At STL propaganda indeed a realistic model was developed of the Chameleon P-Loop2 on 20m, similar to that used in the experiment Comparing the performance of an inverted vee dipole with a small transmitting loop on 20m.
This article presents NEC-4.2 derived radiation patterns for both the loop and Inverted V Dipole used for the experiment using data published in the experiment writeup.
The effect of radiation pattern
The original experiment cited at the start compared WSPR signals received by a number of stations at moderate distance, and a key parameter becomes not so much the maximum gain of the two antennas compared but the gain at the relevant path elevations and the higher dipole will tend to have relatively better gain at lower elevation than the lower STL, so that further disadvantages the STL in the test scenario. This factor would be additional to the relative maximum gain of both antennas.
That is not to suggest that the test somehow set out to disadvantage the STL, both antennas were quite typical of SOTA deployments and the relative performance over moderate distance paths is highly relevant to that application.
Patterns from the models
The following patterns are from an NEC model that tries to capture realistic values for significant loss elements that affect the gain of each of the antennas.
The major lobe axis is shown above, and the difference in the patterns varies a little with elevation. at 45° elevation the difference is 6.11–7.72=13.8dB. It should be no surprise to an open mind that Richard concluded there as an advantage of 12.77dB to the dipole his experiment.
Realistic models of a dipole and STL similar to those used by G3CWI in his experiment reconcile well with his observed 12.77dB advantage of the Inverted V half wave dipole over the 0.86m dia STL used.