# Is Your Favourite Baker Overdelegated? Understanding Self-Bond Requirements in Tezos

Almost all websites that list bakers currently assume a fixed self-bond requirement of `8.25%` to determine whether a specific baker is over-delegated or not. However, the fixed self-bond requirement of `8.25%` that most websites currently base their calculations on does not apply yet, meaning that some bakers might be wrongly marked as over-delegated.

We acknowledged that both informative websites, such as the listings pages, and participants in the Tezos ecosystem, especially delegators, might be exposed to inaccurate information or might struggle with the economics behind the protocol. Hence, in today’s article, we will explain the formula that we, at Cryptium Labs, use internally.

Furthermore, it will be published on our website (http://tezos.cryptium.ch) as a small feature that performs the calculation to determine the over-delegation status of your favourite baker. For the most curious ones that wish to calculate it by themselves, find the explanation below.

### How Self-bond Requirements are Calculated

The rationality behind the economic and security model of Tezos states that at least `8.25%` of the total XTZ in circulation is at risk or slashable. Two other variables that influence this number are: `time` (measured in cycles) and `% of total supply self-bonded or staked`.

The value of `8.25%` only applies after `Cycle 64`, which is in about 6 months after the betanet launch, considering that every cycle lasts around 2–3 natural days. Taking this value into account, we can conclude that until `Cycle 64`, the percentage of self-bond required scales linearly from `Cycle 0`. This means that, if at `Cycle 0` the self-bond requirement was 0%, it was `0.1289%` at `Cycle 1`(8.25% divided by 64). Every further cycle adds another `0.1289%`. For example, at `Cycle 11`, the self-bond requirement is`1.4179%` (0.1289% * 11).

However, the previous values did not consider the percentage of XTZ at stake. The value of `8.25%` at `Cycle 64`assumes that a `100%` of the total XTZ supply are staked.

In order to calculate the total amount of XTZ at stake, one must aggregate all self-bonded and delegated XTZ. You can find the total amount of XTZ at stake at any cycle at TzScan (https://tzscan.io/rolls-distribution) and calculate it by multiplying the number of rolls by 10,000, (1 Roll = 10,000 XTZ).

In order to find the proportion, we need to know the total supply of XTZ, which you can find here (https://tzscan.io) next to the “Total ICO Supply label”. For instance, after Block `level 63969`, the total supply was 764,317,931 XTZ. During `Cycle 11`, the total supply was ~763,306,930 XTZ.

If less than the total supply is staked (<100%), it linearly increases the self-bond requirement. For example, should only 50% of the total XTZ be at stake, the self-bond requirement would be `16.5%` (8.25% / 50%) at `Cycle 64`. Here’s a Table that gives an overview for different scenarios:

As you can see from the previous Table, at `Cycle 11`, the staked percentage was ~36.4676% (278,360,000 / 763,306,930), and the amount of self-bond requirement would be 1.4179% (0.1289% * 11), IF a 100% were at stake, but as only ~36% is at stake, then the amount of self-bond requirement is ~3.8883% (1.4179% / 36.4676%).

### Practical Example with our Baker, Cryptium Labs

#### The Global Variables:

`Cycle = 11`
`Percentage of XTZ staked = 36.4676% (278,360,000/763,306,930)`
`Time-based self-bond requirement: 1.4179% (0.1289% * 11)`
`Using the previous values, we can find the global baker self-bond requirement: `
`~3.8883% (1.4179% / 36.4676%).`

#### The Cryptium Lab Variables (adapt to your favourite baker’s) at Cycle 11:

`Self-bond = 20,000 XTZ`
`Total Delegation = 44,819.35 XTZ`
`Staking Balance = 64,819.35 XTZ`
`Cryptium Labs maximum delegation = 514,363.60 XTZ (20,000 / 3.8883%)`

Taking all these values into account, Cryptium Labs had a self-bond of ~30.86% (20,000 / 64,819.35), which is higher than the minimum global self-bond requirement (>3.8883%). Meaning that at that time, we could have received up to 514,363.60 XTZ in on-chain delegation before being overdelegated (slightly less in practice to keep a safety margin), which will give us a total self-bond of ~3.8883% (20,000 / 514,363.60).

### Concluding Remarks

We hope that this gives everyone, delegators and bakers, a better understanding of what the self-bond requirements are. We also hope that you can use this formulae to make calculations at your convenience. Finally, I would like to remark on an interesting implication of Tezos’ economics: the more XTZ is globally at Stake, the more delegation each baker can take without having to increase their self-bond.

If you have any questions around delegation, baking, Tezos, Michelson (the smart contracting language) or anything else related to Tezos, please feel free to connect with us.Feedback and discussions are extremely welcomed and encouraged.

### A Little Bit on Cryptium Labs

Cryptium Labs is an infrastructure operator for Proof-of-Stake networks, such as Tezos. We are a baker, based in Switzerland. To the best of our knowledge, there are still few bakers that use the Nano Ledger S’ Baking application to prevent double-signing on the secure element of the HSM instead of the host. Adding an extra security layer, so in the event of all our servers getting compromised, it would be practically infeasible for the attacker to trigger double-signing. We charge a 10% fee and pay compound interest on all delegation rewards. Finally, we are committed to increase our self-bond as more and more delegators reach out to us showing interest in delegating to Cryptium Labs.

#### Details on Cryptium Labs’ Baker service:

• 10% realised delegation fee
• Compounding interest paid for all delegation
• Rewards are paid every cycle, as soon as they become available
• Run by core developers and researcher
• Will self-bond more XTZ as we become over-delegated