VAR in football refereeing.

I have often wondered about this. One of the harder, yet most rewarding, things to teach grad students is to estimate orders of magnitude and formulate rules of thumb. So let's have a quick look. The goal shown below was cancelled after VAR review because half the boot of the goal scorer, Yildiz, was judged to before the ball when it was flicked on by Kökçü. The two were some 3 metres apart and the ball appears to be travelling at some 6 metres per second. Yildiz' boot must have been moving at some 8 metres per second. The frame rate of the footage is probably some 60(fps), possibly after combining feeds from more than one camera. Thus, from one frame to the other, Yildiz' boot moved by some 13(cm), that being about half a size 41 (US size 10).

So at what moment was the video stopped? The laws of that game state that the critical moment is when the boot of the assistor (?) first makes contact with the ball. The contact can last some 0.05(s), or 3 frames, during which Yildiz' boot moved over 40(cm) or 1.5 times that size 41. One must have great confidence in the synchronization of the cameras; the ability of the the referees, on the pitch and remote, to follow the law to the letter; the geometry of the reconstruction that should undo projection effects and many other cogs in this machine!

On several occasions, FIFA and UEFA have announced that they wish to encourage attacking football by giving the benefit of the doubt to the attacker when the call is too close to make. VAR has led to the exact opposite - FIFA and UEFA are using VAR as if they have found a way to monetize cancelled goals. I simply wonder whether any applied mathematicians worth their salt were involved in designing the system that is now in place.</p>