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The repeatability is pretty amazing - measuring the same surface over and over was usually exactly the same - sometimes off by 0.0001 even with a crappy homemade stylus that isn't concentric (have a real M4 stylus on order).
The Renishaw probes generally have a repeatability of well under 0.1 mil. My quite dated TP1S probes are rated at better than 0.1 mil for both repeatability and accuracy coming from any direction. This style of contact probe always has a bloated triangular sensitivity polar plot due to the three internal arms. The variation between the triangle maxima and minima adds to the inaccuracy but with the probe interface box this gets complete buried within the better than 0.1 mil accuracy spec. You can easily measure the polar angular sensitivity by taping a paper scale with marks every 15 degrees around the probe body and then measuring the touch point in the X axis with each orientation. Rotate the probe between measurements so that you only use the X axis for movement and always come from the same mill table direction. If the resulting polar plot shows up as a circle your probe is simply tilted.