Their math is nonsense because that document compares total energy consumption instead of consumption per transaction. That's like saying Lamborghinis are the most efficient cars on the road because their summed up fuel consumption is lower than that of all VWs or all Toyotas (or probably even all bicycles).

There.

/edit I just needed to come back to this comment because that document really makes me irrationally angry. It's not just that it doesn't compare energy consumption per transaction, it's also that especially btc is pretty much the worst offender when it comes to energy per transaction. It's not just that it consumes more energy if more transactions are scheduled... Once the blocks are full, the users spend horrendous fees to get their transactions through in time, meaning that suddenly it becomes economically viable to spend a lot more on mining to be the one to find the next block with all those precious transaction fees. Btc's energy footprint literally explodes once the blocks are at capacity - and at that point btc is still orders of magnitude away from visa or banks and their transaction volume. That problem is so bad that other cryptos have written their protocols to automatically increase block size once the volume increases or simply forked away from btc to allow bigger blocks (which was necessary because the miners have absolutely no incentive to increase the block size as it's obviously in their best interest to earn money with transaction fees). Proof of work crypto is literally the worst offender when it comes to energy efficiency, with high performance computing centres spending incomprehensible amounts of energy to solve the mathematical equivalent of Sudokus, just to be eligible to retrieve the next prize as the first solver of that puzzle with no gain for humanity from all that spent energy whatsoever. It's as if banks insisted on all transfers being brought to the next bank using a pick up truck that is only allowed to drive in first gear and at max rpm, just because.

And for what? Power to the people? Instead of a handful of banks, the important cryptos are now in the hands of a handful of miners, but without the consumer protection laws that banks have to follow. Great job.