The DBXEN Protocol Fee Formula

The formula to calculate the protocol fee is given by:

PF=GS×(1−0.00005×NB)×NB

Where:
PF is the Protocol Fee.
GS is the Gas Spent.
NB is the Number of Batches.

Scenario 1: Burning One Batch

When burning just one batch, the number of batches NB is equal to 1. The fee for burning one batch is almost the exact amount of gas spent, reduced by a very small factor (0.99995 times the gas).

PF(1batch)=GS×(1−0.00005×1)×1
PF(1batch)=GS×(1−0.00005)
PF(1batch)=GS×0.99995

Scenario 2: Burning 10,000 Batches

When burning 10,000 batches, NB is equal to 10,000. When burning 10,000 batches, the total cost increases simply due to the sheer number of batches, but there's a 50% discount per batch. Essentially, each individual batch is subjected to a larger discount compared to the one before.

PF (10,000batches)=GS×(1−0.00005×10000)×10000
PF (10,000batches)=GS×0.5×10000
PF (10,000batches)=5000×GS

Comparing the Two Scenarios

So to summarize, while the absolute cost for 10,000 batches is high, the cost per batch is halved, leading to significant savings when burning in bulk.
Meaning, if you burn batches individually, each time you'll pay nearly the full gas cost, but if you burn 10,000 batches all at once, the average fee per batch is just half the gas cost.
Hence, you'd achieve better economies of scale by burning XEN for DBXEN in larger quantities.

Reference

DBXEN LITEPAPER: https://dbxen.gitbook.io/dbxen-litepaper/dbxen-functionalities

Excerpt: