First, seven Hyperheats (even the smallest ones) are only a solution to the installers boat-payment problems, not a heating/cooling solution. The heating capacity at +5F (colder than Cambridge's 99% outside design temp) of seven FH09s (the smallest individual hyper heat) to deliver over 75,000 BTU/hr into the house- more heat than what you're getting out of your baseboards. Tell me the exact model(s), and I can tell you more.
Then efficiency is one thing, cost is another. Efficeincy of the boiler is no better than 0.87. Even at -10F the efficiency of a HyperHeat going at it's maximum rate is about 1.8, or about 2x as efficient from a energy-in to energy out basis. So I'll assume the HVAC guy was talking about cost.
If sized correctly for the loads you'll get a seasonal coefficient of performance (COP) between 3.0-3.5 with the latest-greatest Mitsubishis. That means for every kwh of power used, you get 3-3.5kwh out as heat.
Converting that to BTUs, at 3412 BTU /kwh, a COP of 3.0 means you're getting 3.0 x 3412= 10,236 BTU of heat into the house. Normalizing that to kwh per million BTUs (MMBTU), that's 1,000,000/10,236= 98 kwh/MMBTU. Assuming wintertime rates of 22 cents (don't know what you're actually paying in Cambridge- probably less than that), the cost of heat is then 98 x $0.22= $21.56/MMBTU.
A gallon of heating oil contains 138,000 BTU of source fuel energy, and burned at 87% efficiency delivers 0.87 x 138,000 = 120,060 BTU/gallon of heat into the heating system (less distribution losses, less pumping & control power use). Normalizing that to MMBTU, it's 1,000,000/120,060= 8.33 gallons/MMBTU
At
this week's average price of $2.33/gallon, the cost of heat is (best case, not counting power use or distribution losses) is $2.33 x 8.33= $19.41 , or about 10% cheaper, assuming it uses no power (not true), and has no distribution losses (also not true.)
So at a COP of 3 it's roughly a wash with 22 cent electricity, cheaper to heat with the ductless all season at 20 cents or lower electricity.
But that average COP includes operation when it's colder than +15F outside, when the COP is going to be 2.5 or less (again assuming correct sizing to the loads). The exact outdoor temperature at which there's a crossover in operational cost varies with the size of the mini-splits relative to the load. At part load the COPs can be quite high, and at 30F the COP would typically be about 3.5-4, with a clear cost advantage.
When it's in the 40s outside the COPs are north of 4 as long as it's still modulating more than cycling on/off. If the capacity is so ridiculously oversized for the heat load that it's cycling any time it's warmer than 30F your seasonal average COP is going to be less than 3.0. So if you have multiple units, it's worth turning some off until they're really needed.
Another factor with mini-splits that kills efficiency is setbacks. Any savings from temperature setbacks gets more than eaten up by lower efficiency operation when it's running full blast on the recovery ramp. Unlike an oil boiler, a deep overnight setback uses MORE energy than just leaving it at temperature(!), and it's quite a bit more. If you set them back 8F overnight every night you won't do better than a seasonal average COP of 2.2-2.5. But since you have so MANY of them it's clearly micro-zoned. Set the bedroom mini-splits to your preferred sleeping temp and leave them, set the living space mini-splits at the temperature you like during the day and leave them. Rooms that are used less often, leave off. Most houses can be heated/cooled reasonably with 2-4 mini-split heads.
Since the room over the garage would short-cycle the boiler, consider only heating it with the mini-split, even when it's 0F outside unless it just can't keep up.
