Let's assume the healer has 4 GCDs in which they can turn Cleric Stance on in order to drop some DPS. Pretty sweet! What do the two Healers do with this time?
SCH:
Bio II > Miasma > Bio > Energy Drain > Aero > Energy Drain
WHM:
Aero III > Aero II > Aero > Fluid Aura > Stone III
Let's compare these, shall we?
SCH:
35x10 + 20+35x8 + 40x6 + 50+25x6 +150x2
350 + 300 + 240 + 200 + 300
1390
WHM:
50+40x8 + 50+50x4 + 50+25x6 + 210 + 150
370 + 250 + 200 + 210 + 150
1180
Flat out, the SCH just started /way/ higher than the WHM just did. Easily eclipsing what the WHM can do in that short
burst period. You could even turn that Aero into a Swift Shadowflare for an additional +50 if you don't need to save it for anything else down the road. You could argue squeezing Assize in here, sure, which would bump WHM up above SCH! the problem with this becomes that you're then taking a significantly valuable heal spell away from the party for DPS in single-target. So... I dunno about that!
Either way, we'll continue to ignore Assize for this purpose and discuss the extended DPS rotations of WHM and SCH.
Lots of numbers down there v
WHM is nice and simple.
A3>A2>S3>S3>S3>S3>A2>S3>S3>S3>repeat.
The total potency of this is
9 gcds (2.45s each) + 1 A3 (2.95s) = 25s = 8.33 dot ticks
50x3+210x7+90x8.33 = 2370
2340/24s = 94.8 pot per second
Presence of Mind!
Every 150s, we get +20% attack speed for 15s. 10% of the time +20% speed. This translates into an average of +2% speed, meaning we move 2% faster, so complete 2% more actions in the same amount of time.
97.5 x 1.02 = 96.7
In addition, we have every 30s where we'll replace 1 S3 with 1 A1+Fluid Aura
S3 = 210
A1+FA = 200 + 150 = 350 = +140 pot every 30s = 140/30 = +4.67 pps
Total: 96.7 + 4.67 = 101.37 pps.
SCH is more complex...
Works out something like:
SF>B2>M>B>A>Broilx4>A>B>M>SF>B2>Broilx2>A>B>Broilx2>M>Broil>A>B>SF>B2>Broilx2>A>M>B>Broilx5>repeat.
Adding it up:
SF x3
B2 x3
M x4
B x5
A x5
Broil x16
33 GCDs + 3 Shadowflare = 33x2.45 + 3x2.95 = ~90s = 30 ticks.
DoT potency:
25+35+35+40+25 = 160
Skill potency:
Broil: 170x16 = 2720
Miasma: 20x4 = 80
Aero: 50x5 = 250
Rotational potency:
2720+80+250+160x30 = 7850
7850/90 = 87.2 pps.
But, wait! You also get 3 Energy Drains every minute!
150x3 = 450
450/60 = 7.5 pps
But, what about Dissipation? If I'm going full dps...
That adds an additional +3 Energy Drains in 3 minutes (180s)
450/180 = 2.5 pps
Total overall potency:
87.2 + 7.5 + 2.5 = 97.2
In summary, if you don't feel like reading how I arrived at these numbers...
WHM potency per second = 101.37 pps (Cleric: 111.50)
SCH potency per second = 97.2 pps (Cleric: 106.92)
Difference: 4.17 (Cleric: 4.58)
This isn't taking into account:
1. Assize. (300/90 = +3.3 pps)
2. WHM have naturally more MND than SCH.
3. Foe Requiem - which only expands the disparity.
4. The fact that, each rotation for SCH I listed will miss out on ~4 ticks of Aero and 1 tick of Bio (a loss of ~1.5 pps)
So, yeah. White Mage runs out of Mana faster than Scholar, so they can't go as long doing straight up DPS.
A White Mage doing everything completely right will still hit zero around 3 minutes. This is absolutely accurate.
The issue with this line of thinking when using it to argue that SCH has more sustained DPS is that you're ignoring the fact that in literally any situation where this might be a thing you're concerned about, it's not a thing you're concerned about. Even IF you're going 100% DPS healer 100% of the time in literally any relevant content, there is never a stretch of time where you will be allowed to dps with 100% uptime for a stretch of 3 minutes or longer as a healer OR as a DPS. There's always times for your Mana to regenerate (Boost, between A6 bosses, in the healer Jail/during Searing Wind in heart phase), or periods where you need to be healing, not DPSing (healer Jail A7/A7S, for instance).
Always. So it's a silly argument, basically.
And this isn't the place for this argument.