I had previously discovered a workaround that gave me reasonable behavior but did not reveal the underlying problem. I have revisited the project and have determined the root cause.

> **Two axes were named "Horizontal".**

It seems that the InputManager by default has two axes named "Horizontal" and two axes named "Vertical." **Deleting one of the sets completely solved the issue.**


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The previous solution:

*Setting the axis to inverted causes the returned values to behave in a sensible way. Now if I tilt the stick up, I get values from -0.1 to -0.99 and -1 when the stick is at maximum, and I get values from 0.1 to 0.99 and 1 when I tilt the stick down. I can just as easily write my script expecting an inverted axis, so this allows me to continue. Unfortunately I still don't know what is causing the odd behavior when the axis isn't inverted.*