Fill Probability Curve Decay
The Formal Definition
The quantitative decay curve modeling the declining mathematical likelihood that a resting limit order will execute as time passes without a fill, driven by adverse selection, queue position shifts, and directional price drift away from the order's limit price.
P(Fill | t > T) = P_0 × e^{-γt} × (1 - Adverse Selection Decay Factor)
Cole Barrett's Reality Check
The Unvarnished Bottom Line"A limit order is like fresh produce: it goes bad the longer it sits on the shelf. In the first ten seconds, your limit order has a high probability of a clean fill. If it sits unfilled for ten minutes, it usually means the market is moving away from you, or the only person who will fill it is an informed trader who knows your price is about to get run over."
Interactive Simulator: Test the Math
Real-World Example: Scenario Breakdown
Examining the real numbers for: An intraday trader monitoring a resting limit buy order for 1,000 shares of a stock at $100.00
| Execution Metric | Adaptive Order Replacer | Static Limit Order Submitter |
|---|---|---|
| Fee / Rate | $0.0035/share DMA rate | $0.0035/share rate |
| Spread / Buffer | Monitored fill probability decay: cancelled and repriced limit orders that sat unfilled for more than 45 seconds | Left a static $100.00 limit buy order resting on the book for 45 minutes as the market moved up to $100.80 |
| Execution / Status | Repriced dynamically to the new midpoint at $100.05 as the stock trended upward; filled immediately | Fill probability decayed to near zero; order was completely forgotten until an unexpected negative news drop hit |
| Total Cost / Result | Maintained high fill probability through dynamic order cancellation and replacement | Suffered severe adverse selection on an abandoned, decaying limit order |
How Brokers Weaponize This Term
Never leave passive limit orders resting on illiquid books without an automated Time-in-Force expiration or cancel-and-replace algorithm. Orders that sit unfilled for extended periods are statistically prone to adverse selection fills on breaking news.
Broker Evaluation Matrix
Cole Approves
Interactive Brokers: Provides institutional algorithmic order types (Accumulate/Distribute, Adaptive Algo) that cancel and replace stale limit orders before fill probability decays.
Read Audit →Cole Flags / Avoids
Basic Mobile Retail Apps: Lacks automated order-chasing or cancel-and-replace tools, leaving retail limit orders resting indefinitely as stale targets.
View Trap Details →Frequently Asked Questions
What causes fill probability to decay?
Price movement away from your limit price, order queue jumps by competing traders, and cancellations by counterparties all reduce the likelihood of execution over time.
What is an 'Adaptive Algo'?
An adaptive algorithm dynamically adjusts your limit price between the bid and ask based on real-time order book urgency, maximizing fill speed while minimizing spread crossing costs.