While a lot of power amplifiers do use a conventional amount of gain (23 dB? 28? something like that) it’s not a
requirement.
Preamps tend to vary a lot more in the internal total gain, and for
sure, you can’t compare volume knob direction between them, as nothing
is standardized.
Okay, you guys are confusing preamp gain with amplifier gain. These are two completely different things. First, the typical amplifier gain is somewhere between 28 db and 32 db for a normal amp. This describes how much increase the amp naturally "amplifies" from the input voltage to the speaker output voltage. Some amps are set at lower gain such as 23-24db and cater more towards extremely high efficient speakers.
Preamp gain is completely different. You cannot say that the preamp is adding gain to the input signal. For example, your DAC output is generation about 1.2 volts. The preamp is not going to increase this on its output. In reality, it typically outputs a much lower voltage (which depends on where you set your volume control). It could potentially output 1.2 volts (that would be something like max volume) or even higher than the 1.2 volts it sees on the input.
That being said, preamp gain is an internal function of the audio stage / op amp. It is almost always based on a negative feedback circuit. The 1.2 volt input signal is actually de-tuned down to something like 0.05 volts by an input resistor (or whatever the engineer decided to de-tune). Then the gain circuit re-amplifies the signal back up to normal levels. This "re-amplification" audio stage helps with the current required to drive the input stage on amplifiers. The "amount of gain" that actually occurs in the preamp is really dependent on how much "de-tuning" happens on the input signal. This varies from preamp to preamp.
There are two scenarios with volume control. The volume/potentiometer could be an active element in the negative feedback which directly controls "how much gain" the audio circuit is re-amplifying. Or the volume/potentiometer could be located after the gain circuit, in which case it is just reducing the voltage generated by the gain circuit itself.
It's also important to know that preamps with a "high gain" will usually have more hiss/noise in the background of the signal. This hiss/noise is a byproduct of high gain circuits and there's really no way around this. If you have extremely efficient speakers (such as 100db Tektons or something), then this hiss will really become apparent (even if you are not playing any music).
