EWMA Gas Price Penalty

DeepBook implements an exponentially weighted moving average (EWMA) system to dynamically adjust taker fees based on network gas prices. This feature helps prevent toxic takers from using high gas prices to prioritize their transactions and pick off stale maker orders.

Overview

The system tracks gas prices over time and applies a penalty fee to takers when the current gas price is unusually high compared to recent history. This protects makers from having their orders filled during periods of abnormal network activity where toxic takers might try to front-run or take advantage of stale orders.

How it works

The EWMA system calculates a smoothed average and variance of recent gas prices, then compares the current gas price against this historical baseline. When the current gas price is significantly elevated (beyond a threshold measured in standard deviations), an additional taker fee penalty is applied.

Key components

• Mean (μ): Smoothed average of recent gas prices.
• Variance (σ²): Measure of gas price volatility.
• Standard Deviation (σ): Square root of variance, used for z-score calculation.
• Z-Score: How many standard deviations the current gas price is from the mean.
• Z-Score Threshold: Trigger point for applying the penalty.

The formula

z_score = (current_gas_price - mean) / standard_deviation

if z_score > z_score_threshold:
    apply additional_taker_fee

Configuration parameters

The following table shows a sample configuration parameters for the EWMA system:

When does the penalty apply?

The penalty is applied only when all of the following conditions are met:

1. EWMA is enabled for the pool.
2. Current gas price ≥ mean (must be above average).
3. Z-Score > threshold (must exceed 3.0 standard deviations).

Penalty threshold calculation

Penalty Threshold = Mean + (Z-Score Threshold × Std Dev)
Penalty Threshold = 1,478 + (3.0 × 6,578)
Penalty Threshold = 1,478 + 19,734
Penalty Threshold ≈ 21,212

Practical examples

Example 1: Normal conditions (current)

• Gas price: 1,000
• Calculation: (1,000 - 1,478) / 6,578 = -0.073
• Z-score: Negative, below mean
• Result: No penalty - Base taker fee only

Example 2: Slightly elevated

• Gas price: 5,000
• Calculation: (5,000 - 1,478) / 6,578 = 0.54
• Z-score: 0.54
• Result: No penalty - Below 3.0 threshold

Example 3: High spike

• Gas price: 15,000
• Calculation: (15,000 - 1,478) / 6,578 = 2.06
• Z-score: 2.06
• Result: No penalty - Still below 3.0 threshold

Example 4: Extreme spike (penalty triggered)

• Gas price: 25,000
• Calculation: (25,000 - 1,478) / 6,578 = 3.58
• Z-score: 3.58
• Result: Penalty applied - Additional 0.1% fee added

Benefits

• Maker protection: Discourages takers from picking off stale maker orders during network congestion.
• Dynamic adjustment: Automatically adapts to changing gas price patterns over time.
• Fair pricing: Only penalizes during extreme conditions (3 standard deviations).
• Statistical rigor: Uses well-established statistical methods to identify outliers.

Technical notes

• Update frequency: EWMA updates when an order is submitted. Only counts if the timestamp is different (multiple orders within the same transaction will only be counted once).
• Alpha value: 0.1 means the system adapts relatively quickly to new price levels while maintaining historical context.
• 3-sigma threshold: Statistically, only ~0.3% of observations exceed 3 standard deviations in a normal distribution (~0.15% above 3 standard deviations).
• Pool-specific: Each pool has its own EWMA state tracked independently.