If you are trying to improve the performance of existing operations in known markets, it is an analytical problem where it's just a question of aligning your execution engine in the right way. If it is about creating something new and different, you can't derive the right answer analytically.

What looks like resistance in many cases is rational responses to incentives and ingrained resource-allocation processes.

It's one of the underappreciated skills required by an innovator - they have to be able to convince lots of people to do things that might not be fully rational (invest in the company, join something that is likely to fail, try a product they've never seen before), and if you can't tell a good story it is just very hard to make that happen.

The reality is customers lie - not because they want to want to deceive you, but because they don't do a good job of predicting what they will do in the future.

Innovation is doubly hard inside big companies.

Document, evaluate, focus, test.

Of course, it is worth it to take the time to think carefully through your assumptions, and ensure you at least have hypotheses around how you will create value. But use the analysis as a way to focus attention on the most critical assumptions, rather than spend a ton of time massaging the numbers.