"Frank's" wrote
W7EL tells us that EZNEC doesn't display the surface
wave which obviously contains power. Would that affect
the efficiency using the integration technique?
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The surface or ground wave is the most important fraction of total
radiated power. The correct radiation pattern of a vertical antenna
shows maximum radiation along the ground. Angle of maximum radiation =
0 degrees.

When deducing efficiency, to omit power radiated along the ground from
the hemispherical integration will result in serious error.

( Efficiency by NEC4 ) / ( Efficiency by formula ) = 0.38

I can imagine other losses in addition to loss in the radials but to
have the other losses several times greater is a bit much. Where are
these large losses? Are they in the soil surface - the only other
candidate?
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Reg.