How do you know if you need to add a sub (without auditioning one, I mean)?

You need a sub if you can not play the music you like with sufficient bass and image size and restricted volume levels if you have any of those problems a sub or larger speakers will fix those issues in most cases.

To answer your question if you need a sub, get a sub with a Bluetooth App. SVS and Paradigm are two of the few offering that feature. With a swipe of your finger you can mute the sub. A/B ing with only a few tracks will let you see the NIGHT and DAY difference. The most important part is you are doing this from the listening position.  No more running behind the sub. A quality sub will fill in the missing frequencies 40-20 Hz or lower, even the most pricey floor standers can’t produce. Check out Paul’s of PS Audio YouTube videos on the subject. Even my Golden Ear Triton 2’s which have powered bass modules built in benefit from my SVS SB-3000!

Just TRY a sub. We're beating a dead horse now.

A video I watched said even a violin sounds better with a sub. That did it. 
I was associating a sub with that annoying thump from a car truck and didn’t understand why anyone would be happy adding that to a 2 channel system. I’m new to better hifi and quickly learned you don’t know what you don’t know. 
Just found out my second sub is on the way. Planning for all four by years end. 
Whatever you do, do it!

I use a pair of subs with my main stereo pile (RELs bought used in great shape...inexpensive...I now own 3 of them) and this does help with the dreaded standing wave issues, but I also experienced a huge improvement when I used just one sub. Note that the world in general, meaning simply the sound of life, has a very wide frequency range...most speakers can cover from maybe mid bass to relatively high frequencies, but subs provide a more life-like element including some ambient sound as well as accurate bass and often make your main speakers sound much better. I check where my main speakers drop off and put the subs close to that point...adjust for taste...I also use a Loki sometimes if a recording sounds like it needs help from Knob Turner, and I have a new version coming from Schiit (back ordered) and it will be interesting to see how they improved the thing.