Just how much is the proc on Sextant worth? I have heard quite a few people inquire about this, so I did the math. To start, take a caster with a crit rate of C, who casts spells that can crit at regular intervals of T. (so, for example, a fire mage might have C=.3 and T=3.2). First we need to find the expected time before the Sextant procs, which can be expressed as

(T)(C/2) + (2T)(C/2)(1-C/2) + (3T)(C/2)(1-C/2)^2 . . .

That is, the chance of it procing at any point in time, weighted with the probability of the proc occurring at that point in time. To get this expression into a reducible form, we factor out (TC/(2-C)), leaving us with

(TC/(2-C))((1-C/2) + (2)(1-C/2)^2 + (3)(1-C/2)^2 + (4)(1-C/2)^4 . . . )

Summing the infinite series yields

(TC/(2-C))((1-C/2)/(C/2)^2)

. . . and this simplifies quite nicely to 2T/C. So, on average, it will take 2T/C seconds from the start of a fight for the Sextant to trigger. That fire mage can expect to caste fireballs for (2)(3.2)/(.3) ~= 21 seconds before the Sextant procs. There is, unfortunately, more to it. A hidden cooldown of 45 seconds means that the chance that the proc will be active at any given moment is 15/(45+(2T/C)). Multiplying this by the damage bonus of 175 yields an average damage bonus of 2625/(45+(2T/C)). Some representative values:

Elemental shaman, T=2.2 and C=.25: 41.9 damage
Elemental shaman, T=2.2 and C=.3: 44.0 damage
Frost mage, T=2.7 and C=.25: 39.4 damage
Frost mage, T=2.7 and C=.3: 41.7 damage
Fire mage, T=3.2 and C=.25: 37.2 damage
Fire mage, T=3.2 and C=.3: 39.6 damage
Shadow priest, T~=6 and C=.25: 28.2 damage
Shadow priest, T~=6 and C=.3: 30.9 damage

As it stands now, the benefit the trinket provides is surprisingly uniform - in the neighborhood of 40 damage for nearly everyone. With the recently-described nerf, the Sextant only procs on 20% of crits, and the formula to model it (without going through all the math again) is 2625/(45+(5T/C)). Representative values:

Elemental shaman, T=2.2 and C=.25: 29.5 damage
Elemental shaman, T=2.2 and C=.3: 32.1 damage
Frost mage, T=2.7 and C=.25: 26.5 damage
Frost mage, T=2.7 and C=.3: 29.2 damage
Fire mage, T=3.2 and C=.25: 24.1 damage
Fire mage, T=3.2 and C=.3: 26.7 damage
Shadow priest, T~=6 and C=.25: 15.9 damage
Shadow priest, T~=6 and C=.3: 18.1 damage

The change, therefore, is about a 12-13 damage hit across the board.

Is it possible to apply the sextant formula to Heals and attribute this accordingly to Paladins? It seems like one mean Paladin trinket since it currently adds 350 healing on procs. I'm not mathematically minded, so I'm not even sure where to begin equating this.

Don't forget the passive 35 crit rating - I think that makes it a bit better than Briarwood. As an added note, the math is basically identical for the Nexus Horn. To find the value of the Horn's proc, plug your numbers into the new Sextant formula and multiply by 1.29 (yes, this means that the Horn is pretty much always better than the Sextant).

For a paladin spamming Flash Heal with 0.2s lag, T=1.7 and C=.2 (just did a poll of some good paladins, this seems to be an average-ish crit number). The value on the proc works out to 84 damage with the old version, 30 with the new. Probably not better than Essence of the Martyr or Scarab of the Infinite Cycle. They halved the healing increase to 175 in the new version, so that hurts it a lot.

Arcane Mage using ABx2, AM, Scorch cycles has an average time T of (2.4+2.2+5.2+1.7)/8 => 1.44

AM Mage, T=1.44 & C=.25: 35.6 damage (*1.29 for nexus 46 dam)
AM Mage, T=1.44 & C=.3: 38 damage (*1.29 for nexus 49 dam)