Expected Rewards of a Solo Baker

A solo baker is a token holder that is operating his/her own Tezos bakery. The solo baker possesses at least 10,000 XTZ, which is the minimum required to participate.

In this section, I will calculate how much a solo baker, with different initial balances of XTZ, can expect to generate at the end of Cycle 34 — in the most optimistic scenario. One can extrapolate to the following Cycles, assuming that the Rolls Distribution percentages do not vary significantly.

In the tables below, you can find the calculations for three different token holders: Thurar, Leenkath, and Anry, who hold respectively 1, 10, and 100K XTZ. They all want to become a solo baker and will not take public delegation*.

*Technically, a baker cannot deny delegations. Delegators might generate the originations and appoint any baker to it. The only measurement that a baker, who does not want to provide the service, can take is simply refuse to pay out the corresponding rewards to the delegators.

The Global Parameters

The global parameters I took are from Cycle 34, you can find the values if you check TzScan:

Global supply of XTZ is the total XTZ in circulation, 764,317,931 XTZ during Cycle 34

during Cycle 34 Global rolls is 41,074 , which equals to 410,740,000 XTZ staked

, which equals to The ratio of staked / total supply is 53.7394%

Which gives a Global Self-Bond Requirement of 8.1557% (you can check for other values in this gist):

(you can check for other values in this gist): I will assume that transaction fees (gas prices) are 0 in every block

For simplicity, I will assume the most optimistic case, where endorsement rewards are always 2 XTZ .

Thurar’s Solo Baking

Now that I have the global parameters, let’s walk through the calculations using Thurar’s case.

Thurar has an initial balance of 10,000 XTZ, just enough to become a baker. 10,000 XTZ earns Thurar 1 Roll, which in Cycle 34 represents 0.0024% of the Global Rolls Distribution:

Thurar's Roll Distribution = Thurar's Rolls / Global Rolls Thurar's Roll Distribution = 1 / 41074 = 0.0024%

Because the Tezos Protocol assigns baking and endorsement slots pseudo-randomly, a way of reading Thurar’s Roll Distribution is the likelihood of Thurar getting the next baking and or endorsement slot.

In the longer term, Thurar should receive 0.0024% of the total inflation (assuming that the rolls distributions do not change overtime). However, in the shorter term Thurar’s slots will depend on luck (in some cycles he might get more or less than 0.0024%).

For the purpose of this example, I will assume the most optimistic scenario, where Thurar gets exactly 0.0024% of all bakings and endorsements of an entire cycle. Considering that a cycle has 4096 blocks and that the maximum time between blocks is 1 minute, then:

Likely Received Baking Slots = 0.0024% * 4096 = 0.0997 Units Likely Received Endorsement Slots = 0.0024% * 131072 = 3.1911 Units # the 131072 comes from 32 (max endorsements per block) * 4096

Following this, the rewards that Thurar would earn at the end of this cycle would be:

Total Baking Rewards = 0.0997 * 16 = 1.5956 XTZ Total Endorsement Rewards = 3.1911 * 2 = 6.3822 XTZ

Of course, these values are not possible: Either you get a slot or not, but you can’t get half a slot. Similarly, if you bake a block, you will receive 16 XTZ, if you make an endorsement you will receive 2 XTZ.

But a way one can read these numbers is that for a baker with the same conditions as Thurar, it might take more than a cycle to receive a baking slot, baking an average of 0.0997 blocks/cycle, and endorse on average 3.1911 endorsement slots/cycle over cycles.

Thurar, Leenkath, and Anry

In the previous section, we walked through the calculation process. The following table shows all the numbers broken down, together with the three different cases: