Parameters \sigma and s and z_0 of the pledging reward formula (https://docs.cardano.org/core-concepts/pledging-rewards) are said to be given in proportion to the total amount of ADA supply.
However, when it comes to the pool performance factor, the doc is using \beta / \sigma as a measure of how “ideal” the mining pool performed. However, it seems to me that this factor is false since \sigma is computed with respect to the total ADA supply and not the total amount of staked ADA.
Indeed, I believe that the probablity for a mining pool to mine a block is “total ADA delegated to the pool” / “total ADA delegated in general” and not “total ADA delegated to the pool” / “total ADA supply”.
Could you possibly help me on that?