, not on volatility, fee, or trade size.
Tail shape matters. The threshold’s response to toxicity is governed by the expected loss on an executed informed order, so a fat-tailed innovation and a Gaussian one of equal variance imply very different spreads and screening thresholds: the shape of the tail, not just its width, is what the maker prices.
Drift is a centering problem. A predictable price component tilts which side gets picked off and widens a quote held at the current reference, but a maker that centers its quote on the expected reference recovers the driftless spread.
2. Data
We use the Binance ETH-USDT best bid and ask as the benchmark, reduced to a one-second midpoint m_t over the period from 1 June to 29 August 2026. On-chain execution is decoded from raw swap logs for four USDC-WETH pools spanning two AMM generations, Uniswap v2 and v3. Each swap is timed at its block’s slot time, read from the block header, and after removing dust swaps, the sample holds 1,725,539 swaps. The batch-netting statistic uses the full Binance trade tape of 260 million trades.
Pool (fee tier)
Number of swaps
Volume in $M
Uniswap v3 (1 bp)
1,290,417
2,809
Uniswap v3 (5 bps)
349,391
6,261
Uniswap v2 (30 bps)
56,378
57
Uniswap v3 (30 bps)
29,353
259
For a fill j at pool v, time t_j, taker direction q_j \in \{-1, +1\}, and execution price p_j^{\text{ex}}, we build the signed markout, the effective spread, and the elapsed staleness:
\mathrm{MO}_j (\tau) = q_j \frac{m_{t_j + \tau} - m_{t_j}}{m_{t_j}}, \ \mathrm{ES}_j = 2q_j \frac{p_j^{\text{ex}} - m_{t_j}}{m_{t_j}}, \ a_j = t_j - t^{\text{last-upd}}_v,
where t^{\text{last-upd}}_v is the time of the previous swap in pool v. Both ratios are reported in basis points throughout. The local drift \hat{\mu}_t is the trailing sixty-second benchmark return, and a second is trending when |\hat{\mu}_t| > 10 bps; by this cut, 88.9% of seconds are range-bound and 11.1% trending, and 318,822 of the swaps fall in trending seconds.
Feature engineering
For the v3 pools, we read the direction and the price from the signed amounts: the taker direction is the sign of the pool’s signed USDC amount, and the executed price is the ratio of the traded amounts. Wherever consecutive swap records chain, this direction agrees with the post-swap price path on 99.88–100% of fills. The pool-minus-benchmark deviation is then basis-adjusted by subtracting its own three-hundred-second rolling median, which absorbs the slow USDC/USDT basis.
Against the raw ETH-USDT mid, the median effective spread is 7.7 to 29.7 bps across pools, and after the adjustment it is 1.0 to 10.2 bps. Panel B is a diagnostic of the toxicity proxy we ultimately discard: the share of trades with a positive five-second markout sits at 0.34–0.40 in every pool, as expected of a statistic driven by the symmetric innovation rather than by the informed share. The persistent pool-benchmark gap is a slow stablecoin basis, typically -5 to -10 bps, that drifts over weeks, not intra-slot staleness.
The reference and identification
The Binance quoted spread is one tick wide almost always, with a median of 0.0538 bps. This is the empirical floor, i.e., the price of liquidity under no cadence constraint whatsoever, and it is the number every model spread below should be read against. Re-pricing every pool against the last trade instead of the mid leaves the basis-adjusted effective spread essentially unchanged.
Every causal statement rests on one assumption: at the one-second to one-minute horizon, the benchmark mid, its increments, and the drift are predetermined with respect to any single pool’s idiosyncratic order flow. Binance turns over orders of magnitude more volume than the four pools and leads price discovery, so the pools are price-takers that re-converge to the benchmark through arbitrage. A slot-level lead-lag regression confirms this ordering directly: the pool absorbs 96% of a Binance move within a minute and does not lead it.
3. Model
The model combines the option interpretation of posted quotes in Copeland and Galai with the competitive adverse-selection pricing logic of Glosten and Milgrom. Let p_t=\log P_t be the external reference price, and let the innovation over the maker’s quote-exposure horizon h be
Z_h := p\_{t+h}-p_t, \quad \mathbb{E}[Z_h]=0, \quad 0<\mathbb{E}|Z_h|<\infty
We call h the quote-exposure horizon: it is the elapsed time between the reference observation used to set the quote and the execution opportunity. The maker posts a symmetric half-spread s around P_t; for an AMM, we interpret it as a reduced-form marginal execution wedge, s=-\log(1-f)\simeq f.
Suppose that a fraction \theta of potential flow is informed. Uninformed traders execute for liquidity reasons and earn the maker s on average. Informed traders observe Z_h before execution, choose D_i=\operatorname{sign}(Z_h), and execute only when |Z_h|>s. Their expected cost to the maker is
A_h(s):=\mathbb{E} \left[(|Z_h|-s)_+ \right]
Movements within the spread generate no informed trade, while movements beyond it generate a loss equal to the excess. A maker that screens rejects a fraction \eta of informed opportunities, independently of the realized innovation, and preserves every uninformed order. The competitive break-even half-spread s^* then satisfies
s^* = \frac{\theta(1-\eta)}{1-\theta} A_h(s^*)
Note that this equation has a unique solution; the spread is strictly increasing in toxicity \theta, strictly decreasing in screening \eta, and nondecreasing in the exposure horizon h. Longer exposure adds independent mean-zero innovations to the pricing error, and because the informed-loss payoff is convex in that error, the additional uncertainty weakly raises expected loss at every fixed spread, without requiring a variance or a Gaussian return distribution.
Screening versus execution speed
Let the reference layer quote at horizon h_0 without screening, with spread s_0, and let a proprietary maker quote at h_P\geq h_0. Then, the exact screening threshold is
\eta_{\mathrm{crit}}(h_P,\theta) := 1-\frac{A_{h_0}(s_0)}{A_{h_P}(s_0)}
The slower maker supports a narrower spread than the reference layer if and only if \eta>\eta_{\mathrm{crit}}, an equal one exactly at \eta=\eta_{\mathrm{crit}}, and a wider one otherwise. At the reference spread s_0, the slower maker would incur the unscreened loss A_{h_P}(s_0), whereas the reference layer incurs A_{h_0}(s_0); the threshold is the fraction of the former that must be removed to make these losses equal.
As informed opportunities become rare, both spreads approach zero, and the threshold converges to a ratio of expected absolute innovations:
\lim_{\theta\downarrow0}\eta_{\mathrm{crit}}(h_P,\theta) = 1-\frac{\mathbb E|Z\_{h_0}|}{\mathbb E|Z_{h_P}|}
Under a driftless Gaussian, this limit is 1-\sqrt{h_0/h_P}, the spread grows with the square root of the exposure horizon, and the threshold strictly increases with toxicity. Away from the Gaussian, the threshold’s response to toxicity depends on expected loss per executed informed order, A_h(s_0)/\mathbb{P}(|Z_h|>s_0), and can have either sign.
Predictable drift
With a known drift \mu, a quote held at the current reference faces the innovation Z_h(\mu)=\mu h+M_h. Under symmetric residual innovations and balanced uninformed flow, upward and downward drift have the same spread cost, and the spread rises with |\mu|: at second order near zero drift under Gaussian innovations, and linearly in the exposure horizon when residual uncertainty vanishes. However, a maker that centers its quote at p_t+\mu h faces only M_h and recovers exactly the zero-drift spread. The drift premium therefore measures the cost of a centering restriction or an uncorrected forecast error.
4. Results
Throughout, the reference execution layer is the one-second subslot, i.e., h_0 = 1 s, and both the slow unscreened benchmark and the screened proprietary maker quote at the twelve-second slot, i.e., h_C = h_P = 12 s.
Calibration and innovation
We estimate a one-second volatility of \hat{\sigma} = 0.85 \text{bps}/\sqrt{\text{s}} (47.8% annualized). The trending volatility is 1.82 \text{bps}/\sqrt{\text{s}} against 0.63 \text{bps}/\sqrt{\text{s}} in range-bound seconds, so the trending state is 2.9\times as volatile.
The subslot innovation is, however, sharply non-Gaussian in two ways. First, it is heavily discrete, with a zero atom no Gaussian can place: at a one-second cadence, 73.4% of subslots see no change in the mid. This is not a tick-coarseness effect: one tick, 0.054 bps, is sixteen times finer than \hat{\sigma}. The atom reflects how rarely the mid updates; \hat{\sigma}^2 is carried by the seconds in which it does move, when it jumps roughly twenty ticks. Second, it is fat-tailed, with an excess kurtosis of 154 at one second.
The joint consequence is that the Gaussian closed form overstates the typical shock at short horizons: the realized mean absolute innovation is only \kappa(1\text{s}) = 0.29 bps, 0.43 of the Gaussian value there, a ratio that climbs to 0.80 at twelve seconds as aggregation averages the calm seconds and the bursts.
The cost of staleness
Under regime-conditional Gaussian calibration, shortening cadence from twelve seconds to one lowers the expected shock by 71.1% in both regimes: the venue that quotes fastest sheds most of the risk, in calm and trending markets alike. On the pooled empirical innovation, the reduction is larger, 84.5% (\kappa falls from 1.880 to 0.292 bps).
Regime
\kappa(1\text{s})
\kappa(4\text{s})
\kappa(12\text{s})
Cut, 12s to 1s
Range-bound
0.504
1.009
1.748
-71.1%
Trending
1.455
2.910
5.041
-71.1%
Pooled empirical
0.292
—
1.880
-84.5%
Drift is a negligible share of the shock’s magnitude; its role in the model is directional. In the trending regime, drift accounts for 0.01% of the shock at twelve seconds and 0.001% at one second, because drift enters the innovation linearly in h while diffusion enters as \sqrt{h}. At block and subslot cadence, therefore, the risk is almost entirely diffusion.
Staleness and the accumulated discrepancy
The pools themselves show how the discrepancy a stale quote must absorb grows with the time it has been exposed. We regress the log discrepancy on log elapsed staleness with pool fixed effects. Elapsed staleness is endogenous, because arbitrageurs update a pool sooner after a large benchmark move, which biases OLS downward. We therefore instrument it with the log block gap: a missed proposer slot lengthens the gap from twelve seconds to twenty-four or thirty-six for reasons unrelated to the market.
All
Range-bound
Trending
Benchmark move since previous update (IV)
0.448 (0.054)
0.408 (0.055)
0.595 (0.099)
Pre-trade pool deviation, v3 pools (IV)
0.318 (0.043)
0.273 (0.044)
0.412 (0.072)
First-stage F (benchmark move)
3,046
2,506
658
The instrumented elasticity of the benchmark move is 0.45, in line with the diffusion rate of one-half; its point estimate is higher in trending markets (0.60) than in range-bound ones (0.41), the ordering the model predicts. OLS lies below IV in every column, as the endogeneity of update timing implies. Each additional second of staleness therefore raises the discrepancy a pool must absorb at close to the diffusion rate, which is the cost that subslot cadence removes.
The endogenous spread
The half-spread s^* is participation-constrained, and it departs from the volatility-anchored rule of thumb \theta\sigma\sqrt{h}/(1-\theta), which charges as if every informed order traded against a shock of size \sigma\sqrt{h}. The rule of thumb overstates s^* by a factor that grows with toxicity, from about 1.7 \times at \theta=0.10 to about 7 \times at \theta=0.90 on the empirical law.
\theta
Naive \frac{\theta}{1-\theta}\sigma\sqrt{h}
Gaussian
Empirical
0.10
0.33
0.24
0.19
0.25
0.98
0.60
0.51
0.50
2.95
1.29
1.15
0.75
8.84
2.26
2.24
0.90
26.53
3.36
3.82
Evaluating A_h on the empirical law rather than the Gaussian is not a one-way correction: the empirical spread is tighter below \theta \approx 0.76 and wider above. Going from twelve seconds to one cuts the empirical break-even half-spread by 73% to 85%, against 71% under the Gaussian. At \theta =\nu (1\text{s}), the unscreened one-second half-spread, 0.454 bps, remains more than ten times the 0.027 bps half-spread quoted on the CEX.
Toxicity
Toxicity is disciplined by the batch-netting residual \nu(h): the share of benchmark volume that fails to net inside an h-second batch, in excess of a sign-randomized null. It falls monotonically with batch length, from \nu(1\text{s}) = 0.706 through \nu(12\text{s}) = 0.402 to \nu(60\text{s}) = 0.257. A run-preserving null explains almost all of the directional imbalance, so \nu bounds toxicity from above rather than identifying it. We therefore treat \theta as a parameter, with \nu(60\text{s}) = 0.257 as the binding upper bound.
One-sided staleness in trending markets
The model’s sharpest prediction concerns the direction of the staleness cost. In a trend, the informed hit the stale quote on the side toward which the price is moving: executed informed orders are disproportionately with-trend, and the with-trend side carries the larger expected loss.
The pooled pick-off gap, i.e., the difference in effective spread between with-trend and against-trend fills in the trending regime, equals -11.1 bps with pool fixed effects (hour-clustered standard error 0.41, t = -27.3; shift test p < 0.002). With-trend fills execute at -1.71 bps, better than the benchmark mid, while against-trend fills pay 6.97 bps. The gap has the predicted sign and is significant in all four pools: -7.6 bps in the v3 1 bp pool, -11.3 bps in the v3 5 bps pool, -69.4 bps in the v3 30 bps pool, and -60.9 bps in the v2 pool. In the two thirty-basis-point pools it is about twice the fee, because with-trend flow there trades when the stale price covers the fee, while against-trend flow pays the fee in full.
With-trend takers also arrive after a larger benchmark move: over the twelve seconds before the block, the benchmark moves 4.85 bps in the trend’s direction before with-trend fills and 2.77 bps before against-trend fills. Once the block lands, the benchmark does not move further in the taker’s favor: the five-second markout gap is -0.06 bps and not significant, so the stale-quote loss is realized at execution rather than after it.
The screening threshold
The model’s central comparison has a direct empirical counterpart: the rate at which a twelve-second maker must screen to match a one-second venue. In the low-toxicity limit, evaluated on the empirical innovation, it equals 1 - 0.292/1.880 \approx 84.5\%, 13.3 percentage points above the driftless Gaussian benchmark of 1 - 1/\sqrt{12} \approx 71.1\%, because \kappa falls faster with cadence than \sqrt{h} would predict. Positive serial dependence at the one-second horizon accounts for about 3 points of the gap, and the shape of the one-second innovation for the remaining 10: most seconds are calm and a minority carry large moves, which aggregation to twelve seconds averages out. Across alternative references (the BBA mid, the microprice, a trade-implied mid, and the last trade), it ranges from 84.0% to 85.1%.
Solving the exact break-even at positive toxicity raises both curves and, because the empirical curve is the flatter of the two, they nearly meet at high toxicity: at \theta = 0.706 the empirical threshold is 87.8% against the Gaussian 86.4%. Over the informed shares admitted by the tightest netting bound, the empirical threshold stays between 84.5% and 85.2%, and up to \theta = 0.9 between 84.5% and 90.9%, so the conclusion does not depend on pinning toxicity down.
Screening would have to be extraordinarily effective, rejecting on the order of 85% of informed opportunities, for a block-cadence maker to match one-second execution on this pair. The equal-cadence premium quantifies the converse: a one-second maker that screens even a quarter of informed flow already prices 0.084 bps inside an unscreened one-second venue, whose half-spread is 0.454 bps, rising to 0.302 bps at three-quarters screening.
Robustness
Moving the drift-sign series circularly by at least an hour preserves its persistence and the timing of every fill while breaking its alignment with the fills; over 500 such shifts, no draw exceeds 1.1 bps in absolute value against the observed -11.1 bps. On a chronological holdout, the benchmark return in the direction of the trailing drift averages only +0.064 bps over the next twelve seconds: predictable drift is small in this sample, so the pick-off documented above reflects staleness rather than drift, and a recentered quote would gain little over a spot-centered one. The calm-window placebo is passed: outside trends the markout gap is accounted for by the benchmark’s own continuation.
5. What this means for liquidity providers
1. Speed is the cheap defense. Cutting cadence from twelve seconds to one sheds 84.5% of the expected shock and cuts the break-even half-spread by 73% to 85% at a fixed informed share.
2. Screening alone rarely substitutes for speed. Matching one-second execution from a twelve-second slot is worth screening out roughly six in seven informed orders, and more at higher toxicity.
3. At equal speed, screening still pays. Screening narrows the spread by strictly less than the screening rate times the unscreened spread, because the narrower spread makes additional informed opportunities profitable, but a quarter of informed flow screened already prices 0.084 bps inside an unscreened venue.
4. Do not price with Gaussian rules of thumb. The tail shape, not just its width, is what the maker prices; the volatility-anchored rule overstates the spread by up to 7 \times, and the Gaussian understates the screening threshold by 13 points.
5. Recenter rather than widen. Predictable drift is a centering problem rather than a spread problem: a maker that centers its quote on the expected terminal reference removes the drift premium entirely.
6. Limitations
Toxicity is not point-identified. The batch-netting residual is an upper bound whose excess over a run-preserving null is indistinguishable from zero, so we report the threshold across informed shares up to that bound, over which it moves by less than one percentage point. The model holds potential flow fixed and resets each quote to the reference, which abstracts both from the change in counterparty composition that faster repricing can induce and from the fee-determined no-arbitrage band of an AMM. Screening is costless and independent of opportunity size, whereas a classifier that preferentially rejects the most profitable informed orders would call for a loss-weighted threshold.

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