How are Staking rewards calculated?

Question

I remember that initially the percentage of rewards for delegators was around 5.12% visiting Cardano Calculator. Now they are approximately 4.6083%.

How this is calculated? Will the percentage decrease over the years?

Answer 1

As explained in the docs, rewards come from:

• Transaction fees (increases in time if adoption and network traffic increases)
• Monetary expansion (decreases in time)

The sum of these is denoted by R and the share of rewards that a given pool gets is given by:

where: R - total available rewards for this epoch

a0 - pledge influence factor (can be between 0 and infinity)

z0 - relative pool saturation size, i.e. 0.5% based on a number of desired pools (k=200)

σ - stake delegated to the pool (including stake pledged by the owners and stake delegated by others)

σ’ = min(σ, z0) - as σ, but capped at z0

s - stake pledged by the owners

s’ = min(s, z0) - as s, but capped at z0

About monetary expansion and issuance, you may check this section of the docs. Essentially, every epoch, a fixed fraction ρ is taken from the ADA reserves and is added into R. From the docs:

Calculating the ‘reserve half life’ (that is, the time that it takes for half of the reserve to be used up) visualizes the impact of choosing a specific value of ρ over another. This was the subject of much discussion, and eventually, the value assigned was 0.3%. The reason why is that mathematical projections showed that a ρ (the fixed percentage of ada going into the virtual pot every epoch) value of 0.3% would mean a reserve half-life of four to five years. In simple terms, just half of the remaining reserve would be used every four to five years.