If your strafing is pulling the crosshair off the point or your target is out-running the cursor in a MOBA, you are 'undershooting' what you are aiming for and your DPI or Sensitivity is too low.Otherwise you'll have to lower your Sensitivity below 1 to compensate instead. If you can lower your DPI to fix this whilst keeping your Sensitivity at 1, do so. If your mouse-hand is pulling the crosshair off the point / cursor off your character you are 'overshooting' what you are aiming for, and as such either your DPI or your Sensitivity is too high.In a MOBA, set your character walking around the map (with your view fixed, not locked to the character, of course) and keep your cursor following him or else any other moving target on the map (a creep, for example). In a first-person shooter pick one fixed position, strafe left-and-right (ideally as one of the faster characters in the game) and try to keep your crosshair on that fixed point. Test your crosshair or cursor's ability to track.
