Beta 1, 2, 3 numbers are still based from a chronological order considering the main exe date, the PVD, or the hand notes from what's written on the disc.
To be honest, i like using the PVD date more, because it's a clear identification for the disc.
For example, considering PC games, when there's an Original release and two Rereleases for the same game, we call them
Game Name (Region)
Game Name (Region) (Rerelease) (PVD Date 1)
Game Name (Region) (Rerelease) (PVD Date 2)
and that's what i would like to do with beta discs. Also, when the two rereleases have the exact same data track (100% identical checksum) and the audio tracks are different, we're adding them as
Game Name (Region)
Game Name (Region) (Rerelease)
Game Name (Region) (Rerelease) (Alt)
and this second example can be also used for Beta discs with audio tracks variations.
And to take this discussion to another level, we're doing the same for some system demos, where it's Demo 1 or Demo 2 for PS1, when we're doing a different thing on PS2 demos, calling them Demo, Trade Demo, Taikenban, Tentou-you Taikenban, etc. based on the specific name.
IF we ever decide to not use Beta 1, 2, 3 names we should to the same for the PS1 demos, if that makes sense for you guys.
