Staking rewards

 Ouroboros algorithm to calculate staking rewards

Each Stake Pool gets a share of the "R" Rewards Container, which is proportional to the size of its Active Stake (σ) and the amount of Pledge(s).

The more Stake and Pledge you have in a Stake Pool, the more you get from the Rewards Container.

This is obvious, between a 1K ADA branch and a 1M ADA branch, you expect to get more rewards from the larger branch.

Also, the larger the Reward Container, the more rewards there will be for the Stake Pools, this is also obvious.

Every ADA transaction in the Cardano blockchain has a commission. All transactions within an epoch are added to the Rewards Container.

Cardano began with 31B of ADA in circulation, leaving 14B of ADA to be used for monetary expansion. These reserves are extracted with an expansion rate p (currently 0.3%) to finance the Rewards Container.

A portion of the Rewards Container is taken to finance the treasury at an index τ (currently 20%). The remainder is distributed to the Stake Pools where each Pool calculates how much they will earn through the rewards equation ( f(s,σ) ) shown at the beginning of the article. Each Stake Pool reward is affected by its apparent "p" performance, similar to the ADA Reserve. The expected number of blocks produced by a Stake Pool was explained previously. If a Pool produces more blocks than expected, then its "p" yield will be greater than 1, thus increasing the amount of rewards obtained for that epoch.

Any ADA left in the Reward Container is returned to the Reserve. Some Rewards may be unpaid, this happens under two conditions.

  1. The Stake Pool does not have the declared Pledge available in its wallet.
  2. The Stake Pool is overflowing.

If a Stake Pool does not honor its declared Pledge, all of its possible rewards will not be paid in that Epoch.

If a Stake Pool is saturated, then its rewards are at the top, resulting in a higher Stake, but you have to distribute the same amount of Rewards to more delegates, thus giving less Rewards to all.

The K parameter determines, among other things, the saturation of a Stake Pool. To calculate the saturation we have:

    z0 (used to calculate the rewards) = 1 / k

    Saturation in ADA = Total supply of ADA / k

How is the Annual Return (%ROA) calculated?

Annual Return %ROA = ((Delegates' Rewards in ADA / Active Stake in ADA) * 73 Epochs per Year) * 100

The amount of ADA in the reserve will be less in each Epoch, due to the percentage that is always subtracted. This means, therefore, that the amount of ADA in the Rewards Container will be reduced each Epoch as well.

That's 73 epochs in one year. For a maximum return and with negligible transaction fees, the % ROA of the Reserve will be halved in almost 3 years.

In the Rewards equation, there is the "a0" parameter, which represents how the Stake Pool Pledge will affect its % ROA. Currently "a0" is set at 0.3.

There are many proposals from the community to improve the Pledge, and make it take a different effect.

The minimum fixed fee of 340 ADA heavily penalizes small Stake Pools, as they get a large part of the rewards, but this doesn't mean that it's not worth delegating to small Stake Pools.

There are two main reasons why small Stake Pools are still relevant

Small Stake Pools will potentially and inherently benefit from good luck. A difference of 1 or 2 blocks would mean a large over-performance, getting much more from the Reward Container. While 1 or 2 extra blocks in a large Stake Pool does not make much difference in performance. But the opposite example is true as well. Bad luck will give very little, if any, reward to small Stake Pools. Over time, the % ROA graph shown above should match, but in the short term it is possible to get a large % ROA if you are lucky in a small Stake Pool.

  • Big difference in "p" performance.
  • They support the security of the Cardano network through centralization.

 

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