With a capacitor in series with the lamp, wouldn't the power factor be .9 or better?
Ironically with capacitor in series, so a lead type ballast, the lamp power factor will be even lower.
The power factor is defined as a ratio between the real net powertransfer vs the product of rms voltage and current.
Mathematically it says, how much the voltage and current correlate to each other. And so unity power factor means they bave the same frequency and phase of all harmonic components. In other word the same frequency, phase and shape of the waveform.
With just linear coils, capacitors and resistors on a sinewave supply the shape of all signals remains sinewave on the same frequency as the supply, so the only possible cause for lower power factor is the phase shift. Because most real things in the AC power distribution are linear inductances and resistances, that is all what electricians think of, when speaking about power factor.
But discharges are a nonlinear devices, such they virtually convert any current feed shape into roughly rectangular voltage. That means the lamps generate higher harmonics in their voltage.
With just inductive impedances as ballasts, the higher harmonics see higher reactance, so practically do not generate any harmonics in the current at all. With resistive and mainly capacitive ballast some of the higher harmonics are not filtered out, so they form an extra current component in the feed, but in a different phase than generated with the lamp.
Because the higher harmonics are not present in the current, or are in a wrong phase, they do contribute to the rms values of the voltage and current, so contribute to the Vrm×Arms product but they either do not form any power. Hence the power is smaller.
With plain inductive ballast, so a sinewave current and a rectangular voltage the power factor is exactly 2×sqrt(2)/pi=0.900316...
The ballast with a series capacitor tend to feed the lamp with rather spiky current,where the spikes add up quite significant,y on the rms (the nature of the squaring), but not that much with the power (just linear dependence,whe the voltage is constant inthat section of the square). As a consequence, the power factor of about 0.7 or 0.8 is not that uncommon with e.g. CWA (adds its own spikes due to the saturation based magnetic regulation).