In and out variances over distance

No - the error doeesn't double for every 100 yards. The variances left and right of the target are affected by two types of factors:

1. Misalignment of the scope and systemic error by the shooter - this type of error should be proportional to the distance to the target, so if the error is 2" at 200 yards you would expect the error to be 3" at 300 yards, 4" at 400 yards, 6 inches at 600 yards, etc. It doesn't double with every 100 yards, but rather increases by 1 inch for every 100 yards.

2. Errors caused by the effects of wind and air variability. This type of error increases by more than the ratio of distances because the bullet slows in flight due to air resistance. Hence if you double the distance to the target it takes more than twice as long for the bullet to reach the target, so it has time to be affected more than twice as much by the wind. For example if this kind of error introduced 2" of variability at 200 yards you might expect about 4" at 300 yards an maybe 6" at 400 yards. But that's just a guess - the actual numbers will depend on how much the bullet slows in flight.