> a heat pump is often 3x as efficient at heating a house vs electric baseboards.

Not if you consider the whole "indoor + outdoor" referential, in that case you will always get below 100% efficiency.

True, but no one cares if they make the outside air 0.05ºC hotter in the summertime or 0.1ºC colder in the wintertime.

On an individual level for sure, multiply this by a state / country population, and you get non-negligible impact.

Draw a boundary around a city and any lasting temperature change is solely an energy balance question.

Any heat that you move into the house in the winter leaks out within the day (asymptotically), so this doesn’t become a localized runaway effect.

> What is wrong with the concept of a heat pump?

Something overlooked is that heat pump will leak refrigerant. It's not really not a matter of "if" but "when", physical systems fail.

Refrigerants are pretty nasty greenhouse gases.

Ok then the electric baseboard is 30% efficient vs the heatpump which is 100% efficient.

No; you're missing the point - 100% of the energy in an electric baseboard system is converted into heat. It's 100% efficient. There is no more effective way to turn electricity into heat than resistively.

A heat pump doesn't turn electricity into heat. It moves heat from one place (outside) to another place (inside); and can seem more efficient because the system isn't closed.

Ah makes sense. Thanks for taking the time to explain

But a resistor converts 100% of the electrical energy it consumes into heat. So if you were to take the same amount of electrical energy and run a heat pump, you could get 3x more heat into a room. In that sense, the heatpump is 300% efficient.

Yeah one can argue semantics all one wants but you still get 3 to 4 times more low grade heat per kwh from a heat pump than a resistive heater. And that's what you actually care about.

How are you calculating efficiency? It's usually:

efficiency = useful work / energy input

Efficiency is not calculated relative to the best performing machine.