My heat pump has electric heat strips for emergency and auxiliary heat. My thermostat is designed to call for strip heat if there is more than a 2 degree difference between the set point and the ambient temperature in the room.

It's clear that the efficiency of a heat pump decreases as the outside air temperature decreases, and at some point, it's more efficient to operate the strip heat than the heat pump. It's also clear that the strip heat must be used when the heat demand is greater than the heat pump can supply.

My question is how do I determine the optimum point to switch from heat pump to strip heat in some scientific manner.

1kwh of strip resistance heat will produce x btus of heat. 1 kwh will also produce x btus of heat from the heat pump. As the outside temperature drops, the heat pump produces less and less buts of heat for the same 1kwh of power consumed, so there is a point when the strip heat is more cost effective.

What you are referring to is the coefficient of performance (COP). Electric resistive heat has a COP of 1. So it is economically advantageous to run your HP when the COP is greater than 1.

Contact the manufacturer to get this data, as it is used to calculate EER, SEER and HSPF. I think you will be surprised as to how low a temp you can run your HP at and still have a COP > 1.

When your COP = 1 that is your economical balance point, but not your comfort balance point. Some folks don't like their HP blowing luke-warm air so their comfort balance point is much higher than their economic.