How many watts??

If I have a 80 watt stereo amp and I normally listen at quarter volume and never play at levels higher than this. Do I really need 80 watts could I use a 15 watt amp at half volume?

No, it depends on the input levels and your amp's gain. If your input level is very high, you could exceed your amplifiers output even when your volume knob is lower than half volume. It the input is very low, you could possibly not even come near your amplier's total output even with the volume turned all the way up.

There is no "golden ratio" between amps.

... if I have speakers that my mfg states needs min 50 watts to really make them sound good with my current amp rated at 80 watts but played at qtr volume does that mean I am not really getting the best from these speakers.

No, the manufacturers are engaging in a CYA exercise. The "best from your speakers" is what sounds the best to you. Don't sweat it, sit back and enjoy your sound. You are over thinking things.

Yup. What he said.

Your volume control is most likely logarithmic so you cannot use that as an indicator.  Go to Home Depot, Lowe’s or Amazon.  Order a volt meter.  Set the meter to AC voltage and measure the voltage across the speaker terminals while playing.  This will tell you how many volts you are using.  Amps or current drive is volts divide by speaker nominal resistance.  Power is amps time volts.  Most modern music is fairly compressed so 6dBs or a gain of 2 and 9dB or a gain of 2.8 will do.  A gain of 10 is 20dB which is way more than you will need.

The volume knob is just a gain attenuator in the preamp section of your amp and has NOTHING to do with understanding how much power your amp is actually putting out.   You can't think that it's 1/4 turned, so you're using 20 watts.    Your amp would have to have metering to show you how much power is being used, which is why many amps back in the 70s and 80s had them.

It sounds like you've already got a good match between the power in your amp, the demands of your loudspeakers and how loud you care to listen.  Relax.  You're already set.

Back in the late 60s ,100 watts a channel was unheard of then the 70s hit and the wattage started to increase...by 1975....if your reciever didn't put out 100 wpc...you received sucked...then it was 100-150-200 you were told you need more power 300 wpc ....now its 800 wpc to 1,000 Please stop the crap....tubes were always like 8 wpc to 15.....now you see 100wpc tube amps....Stop it ...its nuts and crazy......I gave polk lsim707 they say you need 300 wpc to achieve the sound you need ,I  SAY baloney....I'm running them with a caryin 55 it puts out 30 wpc and it sounds great..
.I can't knock the walls down but I live in a condo village....and it plays loud enough for me....