Initialization Issue in Time-Weighted Average Calculation

Summary

The current implementation of the TimeWeightedAverage in the BaseGauge contract initializes the first period with a weight of zero. This leads to incorrect calculations of time-weighted averages (TWAP), resulting in ineffective reward distribution and potential user attrition. The report outlines the implications of this flaw, provides a concrete example, and presents recommended fixes.

Current Code Issue

The problematic line of code is as follows:

What's Wrong?

• Zero Initialization: Time-weighted averages (TWAP) start at zero, making the first period's calculations meaningless until updated.

• Impact on Reward Distribution: If the first period is initialized with a weight of zero, the TWAP will remain zero until the next update, leading to no rewards being distributed.

Concrete Example

1. Initialization:

   • Period starts at T=0 with weight=0.

   • First update occurs at T=7 days with weight=5000.

2. TWAP Calculation:

   TWAP = (sum(weight * time)) / totalTime

   = (0 * 7 days + 5000 * 0) / 7 days

   = 0

   ​

   ​

3. Result:

   • The first period shows a TWAP of 0.

   • Rewards are distributed as if the protocol is inactive.

Visual Timeline

Fix

To resolve this issue, the initialization should use a reasonable default weight:

Where INITIAL_WEIGHT could be:

• Historical average from similar gauges.

• Protocol-wide baseline (e.g., 1000).

Fixed Timeline

Combined Impact

1. Reward Distribution:

   • Frozen emissions lead to insufficient incentives, resulting in user attrition.

   • Users may disengage from the protocol due to lack of rewards.

2. Time-Weighted Averages:

   • Zero-weight bootstrap results in misreported activity, leading to a loss of trust in the system.

   • Users may perceive the protocol as inactive or ineffective.

Recommendations

1. Reward Distribution Fix:

   • Allow emission increases up to a global cap to ensure that rewards can be distributed effectively.

   • Implement an emergency override for growth phases to adapt to changing conditions.

2. TWAP Fix:

   • Initialize periods with historical or baseline weights to ensure meaningful calculations from the start.

   • Consider adding a warm-up period for new gauges to gradually adjust to their expected weights.