One of the reasons pilots often chase the needles on an ILS approach is that they don’t have a clear understanding of how the sweet spot narrows as they approach the runway.
From the Pilot and Air Traffic Controller Guide to Wake Turbulence
The Outer Marker, which normally identifies the final approach fix (FAF), is four to seven nautical miles before the runway threshold.
I don’t have a chart for the VOR, but is is similar, just not as sensitive
At 30 NM each dot is approximately 1 NM displacement.
At 15 NM each dot is approximately 1/2 NM displacement.
So when you are tracking a VOR to the airport, at the FAF you are usually about 6 nm from the runway threshold. If the VOR is on the field, then each dot is about 1/5 NM (1,200′) displacement.