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Some of the Math Behind Taostats

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nom/1k/24BTday

This value represents the daily return in tao for everk 1000 tao delegated. We are sometimes a bit lax in the use of "day" vs. "BTDay", but in all these cases, we mean 7200 blocks - which is approximately 24 hours. (We are working to move to BTDay "Bittensor day" which is usually a few seconds longer than 24 hours).

The Basic calculation is:

For validators, this must be calculated per subnet and then is added for a network-wide value.

On taostats, we are using actual returns from nominators on each validator to calculate a daily nom/1ktao/BTday. It accounts for Hotkey swaps, and other myriad ways that the calculation can be obfuscated on chain.

Where you can find nom/1k/24BTday

  • Validator Home This is the instantaneous value - from today's stats.
  • Staking Calculator This is the 30 day average. This smooths out changes in the value that occur from changes in stake.
  • Validator Pages This is the sum of the value across all subnets.

Dominance

Dominance is calculated per subnet. It is the validator stake/total tao staked on the subnet. If measured in the context of a subnet, a healthy validator (High VTrust/low updated) should have dividends that are similar to their dominance.

This can be broken down a number of ways.

  • Child Hotkey dominance: This is the sum of all child & parent stake/ total tao staked in the subnet.
  • Hotkey dominance: Sum of all parent & child stakes for a single hotkey/total tao staked in the subnet.

Daily Return

The amount that the validator has earned in the last 24 hours. It is a sum of validator return across all subnets.

Validator Return

To determine a validator's return in a subnet, we need to account for all places that emission is gained for validators on the subnet:


  • Emission for the registered hotkey.

    • Calculate the % of stake held by the child hotkey * the emission. (Note if there is no parent/child, the % of stake held is 100%)


  • Child hotkey takes. If there is a child hotkey, they can extract a childkey take from parent hotkeys. Find the emission of the parent hotkey, and multiply by the childkey take. Sum for all parent hotkeys.

  • If the hotkey is a parent on one or more child hotkeys, calculate the parent return on other validator's child hotkeys, subtract the childkey take. Sum these across all parents.

These values, summed across the subnet, provide the validator return.

APR: Annual Percentage Return

nom/1k/24BTday is the APD*1000. So, to get to APR, take any nom/1k/24BTday, and divide by 1000. The multiply by 365 to get the annual value.

Updated 3 months ago