@one s post is quite correct.
Essentially we have a 2D picture of a 3D situation. Any point in 3D can be identified as a set of co-ordinates (x,y,z)
(At this point, I’m going to deviate slightly from
@one s excellent analysis: in my model, the touchline is the x axis, the goal line the y axis, and height the z axis.)
Any point on the 2D picture represents a line in the real 3D world. Thus, any point on the 2D picture (eg Firmino’s armpit) could have an infinite number of sets of co-ordinates, although in reality we know his armpit (z co-ordinate) will range from above zero to about 180cm. Below is picture that (hopefully) models this.
Similarly, Ming’s knee will have a range of values for the x (and y) co-ordinate depending on how high it is.
So, with only one 2D image it is impossible compare the co-ordinates of two different points, so this image alone is not enough to determine whether or not he was off-side.
However, with a second image, taken at the same moment but from a different angle it is theoretically simple to determine the exact 3D co-ordinates of any point on the image (the method is called triangulation) but in practice it is impossible to get an accurate measurement due to errors from lens distortion, light from a point spreading/dispersing and other technical factors. But it would be possible, with two (or more cameras) to come up with a set of co-ordinates with a given error range.
Perhaps VAR has used more than one image to come to their decision?
Two possible solutions:
- VAR uses two (or more) cameras to calculate and compare the x-coordinates of the players, and also their error bounds. If the co-ordinates overlap within these error bounds, go with the onfield decision.
- Only use parts of the body that are in direct contact with the pitch (I.e.typically feet) to determine offside, as the z co-ordinate must be zero, therefor the x and y co-ordinates could be accurately determined.
Presentationly, numbers are less subjective than lines, so maybe then giving the x coordinate (or distance to goal line, or whatever), and error bounds, may make it a quicker and easier sell, and take out any human interpretation.
Anyway, I hope the above makes some sense - if not, do say, I suspect that, when I get time, I’ll turn this into a blog post.
Here’s a back of an envelope pic I drew that
may help