What info to use to quantify impact
Quantifying the "impact" an integration can have for your users and your business is as much art as it is science. But, to use "impact" as a comparison metric--to decide which integrations to build using "impact"--you need a consistent way to define it.
Consider the following parameters, which factor in both how an integration would impact various users and how the integration could impact your company.
End customer use cases & goals
What will this integration help an end customer achieve? We define "end customer" as the user of your product and the integrated partner's product.
If you can, use a quantifiable measure of what the integration does for that customer. Will it increase sales X% for them? Will it cut the time of Y process in half? Always start with the end customer in mind. Why would they want or care about this integration? As a bonus, this will help your marketing team later.
To understand the customer's benefits fully, you'll need to have a high level understanding of the individual use cases the integration is planned to include. Stop short of doing a full blown integration design--that comes later-- but have a general idea about use cases. This will help you understand how big or small the impact (and later the cost) might be.
For example, it's not really descriptive enough to say "integrate XYZ eCommerce platform with ABC ERP". It's far more helpful to state use cases like "sync inventory availability from ABC to XYZ" and "sync orders from XYZ to ABC for fulfillment". Again, each use case can be tied to tangible business benefits for the customer.
Consider the market size for the integration. This includes current and future customers.
Start with existing customers. How many of them want this integration? How many of them have told you (or you've assessed) that it's non-negotiable? How many customers will you lose without the integration?
Sometimes integrations are an upsell opportunity as well. How many customers would pay for an upgrade to have this integration?
Then, look at your sales pipeline. How many customers are currently in the pipeline who will or might close if you produce this integration? How many of them view it as a "must have" requirement? Once you begin to market this integration as a feature, how will that impact your leads funneling into your sales team?
As with all sales forecasting, this is an estimation. Use as much data as you can, but also encourage the sales, marketing, and customer success teams to be tracking integration requests in a quantifiable way. Discipline now will pay off later by providing better data for decision making.
How does this integration align with the overall strategic direction of the business? Just because customers demand an integration (or you've assessed there's a market), it doesn't mean that it's the right thing for you to build.
...although, if your customers are demanding it, is that something you can learn from?
You never want to approach a potential integration without understanding how it helps the company achieve its overall goals. Many times the connection is obvious, but it's worth taking the time to document the strategic impact an integration can have.
Your company and your product(s) don't exist in a vacuum. You have competitors. Your customers have indirect alternatives. It's important to understand where the lack of an integration positions you. Likewise, you must assess how launching that integration changes things.
Look to which comparable integrations your primary competitors have. Are you the only one left out? Alternatively, is this integration an opportunity to differentiate? If the latter, make sure there isn't an obvious reason why your competitors don't have this integration. Sometimes there are significant barriers, like a closed API, high technical barriers, or an exclusive relationship that isn't public.
You should also consider your customer's alternative solutions, usually sold by larger companies that provide a suite of products. Can a customer altogether avoid buying your product and your partner's, and of course avoiding the integration? Can they buy something else that addresses their uses case in one package?
Consider what happens if you do nothing, as well. Does the integration address enough of a customer pain point to move? The competitive landscape is heavily influenced by the possibility of a customer doing nothing.