RateTheRef

It's factual, you are on or you are off, even if there is only millimetres in it.  As long as the technology is accurate they have to judge offsides as on or off, they can't say it is too tight to call as that says the technology isn't good enough.

In absolute terms you are right but every measurement has a margin of error.  In the case of goal line technology I'd expect this to be very small because it monitors a relatively small area and the cameras can be positioned to give optimum effect.  However, for offside the error will likely be a bit higher, for a few reasons including: the cameras cannot always be optimally positioned and due to finite time intervals between frames (not withstanding the philosophical choice of whether the ball is played at the moment the foot makes contact with the ball or the moment that it leaves the foot).  An average error could be calculated for these decisions as seems to be the case in cricket LBW decisions where the error is assessed (or guessed?) as half the width of the ball. If we apply the concept of measurement error in the case of an offside decision, lets say that the degree of error is +/- 2.5cm then a line 5cm wide could be drawn centered on the most goalward relevant part of the last defender's body.  Then if any relevant part of an attacker's body is goalside of this line then it is offside irrespective of the original decision on the field.  Alternatively if all of the relevant parts of an attacker are further away from the line then the decision is onside irrespective of the on field decision,  If the nearest relevant point of an attacker to goal is within the width of the line then the decision reverts to the on-field official's decision.