Pointing transfer functions remain predominantly expressed in pixels per input counts, which can generate different visual pointer behaviors with different input and output devices; we show in a first controlled experiment that even small hardware differences impact pointing performance with functions defined in this manner. We also demonstrate the applicability of "hardware-independent" transfer functions defined in physical units. We explore two methods to maintain hardware-independent pointer performance in operating systems that require hardware-dependent definitions: scaling them to the resolutions of the input and output devices, or selecting the OS acceleration setting that produces the closest visual behavior. In a second controlled experiment, we adapted a baseline function to different screen and mouse resolutions using both methods, and the resulting functions provided equivalent performance. Lastly, we provide a tool to calculate equivalent transfer functions between hardware setups, allowing users to match pointer behavior with different devices, and researchers to tune and replicate experiment conditions. Our work emphasizes, and hopefully facilitates, the idea that operating systems should have the capability to formulate pointing transfer functions in physical units, and to adjust them automatically to hardware setups.