Velocity is a metric which estimates the average frequency at which the tokens change hands during some period of time. It mimics to a large extent the Money Velocity metric. å In order to understand how we compute this metric, let's see an example in which Alice, Bob and Charlie exchange tokens. Let's assume that Alice gives Bob 10 tokens at block 1 and Bob gives Charlie 10 tokens at block 2. The total transaction volume which is generated for block 1 and 2 is $10 + 10 = 20$, but we can easily see that the same 10 tokens have been transacted, so the amount of tokens being in circulation is actually $10$. We can say that the Token Velocity for blocks 1 and 2 is $20 / 10 = 2$, which means that the transacted tokens have changes hands twice during these blocks.

In order to understand how all this can be tracked, you should read the article about the token age consumed.

## Formal definition

In order to define this metric formally we need to establish some definitions:

• $vol(a, t)$ - amount of tokens going out of address $a$ at block $t$
• $vol(t) = \sum_{a} vol(a,t)$ - amount of tokens going out of all addresses in block $t$
• $blocks(d) = {t_1, t_2, ..., t_n}$ - the set of all blocks produced during day $d$. For ETH these are usually 5760 blocks

We also need a metric to measure the amount of tokens that are in circulation for a given day. To compute this we will use the metric describe here: https://community.santiment.net/t/the-transaction-stack/36/2?u=valentin. In this article we have a definition for $token\_circulation(t,1\ hour, token)$, let's not specify the $token$ as this is something which we assume is fixed. Let's define the token circulation for a given day, as the circulation in the last block of the day:

$last\_block(d) = max_{t_i \in blocks(d)}(t_i)$
$token\_circulation(d, timespan) = token\_circulation(last\_block(d), timespan)$

Now we can define the Token Velocity at day $d$ as:

$vel(d) = \frac{\sum_{t \in blocks(d)} vol(t)}{token\_circulation(d, 1\ day)}$

Which is the total token volume divided by the amount of tokens in circulation during that day. A similar approach can be taken if we want to compute the metric on a weekly or monthly basis.