How are rewards in DOT calculated from the era points earned by validators in Polkadot?

Question

In the Polkadot wiki I see that "validators are paid proportionally to the amount of era points they have collected" after every era. However there is no info about how many DOTs an era point is or what is the exact proportional relationship between the two.

Moreover, digging into polkadot.js staking interface, one can see that these two variables are directly proportional (see image below). But if we go to the detail, we see that the coefficient of proportionality is not constant between eras and there is a small variance. How is this coefficient calculated? Is there an explicit formula linking era points and rewards in DOTs per validator?

Answer 1

Indeed, the exact DOT value of each era point is not known in advance since it depends on the total number of points earned by all validators in a given era. This is designed this way so that the total payout per era depends on Polkadot's inflation model, and not on the number of payable actions (f.e., authoring a new block) executed.

Concretely, if we define:

• p as the number of points earned by the relevant validator in the era,
• Tp as the total number of points earned by all validators in the era, and
• M as the target total payout to all validators, and their nominators, in that era (in DOTs),

then the rewards in DOT payed to a validator per era are given by:

R = p * M / Tp

This article by Web3 Foundation Research explains all the details and how the constant M is calculated.

From here, we can deduce that the coefficient of proportionality between era points and rewards in DOT is M/Tp, which depends on the total number of points earned by all validators per era, Tp, and this parameter is not constant.