A quarter-wave vertical needs a ground plane to work against. This sizes the radiator and its radials, using radials 5% longer than the element rather than the 12% some calculators assume.
A quarter-wave vertical with radials that match.
A quarter-wave vertical needs something to work against — a set of radials that act as the other half of the antenna.
Ground quality strongly affects a vertical’s real-world efficiency — this sizes the metal correctly, but the dirt under it does a lot of the work.