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The Fill-Probability Trap: Why Easy Fills Can Be Bad Fills

2026-03-08 · finance

The Fill-Probability Trap: Why Easy Fills Can Be Bad Fills

Date: 2026-03-08
Category: explore (market microstructure)

Why this is interesting

A lot of execution logic still assumes:

But in modern limit order books, this can fail hard. Sometimes the orders that fill fastest are exactly the ones with the worst post-fill markout.

This note explores that paradox and how to operationalize it.

Core intuition: queue mechanics create a hidden trade-off

At the touch (best bid/ask), your passive order quality depends on two competing effects:

  1. Execution likelihood (you want this high)
  2. Post-fill return quality / toxicity (you want this not-too-negative)

In stressed or one-sided books, these often move in opposite directions.

If your quote is very likely to be hit, it may be because informed/toxic flow is about to run through that level.

Evidence stack (papers + practitioner tooling)

1) Order-flow imbalance drives short-horizon price moves

Cont, Kukanov, and Stoikov (2011/2014) show short-horizon price changes are strongly linked to order-flow imbalance (OFI) and approximately linear in OFI, with slope tied to depth.

Implication: your fill probability is not independent of future markout; it co-moves with local supply/demand pressure.

Source: https://arxiv.org/abs/1011.6402

2) Queue-reactive dynamics: state matters, not just time averages

Huang, Lehalle, Rosenbaum model the book as a state-dependent queuing system (queue-reactive model), where order-flow intensities depend on current queue state.

Implication: fill outcomes should be conditioned on queue state, not global unconditional rates.

Source: https://arxiv.org/abs/1312.0563

3) Fill probabilities can be modeled semi-analytically under state-dependent flows

Yu et al. derive tractable expressions for fill probabilities at best and deeper levels in state-dependent stochastic LOB models, validated on FX data.

Implication: “probability of fill by horizon T” can be treated as a first-class model output in execution control.

Source: https://arxiv.org/abs/2403.02572

4) Live crypto evidence of the paradox

Albers et al. (2025) report a negative correlation between maker fill likelihood and post-fill returns on live Binance BTC perpetual experiments, framing a practical “market maker’s dilemma.”

Implication: optimizing fill-rate alone can destroy net edge.

Source: https://arxiv.org/abs/2502.18625

5) Practical backtest support: queue model choice matters

hftbacktest explicitly exposes multiple queue-position models (risk-averse, probabilistic variants), and documents that model choice materially changes simulated fills and performance.

Implication: naive queue assumptions create fake strategy quality.

Sources:

The paradox in one equation

If the objective is only:

[ \max ; P(\text{fill in } T) ]

you often end up selecting states with poor conditional post-fill outcomes.

A safer objective is:

[ \max_a ; \mathbb{E}[\text{NetEdge}\mid a] = \mathbb{E}[\text{spread capture} - \text{markout} - \text{fees/slippage} \mid a] ]

with explicit constraints on completion risk and tail outcomes.

Practical operator playbook

1) Track both sides of the trade-off

At minimum, maintain joint dashboards for:

2) Stop using fill-rate as a standalone KPI

Use a paired KPI:

or directly optimize expected net edge with q90/q95 guardrails.

3) Introduce a contrarian safety mode

When imbalance/toxicity proxies are extreme:

4) Calibrate queue model against live, not only backtest

Backtest queue model should be selected by minimizing fill/markout mismatch versus live trading, not by maximizing backtest Sharpe.

5) Keep model governance simple but strict

Promote policy changes only if all hold in canary:

Minimal experiment design (for future implementation)

  1. Partition events by queue-state deciles (imbalance + depth + cancel intensity).
  2. For each bucket, estimate:
    • fill probability by horizon,
    • conditional markout distribution.
  3. Compute Pareto frontier: high fill vs low toxicity.
  4. Deploy policy that stays on/near frontier.
  5. Monitor drift and retrain bucket mapping periodically.

Bottom line

The key microstructure lesson:

Fast fills are not automatically good fills.

Queue position, state-dependent flows, and toxicity make fill probability and post-fill quality a coupled control problem. The edge is not “fill more,” but “fill selectively where conditional markout is survivable.”