It would help if posters would post some facts about where they live. For example, I live in CT and expect 6000-6500 heating degree days per year. My cold weather K factor is around 6, so divide that into 6000 and that means I need about 1000 gallons of fuel oil per year. A gallon of heating oil provides about 138000 BTUs. A kwh provides 3412. The math is pretty easy. My Mitsubishi mini-split heat pump has a coefficient of performance (COP) of about 300% for heating. That means for each kwh in, I get 3 kwh of heat out. I am paying about 30 cents per kwh for electricity (more that most states other than Hawaii). So a gallon of heat pump BTUs is $0.30 * 138000 / (3412 * 3) = $4.04/gallon. Now the calculation is easy. If oil is less than $4.04 then electricity is cheaper to heat with.
Because CT has such high electricity prices, I stopped using the heat pump at all for heating because the equipment is more expensive that the oil burner, and unless I save a lot, it's false economy. My last fuel delivery was $5.449/gallon. So I would save about $1.40/gallon equivalent to use the heat pump. But it's April. I don't use much heat, most of the oil will go towards heating hot water. And anyway, we've had some 80+ degree weather and the A/C is already on. So I will reevaluate in the fall to see where prices are. In any case, the best time to use a heat pump for heat is in the spring & fall when the COP is the highest.