The theory of money is all about energy. However, proof-of-work is not quite the same as proof-of-hash. Until the computing device reaches the theoretical physics limit, hashing power per energy power is always improving. For example, the increasing historical difficulty in a time series can not be totally accounted by increase of energy power. This leads to the necessity of some solution to assess mining rig efficiency in a time series so that a real difficulty time series can be shown. Should efficiency x10 and the raw difficulty x200, the real difficulty only x20.

The data of mining rigs (the hashing rate, the power consumption, the sale price) is public. Rationally, people shall choose the rig with best profit in their business plan horizon. The best rig of a 2 year horizon is not necessarily the best rig of a 1 year horizon. Very often due to the sale price of a rig, the rational choice may not be the one with highest hashing rate per energy power. Recalling the arbitrage-free mining power distribution for different business horizon, one can compile the rig efficiency time series based on the available public data by the following steps:

1. Collect rig data like https://www.asicminervalue.com/
2. Normalize the rig by divide the hashing rate and the sale price by energy power
3. Because the profit of the normalized rig in one second is $\frac{h}{H} \times \frac{C_i+F}{600} \times P - 1 - \frac{I}{T}$, the score of a rig for a business horizon is defined as $\frac{h}{1+\frac{I}{T}}$. When there is no initial purchase cost or the business horizon is infinity, the score is simply h.
4. Given a mining business horizon T in term of era, its share is derived from the arbitrage-free mining power distribution and has share S
5. With T and the normalized rig data on a specific date D, choose the best rig:
   1. Given the electricity fee, say one kwh 0.1 USD, one can know 1 USD represents 36M Joule. Therefore a sale price, say 0.3846 USD, is converted to some amount of Joule, 13846154.
   2. Given the hash per energy power, calculate the score
   3. Run the same task for other rigs. The rig with highest score is the best rig which contributes S market share to the overall hashing rate and overall sale price
6. Run over all T. Then one can compile a list of market share of all the rigs at D and the overall average hashing rate and the overall rig price.
7. Run over all D. With the overall hashing rate and the rig price, one can compile the time series of rig efficiency.

As mentioned, until the speculation period ends, any deduction from arbitrage-free argument needs some grain of salt. Some other ad-hoc method to assess the network overall rig efficiency may be necessary, for examples:

• the market share of a rig is the exponential of that accumulated hash minus the cost in terms of hash.
• a second hand rig market is priced such that it is competitive with the best hashing rate / cost ratio in that business plan horizon.

Whatever approach always concludes the market share of the highest h tends to 100% as the business plan horizon becomes infinity.