May 21 2021, 10:26am
The Fellowship of the Ring: 540 VFX shots for 200 minutes of screentime, totalling 2.7 VFX shots per minute.
The Two Towers: 799/214=3.7
The Return of the King: 1488/240=6.2
An Unexpected Journey: 2135/171=12.4
The Desolation of Smaug: 2000/175=11.4
The Battle of the Five Armies: 1836/150=12.2
I'm not sure these numbers are entirely representative of the truth: for one thing, I'm sure all of them account for the extended editions (although some do) and furthermore, ideally you'd want to time the total amount of screentime taken by VFX shots, as opposed to a number of shots. The Two Towers is said to have 73 minutes of VFX shots, which makes for a different calculation.
Amazingly, the number of VFX shots in the 171-minute An Unexpected Journey from 2013 is LESS than the number of VFX shots in 2002's Attack of the Clones, at 134 minutes long!
(This post was edited by Chen G. on May 21 2021, 10:30am)