Since shouldn't dBi gain vary depending on radial location?
dBi is defined as the ratio of the radiated power of an antenna at its maximum response angle to that radiated by an isotropic (hence the i) antenna, measured in dB. Thus if an antenna radiates twice as much power at its maximum response angle than an isotropic antenna, when the input power to both antennas is the same, than that antenna is said to have a gain of 3 dBi. Isotropic antennas radiate equally at all angles. For most practical antennas, the radiated power varies with angle. This variation is defined as the radiation pattern of the antenna. However, the dBi gain is defined only at the maximum response angle of the antenna so it does not vary with angle. It is quite possible for two antennas to have the same dBi gain, but very different radiation patterns.
Antenna gain is usually defined as the ratio of the power produced by the antenna from a far-field source on the antenna's beam axis to the power produced by a hypothetical lossless isotropic antenna, which is equally sensitive to signals from all directions. Usually this ratio is expressed in decibels, and these units are referred to as "decibels-isotropic" (dBi).
on-axis == best-case