I didn't compare 2 different fights,
I created average values over multiple encounters in each content Tier in an attempt to ease the differences between two encounters.
Sadly, reports expire, so I cannot go back indefinitely or I would have compared reports from the beginning of the tier to reports towards the end.
Still even if I did that, you have to keep in mind that improved group performance on any given boss encounter also increases individual performances independent from your item level. Shorter kill times alone will be quite noticeable in your DPS.
Maybe you got 33% as a tank, being able to play with less shield oath as your group gets more comfortable with the encounter (unless you are a tank like ours, that is batshit insane and close to never touches tank stance
) I don't know, I'm certainly not seeing a raw 33% performance increase in either my numbers or the numbers of my team over 30ish item levels.
Another approach of assessment:
If I use the statistics of FFLogs, Summoners were at 4911 DPS in Alphascape, 5992 DPS in Sigmascape savage (75%) and are at 7230 DPS (75%) now. That would be an increase of 22% from Delta to Sigma and a 20.6% increase from Sigma to Alpha.
I think we can meet in the middle of our two numbers and say, that a Tier jump in item level results in roughly 20% increased player output.
So, a player that doesn't farm tomes and is essentially stuck with the "last Tiers" catchup gear, will lag behind roughly 20-25%.
Lets compare that to WoW (easy since Warcraftlogs is basically the same), Legion, shall we? (We don't have a second Tier in BfA yet, so we cannot compare directly right now)
In Nighthold, the Shadow priest was at 894.244 DPS (75%) in the next raid, Tomb of Sargeras, the Shadow was at 1.631.813 DPS (75%) and in Antorus, the burning Throne, the shadow sits squarely at 2.286.041 DPS (75%).
That is an increase of 82% from Nighthold to Tomb and another 40% from Tomb to Antorus (kinda small, guess they hit the limits of what their engine could handle, hence the repeated squish in BfA).
Going further back:
BRF: 50.400 DPS -> HFC: 126.217 DPS = A whopping 250% !
Now you know where the "myth" was born, I grant you that it may no longer be accurate, we have to see when the second Tier hits BfA.
Still, that wasn't the actual point of the entire discussion with @
Sorrior. He was sort of pissed that raiders get better gear than casuals, which, to be perfectly frank, simply isn't the case in FF-XIV. By the time Alphascape came around, I was decked in i370 just as people were that raided savage. So there is no "item level gap" to bemoan like in WoW. Not even a 50% one.