Day 22: Probabilistic Toxicity Modeling — Predicting P(Δmaker-taker > 0)

Upgrade toxicity routing from binary gating to probabilistic modeling with calibrated probability estimates

Published

Mar 7, 2026

Day 22: Probabilistic Toxicity Modeling

Objective

Upgrade the toxicity routing from binary maker/taker decisions to probabilistic modeling — predict P(Δ_maker-taker > 0 | x) where x = microstructure features, then use calibrated probabilities to make routing decisions.

Key Insight

Previous approaches used hard thresholds: - “If momentum > threshold → use taker” - “If feature score > X → suppress maker”

This loses information. Instead, predict the probability that maker will underperform taker, then decide based on expected value:

E[edge] = P(taker) * E[Δ|taker] + P(maker) * E[Δ|maker]

Only deviate from baseline (always-maker) when E[edge] exceeds uncertainty buffer.

Methodology

Feature Set (same as Day 21 PM)

mom5: 5-minute price momentum (bps)
mom15: 15-minute momentum
vol5: 5-minute volatility (bps)
vol15: 15-minute volatility
spread: Current bid-ask spread (bps)
depth_imbalance: Order book imbalance
time_of_day: Hour indicator

Model

Logistic regression for P(toxicity | x)
Walk-forward training: 6 months train → 1 month test
Calibrate probabilities using isotonic regression

Routing Policy

if P(toxicity) > 0.7 and E[edge_above_threshold]:
    use taker
else:
    use maker (baseline)

Expected Outcome

Probabilistic routing should outperform binary gating because: 1. Uses full distribution information, not just threshold 2. Can weight decisions by confidence 3. Naturally handles feature uncertainty

Run ID

day-22-prob-toxicity