The deviation of a curling stone with 1-5 rotations in a normal game can be explained with the isotropic nature of friction.
Due to isotropy, the lateral force arises as a delta of asymmetric friction forces opposite to the centripetal forces. Considering lubricant accumulation, the quadratic Stribeck-curve on the advancing side is modified to show rather constant values. Below a critical velocity difference of the two sides this will result in a curl.
For few rotations, an exact calculation based on experimental measurements explains the observed deviation of roundabout 1m declining with increasing rotations.
The deviation above 5 rotations can be explained considering statics and additional heuristic calculations that involve Scratch-Theory and the influence of gyroscopic precession. All this then yields a graph that also explains the observed increasing deviation up to 2m for 80 rotations.