Limit Order Fill Probability

The simplest way to backtest a limit order is: if the bar's low is at or below the limit price on a buy, the order fills. That rule assumes two things that are rarely true — that you were the very first order resting at that price, and that reaching the price with the tape means trading through your entire size. Neither holds in a real order book, where you queue behind everyone who arrived earlier at that price level and the market only trades through part of the book before reversing.

Worked example: touch is not fill

A strategy wants to buy 10,000 shares with a limit at the current bid. Over the next bar, the price does trade down to that level — the naive "touch = fill" backtest marks the full 10,000 shares filled at the limit price, no slippage, no cost.

What actually happened at that price level: 60,000 shares of resting buy interest were already queued ahead of the order (the bid had been sitting there for a while), and only 45,000 shares traded through the level before price moved back up. The order never reaches the front of the queue — it gets zero fill, not a full fill.

Now soften the assumption to a realistic queue model: fill probability scales with how much volume traded through the level relative to the resting size ahead of you,

$$P(\text{fill}) \approx \min\!\left(1,\; \frac{\text{volume traded through level}}{\text{queue ahead} + \text{your size}}\right).$$

Plugging in: 45,000 / (60,000 + 10,000) ≈ 64%, so a realistic simulation fills roughly 6,400 of the 10,000 shares, not all 10,000 and not zero.

Model	Fill assumption	Shares filled	Backtest Sharpe
Touch = fill	Any touch fills 100%	10,000	2.0
Queue-aware	Volume-through vs. queue-ahead	~6,400	1.3
Conservative (last-in-line)	Fill only if fully through queue	0	(order never fills)

The three models don't just differ by a scaling factor — the queue-aware one also delays when the fill happens relative to the signal, since the order sits resting while price moves, changing which trades even count as "in the market" when the signal decays.

Where queue position data isn't available, a defensible proxy is to require the bar's traded volume at that price to exceed some multiple of the order size before granting any fill, and to fill only the fraction implied by that ratio.