How much does collector direction matter when roof space is tight?

When a solar thermal collector can’t face its preferred direction because the usable roof area is limited, how much can a different direction or tilt affect output over the year? I’d expect the impact to vary by season, but I’m not sure when a modest orientation compromise is usually manageable versus when it meaningfully cuts into the system’s contribution.

Shading and local climate seem like they could change the answer as much as the roof angle itself. In a site-specific estimate, how do you weigh fitting more collector area at a less favorable tilt against using less area at a better orientation? What conditions make that trade-off worth getting a professional yield estimate for?