Is Zoom Factor Based On Focal Length Or AOV Ratios?

Inspired by Rein Raud's question in chat.

I remember having this same question a while back and deciding it was focal length.

One reason would be that, technically the stated AOV is dependent on the imager size, where as focal length makes no such assumptions.

So with this standard Fuji vari focal lens, with a stated zoom of 2.7x, we get 2.72x by using the focal length, then deciding which imager size we use we get 2.58x and 2.61x, for the 1/3" and 1/4" normal aspect ratio formats, respectively.

I have not done an exhaustive analysis by any means, and do welcome any counter-examples or corrections!

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