If you crank something like- Welcome to the Machine, and the bones in your ears don't vibrate, you need a subwoofer. Need is subjective so this may or not pertain to you.

Did we figure it out yet?

If not I will reiterate. Sound meter app + streamed white noise will inform you for certain. 

You don't need a subwoofer you need two.

I have a pair, the input level and crossover are set so I don't notice them.  However, if one sub is offline I immediately appreciate the sound as flat or less dimensional.  I don't know why but to me the greatest benefit of the subs is the effect on the upper registers, smoothing and airing them out/ opening them up.

I use a REL wireless set up, it really helps with placement not having to be tethered with speaker wire, but it does need AC to power and the SMPS on the transmitter needs to be replaced with a LPS.

How do I know if I need a sub woofer?

When you don"t have one.....or two.....

I guess if I get a sub or two my quest for a very good sound system will be over...thank god.