"Why that pattern specifically if you don't care how it sounds?"
It's an odd hybrid M-S arrangement that I figured out on my own though I bet I just re-invented an old wheel. The results are quite good.
I volunteer at our local community radio station as studio engineer and music festival remote broadcast producer. Earlier this month at Summer Festival here in Bend, Oregon, I tried this setup and am very pleased with how it sounds.
So, at these festivals (two more remaining this summer) we get a split from the PA system sound board, which is pretty dry and totally mono, because the sound mixer isn't interested in giving us a recording mix, he is only interested in how it sounds at FOH. So that's the feed we get, and we've been broadcasting that feed for years.
At this last festival, tried something new: I mixed that feed with an M-S mic arrangement I set up 40-or-so feet back in the audience. It works great.
To time-align the PA feed with the mic array -- the sound board signal gets to our broadcast/recording mixer before the sound hits the mics -- I have a delay fx box inline with the PA feed. I recorded the waveforms of the PA and the M mic during the first song, then stopped the recording and examined the PA and the M mic waveforms to determine how much the PA fed led the M mic signal, and set fx box delay to the appropriate amount. The waveforms line up, the sound is clear.
By then adding the S (side) mics to the mix I got very nice stereo spaciousness while remaining fully mono-compatible for FM broadcasting (the station is currently in mono for technical reasons).
If I was just recording the show, and not broadcasting it live, I could take the PA and mic tracks home then time-align them in my DAW and mix it down. That would be easy. But I have to dial in the delay quickly because we are broadcasting live, and for each festival the mic location will be different, and there's no predicting how much latency the PA board adds because they use different boards all the time. So I will always have to perform this initial calibration process, and I want to be able to do it quickly.
So I'm thinking that having a clearer waveform from the M mic, with less "room" reverb, would speed the process.
The cardioid I used this last time for the M mic picked up quite a bit of "room," so its waveform, compared with the PA feed, is pretty blurred and it takes a while to find an easily-identifiable sharp match between what I'm getting from the board and what the mic picks up. I am thinking that with a shotgun-type mic I'd get less room sound and thus a cleaner signal to use to compare with the board feed, making it easier to quickly dial in the delay. That's my swell idea, anyhow.
Why don't I care how the mic sounds? Because it turns out that once time-aligned, I don't need the M mic in the mix -- the sound board feed sits quite nicely in the middle, and the M mic contributes nothing really useful to the final mix. So that mic is really going to be used for calibration purposes, not for final audio.
I hope this makes sense. Shotgun, phantom powered, under $100, sound quality not so important. As you say, there are plenty of sub-$100 short shotguns on the market for video guys, so yeah, maybe one of those.
I own a couple of Jon's mics, he makes real good stuff.