What’s the relationship between gain (dB) and power (watts)?

A master clinic involves the recognition that in power amps variable gain is just variable negative feedback. See Roger Modjeski for an EE w ears and many successful designs the variable NFB RM-9 being a sonic master class. The cool thing about variable NFB w time and phase accurate speakers is that the intrepid listener ( given a decent recording ) can discern how NFB effects image depth....
carry on....
see also Burning Amp

Often just variable NFB but sometimes just R....

I find that speakers that has a low db rating benefits from a higher gain amp.
speakers that has a higher db rating benefits from a low gain amp.
wattage remains the same.
Also don’t forget your preamp gain.

The relationship between dB and power is logarithmic.
End of story.

This site is cries out for a Audio 101 list of stuff every audiophile should know. This would come right after W=VA.

I think the OP has been answered but I've been trying to come up with a simple way of talking about gain structure for a while. I don't know if this will add much but here goes...

The maximum output voltage of an amplifier can be calculated from the output power spec, this cannot be exceeded and if the signal reaches this level then it will clip and distort.

Dynamic range - is the space between the noise floor and the maximum output voltage. This is the space for the signal and we want this to be big for sound quality.

When we amplify (or add gain) we reduce the dynamic range i.e. the signal and the noise get bigger but the maximum voltage remains the same.

Headroom - is the space between the signal and the maximum voltage which we can think of as a reserve for momentary peaks in signal level.

So in an ideal world we’d just have the gain set to the level that we wanted to listen at with a bit of headroom. It’d be great if it was that simple but…

Most amplifiers (for a variety of reasons) offer the user little or no control of the amount of gain applied.

Different sources have wildly different output voltages, consumer line level is defined as 0.316V RMS but most DACs will put out 2V, that’s 16dB difference!

 

That’s why we have a volume control or attenuator. For a number of reasons this is usually before the main gain stage which means it attenuates the small signal before it is amplified. And the killer is that the noise added to the small signal will be amplified by the following stages (raising the noise floor and reducing the dynamic range).

 

So the point of saying all that is to explain that if your system has excessive amounts of gain then you are sacrificing dynamic range and listening to more noise than you need to… take a look at how far down you have the volume control set. So if you can set a lower level of gain and still get the volume you want you’re best going with that… the maximum output is a constant and won’t change when you adjust the gain – which means it won’t affect your headroom.