Parameters and Calculations
Behaviour of the Cardano network
The behavior of the Cardano network largely controlled by parameters.
They control everything from the reward per block and the speed at which new ADA are mined to the fraction of block minted by the community pools, and the fraction of minted ADA flowing into the Catalyst fund.
Here we will point out some of the critical parameters, and what their function is.
Parameters influencing rewards:
Rho : expansion parameter
The Rho parameter determines the amount of ADA that will be minted in an Epoch. The total reward pot per epoch is equal to the Rho multiplied by the number of ADA left unminted at the begining of the Epoch.
At the time of writing Rho is set to 0.3% and the number of ADA unminted is ~ 13.2 Billion ADA. So the number for newly minted ADA per Epoch is ~ 39.6M ADA
Because the minted ADA per Epoch is be determined based on the amount of available ADA, the rewards pot will become gradually smaller each Epoch, with Rho (0.3%) per Epoch.
Tau : tax percentage
Of all newly minted ADA, a percentage goes to the Catalysts fund. These ADA will be used for further development of the network. The ADA holders are able to vote on which projects will be funded. Tau is the percentage of the newly minted ADA that goes to the Catalyst fund. At the time of writing Tau is 20%, leading to ~7.9M ADA flowing into the funds intended for further development.
k : ideal number of stake pools (nOpt)
The k-parameter determines the optimal number of stake pools on the network.
K influences the how much stake can be in a stake-pool before the rewards are capped. The maximum stake is given by the total amount of minted ADA, divided by k. At the time of writing k = 500, with the plan of increasing it to 1000 in March of 2021. With k = 500, and the total minted ADA at 31.8B ADA, the maximum amount of stake in a stake before the reward gets capped is : ~63.6M ADA
Previous plans to change to k = 1000 have been postponed until further notice.
a0 : pledge influence
The a0 parameter determines the influence of the pledge on reward of a pool.
The reward per block for a pool with full pledge (pledge = max stake) is a0 higher than a pool with 0 pledge. At the time of writing the a0 = 0.3. This means a pool with full pledge gets a 30% higher block reward than pool with 0 pledge.