Im always skeptical about tight offside calls that are 'proved' by TV replays. This is why.
I once attended a football workshop. There was a guy there with a speed gun who told you how fast the ball was travelling after it left your foot. I got chatting to him and he said the hardest he had ever seen a ball being hit was clocked at 67mph. He also said that if you roll the ball with the studs at walking pace, that is 3mph. From those metrics, you can deduce that a fairly well hit pass will probably start out travelling at, say, 30mph. Simple arithmetic tells you that 30miles per hour is the equivalent of 14.6 yards a second, or 21 inches every 25th of a second.
I use 25ths of a second, because when slow motion TV rolls on 'frame by frame' it is usually travelling at a speed of 25 frames a second. Which means that between one frame and the next, a ball travelling at 30mph will have travelled the best part of two feet. But in the same time, a player running at 15mph will have travelled the best part of a foot. So in one frame a player will be level, but three frames - three 25ths of a second - later he will be a yard offside, or even two yards offside if the defender has stepped up as the pass was played.
This is important, because many TV replays seeking to 'prove' a player is offside will freeze the footage a frame after the ball has left the attacking player's foot - they did this for instance on MOTD when showing Jesus' goal on Saturday; the 'freeze' moment came not when Aguero played the through ball but a frame or two after it had left his boot. Had the freeze come at the point at which Aguero was actually playing the ball - i.e. his foot was in contact with the ball in the act of playing the pass through to Jesus - I very much doubt TV would have 'proved' that jesus was offside. The wording of the law is that you have to be offside when the ball is played - not immediately afterwards.
Of course in real time, it is virtually impossible to be completely accurate about what are literally split second calls seen once, in real time, with the naked eye. We couldn't have complained if Jesus' goal had been ruled out on Saturday, just as the two offside goals against Liverpool were 'proved' to have been correct calls.
But when we are told that TV replays 'proved' a goal was offside, it always crosses my mind that the proof is actually no better than the technician who is deciding when exactly to freeze the frame.