Coquito Tezem, Ergo Sum — Expected Rewards from Delegating Tezos to a Baking Service

Coquito Tezem, Ergo Sum (I bake Tezos, therefore I am) — a series of articles focused on the economics behind baking. This series is composed by the following articles:

• Did they Pull the 5.51% Out of their Oven? — Understanding Inflation in the Tezos Protocol: setting the motivations behind why an XTZ holder should avoid hodling.
• (I) Coquito Tezem, Ergo Sum — Expected Rewards from Solo Baking Tezos: With calculations on the expected rewards in case a XTZ holder decides to bake but not offer a delegation service.
• (II) Coquito Tezem, Ergo Sum — Expected Rewards from Offering Tezos Baking Services: With calculations on the expected rewards in case a XTZ holder decides to accept public delegations.
• (III) Coquito Tezem, Ergo Sum — Expected Rewards from Delegating Tezos to a Baker

Unlike (I) and (II), this article (III) will explore the expected rewards in the case the XTZ holder decides to not bake directly, but rather delegate the XTZ to an existing baker. This way, the holder would become a delegator and participate indirectly in block baking and endorsing.

The scenarios we will be covering are of a different holders with an initial balance of 10K, 100K and 1M XTZ.

Note: We will assume that the reader already has a basic understanding of basic concepts, such as overdelegation, inflation, rewards, cycles, and Tezos Liquid Proof-of-Stake. Else, I highly recommend taking a look at them by skimming through some articles, you will the complete list of suggested writings in this Reddit thread.

Alte Bäckerei

What is a XTZ Delegator?

A Tezos delegator is a XTZ holder who created a delegation (origination or smart contract in Tezos) and appointed a baker’s address to the origination. The delegator maintains custody of the funds (only the owner can manage the funds), but they contribute to the staking balance of the appointed baker.

Under common circumstances, the delegator expects to receive a slice of the baking and endorsing rewards that the baker produces. The baker, on the other hand, normally charges a service fee, a percentage of the rewards, in return. What the actual service terms are, fees charged, reward payout schedule, etc, varies from baker to baker.

How much in rewards is a Delegator entitled?

How large or small the slice from the rewards that a delegator is entitled to is proportional to the contribution of the delegation to the baker’s overall staking balance. To clarify, let’s look at the oversimplified example:

• A bakery called Lyptium Crabs has a staking balance of 1M XTZ
• Leenkath, who holds 100K XTZ has delegated to Lyptium Crabs
• Lyptium Crabs produces in total 100 XTZ in total rewards during Cycle x
• Lyptium Crabs charges 10% as service fee

Considering these values, Leenkath would receive:

Leenkath's contribution = 100,000 / 1,000,000 = 10%
Lyptium Crabs Generated Rewards = 100 XTZ
Leenkath's slice of rewards = 100 * 10% = 10 XTZ
Fees to Lyptium Crabs = 10% * 10 XTZ = 1 XTZ
Leenkath's final rewards = 9 XTZ

Leenkath would be entitled to 10 XTZ at the end of Cycle x, as her delegation represented 10% of Lyptium Crab’s staking balance. After deducting the services fees, Lyptium Crabs should send 9 XTZ to Leenkath.

Expected Rewards from Delegating XTZ to a Baker

In the example above, we used fictional numbers. Next, we go into a detailed calculation of how much a delegator can expect from delegating the XTZ to a Tezos baker. We will use the values from Cycle 40, the most current cycle at the time of writing.

The Global Variables

The global parameters I took are from Cycle 40, 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 40
• Global rolls is 42,812, which equals to 428,120,000 XTZ staked
• The ratio of staked / total supply is 56.0133%
• Which gives a Global Self-Bond Requirement of 9.2054% (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.
• All bakers are charging a service fee of 10%
• The bakery will receive the maximum delegation its self-bond can support
• We will ignore time and assume that the bakery can already bake at Cycle 40

The Adventures of Thurar the XTZ Delegator

Thurar is a Tezos enthusiast who owns 10,000 XTZ. Previously, Thurar was solo-baking, but after observing a trendy bakery called Lyptium Crabs for a while, he decided to open his own and name it Thurar Labs.

Thurar Labs was doing great as a bakery, but because he became pretty busy with his day job lately, he decided to close it down. Nonetheless, he still wants to continue baking, so he decided to try out delegation and chose to delegate to his favourite baker: Lyptium Crabs.

This time, considering Thurar’s initial balance of 10,000 XTZ and all the parameters above, we will take the delegators’ perspective throughout the calculations. Thurar decides to delegate to Lyptium Crabs, which is a baker with the following properties:

Staking Balance of 1,209,176.193 XTZ (including Thurar's delegation)
Total Rewards end of Cycle 40 = 925.49 XTZ

Note: If you’re interested in knowing how the staking balance is calculated and how the total rewards are estimated, take a look at the article Coquito Tezem, Ergo Sum — Expected Earnings from Offering Tezos Baking Services.

The first thing to do is to calculate how much Thurar’s delegation has contributed to Lyptium Crab’s staking balance. To do so:

Thurar's Contribution to SB = Thurar's delegation / Lyptium Crab's Staking Balance
Thurar's delegation = 10,000 XTZ
Lyptium Crab's Staking Balance = 1,209,176.193 XTZ
Thurar's Contribution to SB = 10,000 /  1,209,176.193 = 0.8270%

Thurar’s 10,000 XTZ delegation represents 0.827% of Lyptium Crab’s staking balance, which means that Thurar is entitled to 0.827% of the total rewards that Lyptium Crabs’ produces:

Thurar Entitled Rewards = Thurar's Contribution to SB * Total Rewards 
Thurar's Contribution to SB = 0.8270%
Lyptium Crabs' Rewards = 925.49 XTZ
Thurar Entitled Rewards = 0.8270% * 925.49 = 7.65 XTZ

Thurar is entitled to 7.65 XTZ. However, Lyptium Crabs charges a 10% fee, which means that the end rewards that Thurar should receive are:

Thurar Entitled Rewards = 7.65 XTZ
Fee = 10%
Thurar Final Rewards = 7.65 - 10% = 6.89 XTZ

After deducting the service fees, Lyptium Crabs will pay 6.89 XTZ to Thurar as soon as they are available.

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.

In addition to Thurar, there is Leenkath, who has a balance of 100,000 XTZ and, who Anry has a balance of 1,000,000 XTZ. The properties of Lyptium Crabs remain the same:

Expected Rewards from Delegating XTZ to a Tezos Baker

In summary, the expected rewards from delegating XTZ are the following*, assuming that you delegate to Lyptium Crabs, whose staking balance and the global variables are the ones described previously:

• 10,000 XTZ would expect 6.89 XTZ in rewards
• 100,000 XTZ would expect 68.90 XTZ in rewards
• 1,000,000 XTZ would expect 688.85 XTZ in rewards

*Note that these values are probabilistic, consider them estimations based on all the variables above and use only as a reference.