Kagi actually tells you what percentage of the results came from their own index versus external ones near the top when you do a search. E.g., when I search for “iPhone Duo” it says “52% unique Kagi results.”

I also think that there’s a strange X factor that’s hard to describe with search engine quality. I don’t think the index that gets used is everything that goes into it.

I imagine that as soon as you combine or reconcile more than one index source or reorder the results, you’ve produced a unique search engine.

E.g., a search engine could basically only use Bing as the source but if it changed the order or omitted results it would possibly be improving those results despite not having its own index.

Not really. Kagi has its own indexes and says a typical query consults about a dozen sources. [1]

[1] https://help.kagi.com/kagi/search-details/search-sources.htm...

It does, but not exclusively, and it puts its special disenshittification secret sauce (which isn't that good but much better than nothing) on top.