As a sideline to this discussion, about 20 years I installed a TV distribution system with 8 outlets for a friend in a house about 15 km from the local co-located transmission towers, using a 2-way splitter-amplifier followed by 2 and 4 way splitters to distribute the signal without using more metres of cable than necessary.
(Not all the outlets were used but one or more outlets was placed in almost every room for possible future use and to have outlets for PVRs.)
Ten years ago they moved to a house which was about 5 km closer to those same transmission towers - with a similar antenna and a clear line-of-site in each case.
I installed a similar 8 outlet distribution system but the picture received by the TVs was unwatchable - because the signal was too strong and the picture went over the "digital cliff" - in reverse. (The TV input was "overloaded".)
Obviously, the "boosted" signal was then Too Strong
However, everything worked satisfactorily once the "splitter-amplifier" was replaced with a simple splitter.