Would Horizontal Progression Help this Game?

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It really depends. The downsides of horizontal progression are likely what keeps it out of XIV ARR/HW.

Those of us from FFXI should know the downsides of horizontal progression. Have you ever been kicked out of a party or denied entry into one solely because you didn't have a specific piece of gear? I have. It's not a good feeling especially when you weren't going for anything endgame at that point. And some of the gear they expected was a bloody pain to get (with the worst cases being you needed to kill an NM for the piece which only had a 1%-10% drop rate, and unless you were a RDM/NIN or something with super solo abilities you [PRE Abyssea, 99 lvl cap, ilvls above 120] needed to form or join a party to have a chance to kill it. On top of that you needed to possibly be "waiting in line" for the kill and the NM was on a 24 earth hour respawn timer).

FFXI's horizontal progression worked because of the pacing of the game and relied heavily on your luck with the RNG when something couldn't be bought or traded (you waited 5 hours for the pop and got the kill? So sorry, 5% drop rate and no drop). It was a completely different type of grind (but very much a grind). It was a time of patience, a trait which many players lack in XIV. XIV's systems guarantee a drop, even if it's not the piece you want. It's no longer "I have to wait X amount of time before it can pop again asdfwqertuyl;hln" and has become "REPEAT CONTENT 'TIL IT DROPS"

Of course this is never always the case, and the more casual population of XIV are much less likely to lock people out for not having BiS gear. But it still stands that it will happen, and the devs clearly don't want that to happen on a larger scale than it already does for some groups.

Horizontal progression would be very bad for ENDGAME gear. For crafted gear and dungeon gear, however, horizontal progression may not matter nearly as much. You'll still get BiSers telling you which materia you need in said equipment, but it's not raid tier gear, which means you probably won't be booted for having X piece over Y... I think. People will always surprise you lol.