Of course, the size of the object is not the only variable - the other is the lens.
But...perhaps this will help: at a basic level, OOF blur is determined by magnification and aperture (ignoring exceptions like near 1:1 macro and fisheye lenses). In your scenario, you're filling the frame with the subject, therefore magnification is not varying with focal length, although distance to subject will increase with increasing focal length to fully frame the stick. In that case, the determinant of OOF blur amount will be aperture. Thus, the 'best' current Canon lenses will be the 50/1.2 and 85/1.2.
Let's back up a step - why is this important to you? What are you trying to accomplish?
This actually answers my question and also makes sense.
So, Rule of Thumb: the faster the Lens, the bigger an object can be maintaining some blurred background
Now for the "why": I enjoy OOF and i want to know the limitations/dependencies of it. (and i like numbers - might be the case why i study maths)
Thank you for all the answers
Now that the test parameters are fixed, whats the maximum working distance with a 85f/1.2 maintaining mackground blur?