A heat pump can be well over 100% efficient based on the energy input for equivalent resistive / chemical heating. E.g. your heat pump could use 100w of electricity to move 400w worth of heat (if generated resistively) from the outside to inside.
There have been multiple studies done that show that current generation heat pumps are quite a bit more efficient for a given volume of gas to burn it in an electrical generation plant and use a heat pump than it is to burn it in the house / building.
I see, but it's still mostly a theory unless we count in all small nuances. Like for a place where winters are really frosty heat-pump usually can't help enough (my own experience), and it seems they come with resistive heating built-in nowadays. Which may change the picture. Also, I'm not a specialist, but my guess is that delivery (or how they call it in the industry) of electricity can be priced in potentially wide range.
Yup, that was all accounted for in what I read (well over a year ago, can't find the link...sorry). It was also for a northern climate country (possibly the UK, maybe Norway, memory is failing me here), so it was not "best case" for heat pumps. They took into account losses from generation, transmission, number of days so cold that it is acting as close to a resistive heater (100-120% efficiency), etc. It was pretty comprehensive.
It was from a "what is the best way to lower our use of fossil fuels" perspective, and acknowledged that switching out all boiler systems for heat pumps would be a high cost, but it wasn't really a study on the economics of it. Just a resource usage perspective.
There have been multiple studies done that show that current generation heat pumps are quite a bit more efficient for a given volume of gas to burn it in an electrical generation plant and use a heat pump than it is to burn it in the house / building.