That is the Charge Bar. The Charge Bar encourages you to use normal attacks, as it the fastest way for you to charge them and improve the effectiveness of the your Active Skills, where you have to manage your limited mana pool.
The amount of damage that you need to inflict to fill your charge bar scales with your level. If a low DPS weapon for your level will charge slower than a high DPS weapon for your level.
There are Active Skills such as the Embermage's Blazing Pillar (not entirely accurate skill, but good for building charge in grouped up mobs) that builds your charge at a faster rate, and there are skills that don't accumulate any charge (e.g. Magma Mace, Firebombs, Firestorm, and Hailstorm).
Each Charge Bar for each class works in a different manner:
With Berserker, when it's full, you will enter the frenzied state. You will run faster, attack faster, and always crit until the frenzy ends. It's worth noting that the frenzied state countdown doesn't begin until you hit something (after it's been filled up). You could potentially beat up that practice dummy in town to get your frenzied boost and then port into your destination and start the fight with a boost. The charge starts decaying a few seconds after combat and drains at a slower rate than the Outlander's charge bar.
The Outlander's charge bar works a bit differently compared to the other classes. As you fill it up, you will get the passive bonuses (Up to +10% Cast Spd, + 10% Dodge, +10% Crit, +10% Atk Spd) you get. There doesn't seem to be a break point threshold for each +X% bonus gain. The more damage you do, the charge increases, but it's also constantly decaying, so it's pobably the slowest to fill out of all the classes. Filling up the gauge up has no particular effect unlike the other classes. Additionally, it's worth noting that an Outlander with no charge will deal additional damage and stun the next enemy unit they hit. This bonus stacks with bonuses from shotgunnes.
The Engineer's charge bar has specific charge points (up to 5) and that a large number of their abilities use up in order to activate, and/or are more powerful (longer range/more damage) based on how many charges you have. The bar fills and drains much like the Outlanders, but a charge point seems to stay full longer after the charge point has been completely filled.
Embermages are very straight forward, when the gauge fills up, the Embermage goes into a concentration state (for 12 seconds) where all skills cost no Mana and they do 25% more damage on top of any bonuses (tiered, passives, etc.) they've invested in. It's best to save your more powerful mana heavy skills for this state.
First, the following tests have all been done with a Level 2 Berserker with no skillpoints or stat points invested on the dummy in the Estherian Enclave. Critical hits and fumbled attacks are completely excluded from every calculation aswell as attacks from both claws at the same time.
Secondly, this was an interesting thing to test and I'll have to explain a few things/assumptions before I get on with the more related results:
How random is the damage ?
Assuming a constant environment I would assume a constant damage result. This is however not the case, and thus all results by me (and others) will be subject to 'random' fluctuations. I tested this with a 45 dps claw (36 physical damage every 0.8s) which gave me a weapon damage of 39-39. I used no offhand and proceeded to hit (regular attack) the dummy like a madman. I hit either 34, 35 or 36 while i would have expected to hit 35 all the time.
How to account for armor?
In Torchlight 2, every damage you do is decreased by an amount based on the armor value of your enemy. Since all the damage in my tests was Physical Damage, we can focus only on physical armor, but there's no way of knowing the armor of your enemy as far as I know.
When I hit the dummy with my regular claws (13 - 19 weapon damage) I had hits variating between 10 and 17. Removing 1 claw gave me 12 - 18 weapon damage and hits between 9 and 16. I then equiped my high dps claw which gave me 39 - 39 weapon damage and got hits between 34 and 36 (avg. 35).
From this I concluded the damage decrease done by the dummies armor for this range of damage is between 2 and 4.
Note that I by no means claim that armor removes a linear amount of damage nor that it doesn't scale with your damage, level, ...
Is everything an integer ?
That would be nice, but sadly: no. A lot of calculations gave fractions/floating point numbers as a result. Since it's not very nice to display those everything has to be rounded to an integer. I do not know how it is programmed, but I assumed everything is rounded to the nearest integer. This seemed to be most of the time the case.
Now, let's get on with the real results!
Scenario 1: 1 claw, no offhand
With 1 claw in your righthand and no offhand, this does exactly as it says: it takes your claws dps, takes 88% of it and deals that amount as damage (the final result still has to include armor!). So the higher the dps of your claw, the higher the damage of Eviscerate will be.
With my 45 dps claw I mentioned above, my Eviscerate hit for 37 - 39 (avg. 38). Indeed, 88% of 45 is 40. Giving this an armor penalty of 2 gives us the average Eviscerate damage.
Important to note is that this is an increase of damage compared to a regular attack. (an increase of 3 damage in this case)
Scenario 2: 2 claws, equal dps
Now, how does the damage compare to scenario 1? Does it increase because of dual-wielding, is it the same, does it decrease?
Tada ! An increase. But by how much and why? I will return to this at the end of scenario 3.
Scenario 3: 2 claws, different dps
This is the part where it really becomes interesting.
So it's of the most benefit to ALWAYS put your highest dps weapon in your right hand.
Now with that last result in mind, we return to scenario 2, where we got the same damage as with a 22 dps claw in our offhand (twice an average of 18). So the stats of our offhand are not important, as long as it's a weapon (see later: shields) you will gain an increase in damage because of dual-wielding.
So how much is the increase for dual-wielding? I don't know but from these results it would seem like the increase is equal to floor(dps of righthand / 10):
22 dps claw gives an average of 16 damage per Eviscerate hit
22 dps claw with an offhand weapon gives an average of 18 damage per Eviscerate hit
45 dps claw gives an average of 38 damage per Eviscerate hit
45 dps claw with an offhand weapon gives an average of 42 damage per Eviscerate hit
In the first case we see an increase of 2 and in the second case an increase of 4 which could be explained by the formula.
So we can just equip a shield as offhand for better survivability?
No, the damage output will be the same as if you had only a claw in your right hand (a la scenario 1).
But the increase of damage by dual-wielding is very little, why is it worth to dual-wield then?
This was done at level 2 and with no multipliers, skills... so the damage increase by dual-wielding should scale better at higher levels, better gear/skills...
I hope this answers most of your questions!
Best Answer
Your theory on how this works is correct.
I tested out my weapons that "Conveyed x damage over y seconds" by hitting a monster and then backing up and watching their health bar. The health bar went down without me touching the monster, and since I had not burned, froze, poisoned, or otherwise cast a spell to bring the monster's health down, I concluded that the "convey x damage..." deals that amount of damage over time to the monster.