The **Network Value to Metcalfe (NVM) ratio** is a fundamental method of valuing a blockchain network based on the number of active users. Unlike the Network Value to Transactions (NVT) ratio, which accounts for the number of transactions, the NVM evaluates the fair value of a crypto-asset based on Metcalfe’s law.

Simply stated, Metcalfe’s law says that the value of a network is proportional to the square of the number of users. This relationship is based on the network effect which means that the positive effects of more users/businesses joining a network translate into an increased value for other participants.

There are also some other variants of Metcalfe’s law that says the network value is proportional to the number of users to the power of 1.5 (instead of to the power of two). Another variation, known as the Odlyzko law, uses the logarithm of the number of users instead of the square to estimate network value. These three variations are expressed below:

- Metcalfe’s law: Network value = n^2
- Generalised Metcalfe’s law: Network value = n^1.5
- Odlyzko law: Network value = n*log(n)

The NVM ratio was first outlined by Dmirty Kalichkin. In his post, he explains that using Metcalfe’s law probably overestimates network value and can be thought of as an upper bound for valuing the Bitcoin network. Similarly, the Odlyzko formulation of Metcalfe’s law could be used as a lower bound for Bitcoin’s network value. He then uses these two measures to create the NVM ratio from the midpoint of these two models to see where bitcoin is undervalued or overvalued when accounting for active addresses.

The formula below shows the calculation of the NVM ratio using Metcalfe’s law formulation of network value:

Where ln is the natural logarithm, market cap is the market capitalisation of bitcoin and NVM is the Network Value to Metcalfe ratio.

The chart below shows the Network Value to Metcalfe ratio using the 30-day moving average of daily active addresses in the calculation. An alternative calculation for the NVM ratio could be to include the 60-day, 90-day or 180-day moving average of active addresses (or any other moving average) in the formula instead of the raw daily value or 30-day moving average.

Spikes in the NVM ratio align closely with the highs of each market cycle, where the market cap was too high to be justified by the number of active addresses.

If the value of the NVM ratio is at a historically high level, then it suggests that the network is overvalued as compared to the number of active users. When the NVM ratio spikes to high levels, then it means that either the number of active addresses needs to increase to justify the valuation implied by the market capitalisation. Alternatively, the price (and therefore the market capitalisation) needs to fall to ensure that the valuation is in line with the fundamentals (in this case active addresses).

On the other hand, if the NVM ratio is relatively low, then it indicates that the network may be undervalued when taking into account the number of active users. This usually means that the price may rise to reflect the strong fundamentals (or that active addresses will eventually fall to justify the network’s valuation).

Therefore, keeping track of the Network Value to Metcalfe ratio, as well as active addresses, can help identify when bitcoin's network value is overvalued or undervalued. As with other on-chain metrics, they should be analysed along with other data, such as order book data, other on-chain fundamentals and technicals, to complement your analyses.