Yes, you can tell, to a degree, if an amp is a good match for speakers… but a better approach, is simply look for an amp with “good specs”. This kind of an amp will match with many if not all major speakers.
In short, you want an amp than can produce watts into difficult loads (this may explain why some amps lack bass but have a high 8 ohm watt spec… etc.). This is known as a “high current” amp. To see if an amp is such a a thing, look at its specs… a good amp maker will show you the wattage output into different loads (known as ohms). So… a really good amp will put out double the watts for halving of the load. Example spec: 100 watts into 8 ohms, and 200 watts into 4 ohms. That is a great amp spec. Further, some really good (and expensive amps) will describe their output down to 2 ohms… 400 watts into 2 ohms. Now that is a fabulous amp (and unfortunately very expensive). Difficult loads are smaller ohm numbers and require an amp push harder (and run hotter).
Now if you have a limited budget, and can;t afford and amp that produces big current into tough loads, then you must be careful that the speakers you buy do not have a difficult load. You can see this in the makers specs… they will say some ohm number… usually 8 or 4… or something in between. 8 ohm speakers are easy to drive and do not require a beefy amp as I described above. 4 ohm speakers are tougher and require a beefier amp. The problem with speaker specs is that the loads (ohms) change with frequency… makes will say “nominal” which is a fudgy word that means “sort of” or average-like… that is why Stereophile and others graph load against frequency so you can see how low a speaker’s load really goes.
Like everything, the problems go away when you throw money at it… a lesson I learned over the years, is just buy beefy amps and life problems don’t occur. This sometimes confused with higher power amps are “good”… the real issue is their wattage into low ohm numbers… that is what to look for, not the 8 ohm number.
So… let’s look at PS Audio’s BHK 250…:
Output Power Both channels driven 120vac mains, 1kHz, 1% THD
8Ω 250W minimum
4Ω 500W minimum
2Ω Stable for musical transients
This amp is “wow”… fabulous numbers… it can “dump current” into difficult loads (4 ohm) and in the old days, we would call this a welder… seriously, it could create a welding arc to fix an auto body. I don’t know what they mean by 2 ohm there… “stable” … maybe someone from PS Audio can chime in here. But alas, this amp is expensive. But… when an amp has these great specs, it will match very well with just about any speaker out there… this is very important and as I got older, learned this lesson a few times over… (don’t ask!)
BTW, if an amp does not show its wattage output into 4 ohms (only show 8 ohm output), I simply won’t buy it. Period. They are clearly hiding something… they sacrificed current making, to show a high, cheaper-made, watts into 8 ohm. This is not good. Seriously, I would never never buy an amp that did not publish its 4 ohm spec.
Now the above commentary is about “matching” for load… for me, this priority number 1. Second, is how much volume will you get out of your speakers for a given watt of input… and for that, you need to look at a speakers “sensitivity” rating… low efficiency means you will need a higher powered amp to acheive the same volume. But here things get weird because it depends on the type of music you like, listening volume you like, your room acoustics… etc… but… if you stick to the issue of output at load, and you find an amp that will even publish their 4 ohm ratings, then you are 80% of the way there. (BTW, in my experience, any amp maker that publishes their 4 ohm ratings is most likely a maker of good amps.)… now a speaker can have high efficiency and be a difficult load… sheesh!
Oh, just just avoid speakers with “difficult loads”… Stereophile etc can help you there.
One more thing: ignore THD and other distortion numbers. Not relevant… it was in the early '70s but not today.
Bruce in Philly