How do I know if I need a sub woofer?

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.

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

@sounds_real_audio      HaHaHa... I hope your right and not just wandering in another tunnel in your Rabbit Hole.

BTW, I haven't gotten motivated enough to approach the sub placement or settings with an acoustic analyzer as I am very satisfied with just putting the subs where I want them in general and tweaking the crossover and input levels to MY TASTE.  

I think you should consider adding the subs, enjoy the improvement and recognize that doing the acoustic analysis and attempts at room correction as a separate tunnel for another day.