Oops! Between the time I composed my message and the time I finally
reconnected in order to send it, Mike and others had already commented on the
2.6dB directivity. However, I believe my observation offers a way out of
having to consider ground losses twice.
If we refer to vertical pattern directivity and azimuthal pattern
directivity, we understand them to be assumed ideal conditions. Since the
overall gain is the mathematical product of those two factors and the
real-world losses, the losses can legitimately be lumped into one single
factor of the product that affects the whole outcome.
Of course, that factor may be a complicated one to describe mathematically in
the real world, involving in the simplest case the radiation resistance of
the antenna versus losses in the tuning coil and earth; and in more
complicated cases, involving the added problem of other objects in the
vicinity, their conductivity, the mutual impedances between them and the
antenna, and so on.
But I think the important point is, the loss factor can be legitimately
separated from the two directivities, and thus allow us to consider them in
the realm of the ideal. It's just that, when comparing antennas, we need to
specify whether we are talking about overall gain (which includes the loss
factor) or directivity alone.