So we've all studied the interesting graphics of the off-axis dispersion of a speaker. Performance can vary. It made me wonder about a somewhat theoretical question, though the issue that raised it was a practical one.
Suppose you have two speaker models. Both measure the same efficiency [edit: as measured by sensitivity] under standard testing (at a fixed point, x distance away, for a given power input). But one has better off axis response. (Let's assume it's true horizontally and vertically, as well as at various frequencies, etc.)
Doesn't that mean the speaker with greater off-axis response is actually generating more total output, in order to achieve higher response off axis? If you could sum the output around a whole or half or quarter of a sphere, or something relevant, wouldn't the sum for the speaker with greater dispersion be more in total? (And yes, the standard measurement is attractive because it's just that - standard - and relatively simple and repeatable - but let's not get into the difficulty of summing the total output of a speaker just yet!)
Granted, most of the difference will be in the mid and upper frequency range, given the way low frequencies behave, so maybe in power terms it's not a huge difference.
Though for omnipolar speakers and perhaps bi/dipoles, the difference in total might be more significant, as the conventional way of measuring efficiency might not be the best measure of what those speakers are designed to do.
So given the way efficiency is usually measured, at a single point, it might not be a good index of output into a real world room that may have multiple listeners at multiple listening locations.