This is where your problem is.  Their mitigation will NOT be the same.  The illum does low enough damage that the mitigation of its target won't rise unless it's being attacked by multiple illums.  The assailant, on the other hand, deals enough that the mitigation on its target will eventually max out even if the assailant is the only unit attacking.  In other words, in the special case of a 1v1 fight, the illuminator hoovers around max mitigation and the assailant hoovers around minimum.

Not to mention the assailant should bypass mitgation a certain % of the time.

In their statement the the problem wasn't with the lums but with the targeting system. Were lums were winning againts HCs. But honestly in yoru test your still only factoring in a 1v1 senarior were the lums side beams do not come into play. When they do come into play it's GG, or rather BG.

I THINK I FOUND THE PROBLEM

There's a bit of a delay between when the mitigation is upped and when it starts to fall.

Ok, I'm trying my best to show all of the numbers. My understanding of the mitigation factor is this. A ship's mitigation goes up 1% for every 10 damage taken per second, and then goes down constantly at a rate of 1.25%.

So, let's consider the Assailant

-does 78 damage every 6 seconds, that means BEFORE mitigation is applied, 78 damage is applied. I'm not sure if the mitigation factor is determined from how much the ship takes or how much the volley would do in theory (78 vs. 66 for example).  I'll do calculations for both.

EDIT: Ok, I think it has to be BEFORE mitigaiton is applied. I just did a run down calculation. If it was determined by post mitigation, the Illum would die MUCH quicker.

-78 damage raises the mitigation 7.8%. Over the 6 seconds it takes for the next volley to get there, the mitigaiton will go down 7.5%. This means slowly but surely the damage the Assailant does to the Illum is going to go down because with each shot the Illum's mitigaiton shields go up .3%. In theory.

-That's what happens in theory. What I've noticed is there seems to be about a 2 second delay between when the damage hits, and the mitigaiton starts to fall. What I mean is, the damage from the volley is done, the mitigation climbs, but there's a 2 second delay before the mitigation starts to fall. 2 seconds is a rough guess, but I think this is what's throwing off the 1v1.

-You must also take into account shield and health regeneration rates, and not to mention armor. This makes the calculations even more complicated because you have to take into account both "the Shields being hit only" phase and then "the shields gone but regenerating and now hitting the hull which is also regenerating" phase. This makes calculating the 1v1 very very complicated.

So let's take a look at what happens if it's determined by the damage pre-mitigaiton

78 damage is done. 66.3 makes it through to hit the shields because of 15% mitigaiton shields.

The mitigation goes up to 22.8%, but falls back down to 17.8% for the second volley. (falls 6% between volleys)

Of that 66.3 damage, 6 is regenerated by the shields, so really only 60.3 damage has been done to the Illum.

And the Second Volley:

78 more damage is done. 64.116 damage makes it through because of 17.8% mitigation shields.

The mitigation goes up to 24.2% but falls back down to 18.2% for the third volley.

Of that 64.1 damage, 6 is regenerated by the shields, so only 58.1 damage has been down to the Illum.

So if you follow this logic, take a look at the spreadsheet I've made. I've also included charts that take into account updating mitigaiton if it's determined by actual damage taken. (Logic's adjusted, but outcome's the same).

Chart Link

So what are my conclusions?

1. Mitigation increases are determined by the theoretical pre-mitigation values. The missile volleys on the Assailant do 78 damage a pop, and that's what determines how high the mitigation shields go. The mitigation shields climb constantly
2. There is a delay in updating the info on a ship. It looks like it's around 2 seconds. This accounts for why the mitigation climbs faster than it should. The "state" of the ship has delays in it.
   
3. By calculation (and I could be completely wrong), the Illum wins. I found that the Illum will kill off the Assailant in 201 seconds
4. I cannot confirm this, but only go by a post that Howthe? made in your first post about this. The Illum maxed out at 57%, while the Assailants stayed between 15-26% (expected).
   
5. Knowing #4, I managed to produce the results you said you got. It takes ~201 seconds for an Illum to kill an Assailant. I got that the Illum is at 146 health, and that corresponds to a 2 second delay. I'm going to say the randomness of when the shots hit and the ship refreshes accounts for the extra 50+ health the ship has at the end.
6. REGARDLESS, the Illum does more damage because none of it's damage is negated, so it keeps doing 45 damage per volley, or 7dps, while the Assailant starts out at 11dps, but ends up doing 5.6 dps.
   
7. If you follow everything I've said, that means the lack of a constant refreshrate (i.e. the ship updates the info on itself every .01-.1 seconds), the data on the ship will be skewed in a 1v1 situation.

The following spreadsheet is based on the following assumptions

1. Armor reduction is ignored.

2. Shield mitigation change is based on the damage before damage is reduced by shield mitigation.

3. No upgrades, so repair and regen rate of 1/s and the damage numbers given in the OP.  Hull repair is applied after damage has exceeded shield value, which is given in the following post:  https://forums.sinsofasolarempire.com/177682

4. Damage for the first volley occurs at the same time for the assailant and the illuminator.

5. Mitigation reduction occurs instantaneously.

The download link for the spreadsheet I made:

http://rapidshare.com/files/289131848/illum_v_assailant_miti_before_dmg.ods.html

The bold and italicized lines refer to when hull repair is entered, increasing the reduction to damage dealt to 2/s rather than 1/s on just shield  The bold line indicates when the ship has dealt enough damage to destroy the target.  In both cases,

There are two sets of calculations, the first assuming shield mitigation is changed before damage is applied, while the second assumes mitigation changes afterwards.  In the first set, the assailant wins by 20.5s, while in the second, the assailant wins by 30s. While the adjustment of mitigation change timing tilts the balance toward illums, it is insufficient to explain why illums win.  On the other hand, it is more consistent with JJ's observation that we do not have a case where the assailant is hitting 57% mitigation, while the illuminator is hitting 15%.

The devs have some uber spreadsheet of balancing... I would like to say... "please share!"... because that would be freaking awsome to see the entire game-theory-balancing-spreadsheet-of-professionals-of-uber-leet-ness... and it would shed a gigantic beam of light on the the illuminator (*snicker*) issue (and every thing else the community whines about) but i dont think it would happen... (but Please show us anyway? )

I'm not going to get into the details here because I think any 1v1 case is a misleading excercise. We never, ever balance things based on 1v1. Its a non-linear system.

Also, we pay more attention to a holistic balance than a reductionism approach of the individual unit vs unit matchups.

Blair can you explain shield mitigation. Actual numbers. Mitigation increase and decrease per dps.

If the Illum wins with some 200 hull left shouldn't that be a pretty accurate result? Illum is T3 compared to Assailants being T1. Assailants can be Phase Missile upgraded to become much more lethal than they are initially.

Also, isn't Hull and Shield regeneration a certain % meaning the Illum regens more shields over time.

Then again they have the side beams so I don't know. But there's more to overall faction balance than scientific 1v1 calculations. Vasari have their neutral advantage etc. And the Orkulus.

EDITOR'S NOTE: the above was not meant to imply that Blair has more than one personality (while simultaneously not disputing the possibility, lol), rather that Ironclad is comprised of more than one individual.

you want side beams as vas?  get flak... 

Just kidding, as Blair said, it is the races as a whole that is look at.  Right now the Vas have the short stick, but the devs are working on it.  The last patch has helped out greatly.  And your individual playstyle is very important.  (find the secret to playing Vas, it is different than the "normal" method of play)

Thank you for being smart and literate. Karma   

The T3 vs T1 arguement is valid.  Whether you like it or not, it cost more for T3 ships (especially at the start). 

And T2 Javs only use 4 supply, and cost about 2/3's... so that arguement fails.  Especially when use the exact same arguement against lums.

And T2 Advent carriers are NOT better than the other race's T3 carriers.  Advent carriers cost equivalently more in both fleet supply and credits.  I've tested equivalent amounts of carriers/fighters/bombers in LAN games - and they are well matched!

All this whining about LRFs and Vasari is getting annoying.  Vasari have plenty of other advantages!  Vasari are still very popular online... if not the most popular race.  Despite all the claims of Advent being overpowered. 

And I'm a Vasari, or maybe TEC player primarily.  I'm not an Advent lover (like Grey, he he).