HSPF's are useful for comparing one heat pump with another, but using HSPF to infer performance in your climate zone could lead to errors in any calculation. The stated HSPF on the label is for climate zone IV. You're in climate zone V.

There was a cold-climate heat pump study conducted by the Massachusetts Clean Energy Center that might provide some useful insights https://goclean.masscec.com/clean-energy-solutions/air-source-heat-pumps

I use COP (coefficient of performance) to calculate the cost of operating a heat pump. A HPSF of 11 is about a COP value of 3.2. Normally I would use a COP value of 2.5 or 3.0. The cost scales linearly with the COP value. If you post the your natural gas and electric rates the relative costs of each can be calculated.

I am currently paying $2.20/therm for natural gas with annual usage of 498 therms for heating so $1,096 per year moving forward The electric rate is $0.225/kWh however we have a solar array that covers roughly 120% of our current electrical needs without a heat pump/minisplit system. The solar array annually produces about 8000 kWh. Of that, I estimate 5000 kWh is needed for non-heating/cooling electrical needs and 3,000 kWh would be available to help cover the electric consumption of the heat pump/minisplit system. Prior to this year, the annual cost of natural gas for heating had been $800. If I use the $800, that was no longer purchasing natural gas, to purchase roughly 3,500 kWh of electricity, then I have 6,500 kWh annually available for the consumption of the heat pump/minisplit system. If the new system uses up to 6,500 kWh then it is definately worth it as a break even but with comfort improvements. If it uses slightly more, it would still probably be worth it. However, if the electricity needed for the heat pump/minisplits system was much greater than 6,500 kWh, it would become questionable.

Not so fast.

The efficiency of any heat pump in either cooling or heating mode is a function of temperature. For that reason, manufacturers report a seasonal energy efficiency rating (SEER) for cooling mode and a heating seasonal performance factor (HSPF) for heating mode. SEER and HSPFs are intended to give a measure of efficiency over a full cooling season and a full heating season, respectively. I believe the ratings are all stated assuming climate zone IV. The problem with using either SEER or HSPF to infer actual, real-world performance is that cooling and heating seasons are different in different climate zones (and indeed even within climate zones.) So performance in Springfield, MA, which is in climate zone V, will be different from climate zone IV (which I'm blessed to live in.) Further, there are other factors which affect the performance of an installed system (as compared with laboratory results used to establish SEER and HSPFs) including equipment sizing, building thermal envelope properties, duct losses, etc. Accordingly, using either stated SEER or HSPFs to infer energy savings is likely to result in errors.

If you'd like to take a deeper dive into the subject, here's a start:

https://www.aceee.org/files/proceedings/2004/data/papers/SS04_Panel1_Paper08.pdf

So how does a homeowner accurately estimate what the electricity cost will be to heat/cool their home with a specific configuration of heat pumps and mini-splits?

Here are some numbers:

The approximate cost to generate 100K BTU of heat

Gas Furnace at $2.20 per therm and 80% efficiency = $2.75

Gas Furnace at $2.20 per therm and 95% efficiency = $2.32

Heat pump at $0.225 per KWh and COP 2.5 = $2.64

Heat pump at $0.225 per KWh and COP 3.0 = $2.20

The COP of the heat pump varies with the outdoor temperature. You can plug in other values. The gas furnace has a fixed efficiency independent of outdoor temperature. You will have to decide how much of your solar generated electricity will be used for heating.

Tom, I think it's rather unlikely you'll be able to justify the expenditure strictly on a dollars and cents basis, when the costs of the equipment and install are factored in, as they should be.

Justifying mini-splits on a comfort basis, that's a different story. You pay for that and there's nothing wrong with doing so as a home improvement. Will such a project fill a gap currently existing, because they will provide air conditioning too?

Are you thinking of installing wall mounted units? How many will be required?

Why did you choose and pay to have an oversized solar installation?

The excess solar was originally intended to cover the needs of a future electric car, but choosing to do heat pumps/mini-splits would negate that plan. We are only even considering the option because MA is giving out $10,000 rebates to those who convert. It appears to cover about 50-60% of the upfront costs depending on different contractor quotes.

And MA offers 0% financing for the remainder of cost after rebate.

Whether financed at 0% or writing a check, you're still paying for it. Is adding AC or comfort for uneven heat distribution a motivating factor? Again, how many wall units are you expected to need and where would they be placed?

How's your attic insulation and interior air tightness? These are areas where bang for the buck can be significant whether as DIY projects or hired out.

"So how does a homeowner accurately estimate what the electricity cost will be to heat/cool their home with a specific configuration of heat pumps and mini-splits?"

If I recall correctly, the cold-climate heat pump study sponsored by the Massachusetts Clean Energy Center included real-world performance and cost data for heat pumps installed in a variety of new homes as well as retrofits in existing homes in your geographic area. I suggest you contact the Mass CEC and obtain a copy or search for one online. I'm betting you'll find data for a home similar to your home's age, size, and construction from which you could reasonably infer the cost to condition your home. When comparing the heating cost vs. your existing system, don't forget to include the cost of electricity to run the hot water circulating pump.

Charles, I found this study https://www.aceee.org/files/proceedings/2004/data/papers/SS04_Panel1_Paper08.pdf which as you implied roughly indicates that a system rated with a HSPF of 11 in Zone 4, at best might achieve aproximately a performance of HSPF = 9 in Zone 5. So adjusting my original calculations, it might be reasonable to expect I will use between 5,500-6,000 kWh per year to produce 50,000,000 btus of heating. Additional kWh will be needed for cooling, but several sources imply that I should only expect to use 1,500 kWh or less for cooling the home. So I think if I make decisions based on needing 7,500 kWh annually to run the system, I will be in the ballpark. One of the nice things about this conversation going back and forth is it made me discover that the cost of natural gas with my utility Eversource has increased from $1.89 to $2.20 per therm, which means I would have nearly $1,100 in future annual natural gas expenditures that altenatively could purchase 4889 kWh of electricity. Adding that to the 3,000 surplus kWh produced by the solar, means I have 7889 kWh available to run the heat pumps/minisplits system. I do understand that this means I am not actually saving any money and in fact get no return on the investment in purchasing and installing the system. The questions comes down to will the system prove to be a better longterm investment compared to replacing our natural gas boiler within the next 3-5 years (expected due to age)? Will the cost of natural gas increase more rapidly than electricity? Will it provide more constant and comfortable cooling and heating (not to mention not having to put in and take out the 4 window ACs as well as the kids bedrooms getting cooling - we don't have window ACs there). Lastly, will the system add value to the resale of the house when we seek to move in 15 years. Your thoughts?

If you're buying electricity instead of natural gas, where is the savings?

In my experience, HVAC equipment doesn't add to a home's value. Buyers want what's there to work and don't care so much how. Older equipment needing replacement or repair can sometimes give a slight negative in value but telling someone that what you have is efficient isn't likely to attract much attention. In 15 years, what you put in today will be approaching end of life anyway.

Something else to keep in mind - maybe not in your area but certainly in mine, electricity prices are expected to trend upward in the coming years, even substantially, as older paid for and less expensive to operate but environmentally damaging sources are replaced by newer and more environmentally friendly production means that need to be paid for. Photovoltaic prices for home installs should be a reasonable alternative to keep costs down but again, buyers don't much change how much they want to write a check for on that basis either.