Because there are no instruments to anchor the pitch, even a top notch group like Ringmasters will end the song at a slightly different pitch level than they start with. In this case, my "pitch pipe" tells me they end very slightly sharper than they started. They're so close that my ear couldn't tell and I needed an electronic tuner to discern that.
While a group can end either sharp or flat, the vast majority of a cappella groups end flat a majority of the time. This is especially true for bigger groups and often I can easily tell that with just my ear and without any sort of electronic help.
The question is why flat and not sharp? I've not found any of the answers to be compelling. Therefore, I've crafted my own conjecture, but I'm pretty confident that it's at least part of the explanation since it matches my experience recording music. On the other hand, it's so simple and obvious that I would've thought that it would be a common explanation, but I haven't seen it.
When we speak and sing, we usually mostly hear ourselves via internal pathways. In other words, our vocal cords flap about and the vibrations from that flapping are transmitted via our flesh and blood and bone up to our hearing apparatus. There's also reflected sound from the vibrations coming out our mouths (and noses to some extent) and then bouncing off of surfaces around us back to our ears. However, most of what we hear under typical conditions is received by our ears via the internal pathways.
Many of us who are past the half-century mark may have never heard ourselves speak or sing until we were teenagers or older. There simply wasn't all that much access to recording equipment and the early consumer recording devices had dismal accuracy when playing back a recording. I remember being SHOCKED when I first heard what I sounded like. It sounded nothing like I sound to me via my internal pathways.
In particular, I sound slightly sharper to myself via the internal pathways than I do via the external pathways. When singing along with instruments, I always sound very slightly flatter during playback than I expect given what it sounds like to me during recording.
It's very slight. So slight that it's hardly out of tune. The perception is more a matter of the other definition of "flat": dull; lifeless; low-energy. Whereas being very slightly sharp is perceived as alive, brilliant, and exciting! A somewhat related fact is that classical instrumental groups were tuned to ever higher pitch levels over the centuries:
During historical periods when instrumental music rose in prominence (relative to the voice), there was a continuous tendency for pitch levels to rise. This "pitch inflation" seemed largely a product of instrumentalists competing with each other, each attempting to produce a brighter, more "brilliant", sound than that of their rivals.Another experiment that confirmed that I sound sharper internally than externally is what I call the "wall trick." To hear myself better from external reflections, instead of singing into a room, I'll stand facing a wall, about a foot away. It looks kinda silly, but instead of hearing myself mainly internally, I'm also able to hear the external reflections and it gives me an idea of what my pitch and tone sound like to the rest of the world. Recently, I sang a single note into a tuner while walking towards the wall. I maintained the same pitch the whole time. As I got closer to the wall, I sounded progressively flatter even though the tuner said I was singing the same pitch the whole time.
So both record/playback and external reflections confirm that I sound a tiny bit flatter externally than internally. I suspect, but haven't yet proven, that's true for most people. After all, people are similar physiologically, and I think the effect is due to our internal transmission filters being slightly more high-pass than the external transmission filters which probably are more affected by the resonating cavities that form our vowel sounds. Well, that's my conjecture anyway. I really don't know why. All I know is that internally I sound sharper than externally.
When we start a song in an a cappella group, someone blows the root of the key on a pitch pipe or electronic equivalent. If I sing my note and it sounds right to me internally, it will sound very slightly flat to those around me. Everybody around me will also do the same thing and sing very slightly flat. I'm going to sound flat to everyone else and everyone else will sound flat to me. But we want to align so we'll all adjust incrementally downwards a little tiny bit. And then we all sound flatter to each other so we adjust downward again. And again. And again. They're all tiny adjustments, minuscule really. But over the course of a whole song, all those increments add up and the group might end up noticeably flat, maybe even a half-step. Maybe even more. Even for very accomplished groups.