This section of this book: https://www.withouthotair.com/c21/page_150.shtml https://www.withouthotair.com/c21/page_150.shtml Has some calculations that show t

This section of this book: https://www.withouthotair.com/c21/page_150.shtml https://www.withouthotair.com/c21/page_150.shtml Has some calculations that show that using gas to generate electricity (in a modern gas fired power station) which you then use to run heat pumps for heating - is overall more efficient than just using the gas for heat given real world numbers. (It does go on to show the limitations of how much ground-source heat pumping you can do without freezing the ground - his ballpark numbers suggest maybe only 25% of the heating requirements for a typical British suburb could be met with just ground-sourced heat pumps before you'd freeze the available ground...) (That whole chapter starting back on page 140, and the whole book - are well worth reading in my opinion.)