I do believe in electric heat being 100% efficient. That does not mean that it is going to be the cheapest heating source ,and it does not mean that it is the best choice for comfort. What it means is that as the electricity is turned into heat, 100% of the electricity is turned into usable heat.
If you want to compare the cost of heating you will need to do some conversions and then compare price of each fuel source. Btus are the most common unit used for this.
For electricity 1 kWh is equavalent to 3,413 Btus. For gas 1 therm is equavalent to 100,000 Btus. If electricity cost $0.08 per kWh and gas costs $1.35 per therm then:
1 million Btus of electricty costs: $23.44
1 million Btu's of gas costs: $13.50.
If this were the whole story the decision is easy. Gas is clearly cheaper. But this is not the whole story.
The average duct system in the US leaks 25-40% of the air outside of the heated space. Since this loss would be the same for gas or electric we can ignore it. But it is a significant cost (and it makes even electric heat less than 100% efficient, since a portion of the heat does not end up in the space you want it).
While we will ignore the small stuff (like fan efficiency, and holes in the house envelope) the other big piece we must consider is the gas furnace efficiency. The gas furnace efficiency tells you how much of your heat leaves the house thru the chimeny (often called a flue). A 60% furnace loses 40% of its heat, along with the poison gases, out the chimeny. So with that furnace for every 10 Btus you create by burning gas, 6 come into the house and 4 go up the chimeny and outside.
Adjusting our cost of 1 million Btus, to account for only the heat ending up in the house we get:
1 million Btus from gas (delivered into the house with a 60% furnace): $22.50
So under those circumstances they are very close (check your local rates to see it this is comparable to what you pay).
Heat pumps are a different story. Air source heat pumps provide heat at 2 to 4 times the efficiency of an electric furnace.
Skipping over the details, at the same rates as before here is a 92% gas furnace compared to an 18 SEER heat pump (this is heat delivered into the home assuming perfectly sealed ducting):
1 million Btus from 18 SEER heat pump: $7.56
1 million Btus from 92% gas furnace: $14.67
Sorry for all the numbers and so few pictures with this post. Maybe next time I will just post pictures, then the time after that we can start to calculate duct losses. . .
Do we get electricity from natural gas here in Oregon?
Yes, let me see if I can find a picture of the NW energy portfolio. . . Looks like NG is around 9% of the Northwest Electrical Resources. This suggests that he regiong currently gets more electrical power from conservation than from NG. But NG is still a significant portion since it can be called up at any time. Resources like wind and solar (currently too small to show up here) are only available when the wind is blowing or the sun is shining. I have heard a rumor that last year the wind did not blow for 15 days straight. So for that time period the wind farms did not produce a single watt of electricity.