Why dBi compares an antenna to a theoretical isotropic radiator that spreads power equally in all directions, while dBd compares it to a half-wave dipole. The dipole itself already has 2.15 dB of gain over isotropic, so any antenna's gain figure is 2.15 dB larger when referenced to isotropic. For example, a Yagi rated 7 dBd is the same antenna rated 9.15 dBi.
Watch out Reversing the sign is the common trap: subtracting 2.15 would be the way to convert a dBi figure back to dBd, not the way dBi compares to dBd. The 1.25 dB choices are not a real reference conversion at all.
The isotropic reference is the weakest, so dBi numbers look biggest. Remember 2.15: dBi = dBd + 2.15.