The balance rail and fulcrum point of the keys must produce an even feeling between black and white keys. White keys are longer and heavier than black keys so that is why their fulcrum point is further from the action and closer to the keyboard.
I’m not a piano designer or tech but the distance between the balance points must be different for different brands and models and is determined when the piano is designed based on the length, weight and balance point of the keys. From your diagram it looks as if the balance point is close to the center of the key. That means that a longer key will give you a larger distance between the balance points of the white and black keys.
The offset is probably roughly determined by the overall length and weight of the black and white keys. I can’t say exactly what that would be but logically it should be about half of the difference of the key’s overall lengths. Allowances would also have to be made for the difference in weight, especially since white keys have more mass on the playing end.