Just because you pay a positive non-zero amount for less than a quarter of the energy in, it does not mean that a device has greater than 100% efficiency, which is not possible.
If heat pumps are 400% efficient then log burners in cabins in the woods are even better.
A heat pump warms a home more efficiently than using the same amount of electricity for resistive heating. It can do this because it's not generating the heat from scratch; it's moving heat from outside to inside.
A local company has developed a heat pump with a thermal energy storage system. Not sure how they do this, but I imagine there is some sort of insulated cinder blocks on a secondary loop that shuttles heat/cold to where it needs to go.
Unfortunately by that metric other electrical heaters tend to 0% efficiency because they are not making use of the virtually unlimited energy outside the buildings.
The 400% metric let's you compare with other heaters, the 100% is kind of useless.
All energy from log burners comes from the fuel, and some ashes remain unburnt. They're under 100% efficient at converting fuel to heat. You put in x fuel and <x heat.
A heat pump takes heat from outside the system. You put in x fuel and you get >x heat. Getting more energy than you put in makes the efficiency over 100%.
Sure, a slightly irritating turn of phrase, not accurate. I didn't think it would be so controversial to hold terms of art/words with actual scientific meaning to a higher standard though.
If we're willing to be so blasé with 'efficiency' then why not, say, 'functional programming'? If it works it's functional right?
If heat pumps are 400% efficient then log burners in cabins in the woods are even better.