i think you are confounding probability and averages
i posted average hits and average kills for a lunar against swords and against eldar escorts; not probability.
my math has been accurate. you can have an average of 1.66 hits, kills or whatever else.
you came to similar conclusion yet my math is wildly inaccrurate? 
Sigoroth and I are completely clear on the distinction between averages and probabilities. The average is the more helpful number if you want to know how many escorts are expected to die for a given number of Lunars shooting, and to a large extent it is possible to work purely with averages and expected values.
However, you have to understand that just because you're throwing enough firepower at an escort to kill it on average, that does not make its death a certainty. That is where probability comes in. For example, a Lunar with 3 WB dice and 2 L against a sword will kill it on average, but the escort will only end up dead 66% of the time. If it is absolutely critical that a given result is achieved, probability helps you understand how much effort is required vs the risk that the objective will not be achieved. For example, the shooting of 2 Lunars will still leave the Sword alive slightly less than 1 time in 10. This might be an acceptable level of risk vs what you can bring to bear and what firepower is needed in other causes.
If it's simply that you won't get the VPs for the escort squadron in a game that you're already winning, the shooting of 1 lunar or 1/3 risk of failure might be acceptable. If it'll determine the outcome of the game, you may want to go with 2 lunars and a 1/10 risk of failure. If it'll determine the outcome of a 4-month campaign, because the escort is lining up the killing blow on your last remaining transport with VIPs aboard, you may find that you want to absolutely minimise the chance of failure at any cost, in which case you'll want to fire 4-5 Lunars at it. This is firepower far in excess of the 2 average hits you'd expect to be enough to do the job, but the probability shows that the risk of failure is such that you need to expend that firepower anyway.
I'll take this apart more piece by piece; green is where we have no dispute, red is what is causing Sigoroth and I to go wtf.
my simpler math for the lunar has it having 2 WB dice and 2 lance dice against a sword moving away. this on average is .66 hits from batteries and 1 hit from lance for a total of 1.66 hits. on average. given that it takes 2 hits to kill this means 0.83 chance of a sword kill from an lunar.
We are completely agreed that the average number of hits is 1.66. However, "Chance" is by definition a probability, for example "Half a chance" denotes P(X) = 0.5
If, when you say "0.83 chance of a Sword kill from a Lunar", you mean something other than "P(Sword Killed by Lunar) = 0.83", then please enlighten us. Because the probability of a Lunar killing a Sword is actually 0.5554. I don't know where you got this "0.83" figure from, because it appears like you divided the average hits by the required hits, which is statistically meaningless and will do no better than generate a random number. If this isn't what you did, please explain how you came to this 0.83 figure.
against an eldar escort it is 1 WB die and 2 lances for an average of 0.5 hit from the battery and 1 hit from lance, reduced to 0.166 hits after holofield saves for a total of .666 hits on average. given that it only take 1 hit to kill this remain 0.66 eldar kill from a lunar.
0.666 hits on average, agreed. The red bit we also happily agree with providing what you meant was 'on average' rather than '0.66 chance of a kill'. The chance of a kill is actually 0.58, because 42% of the time nothing will hit at all.
versus closing escorts it comes to 0.99 hits from batteries and 1 from lance for a total of 1.99 hits vs the sword (0.99 chance of a kill from a lunar) versus 1 hit from the batteries and 0.166 damage point from the lance on the eldar escort (1.16 chance of a kill). so here the lunar is more effective against the eldar, but this situation should rarely if ever happens with MSM.
Five points here:
1. If the Lunar has 3WB dice, and each hits 1/3 of the time, why 0.99hits instead of 1 hit?
2. This error carriers through: 2 hits on average.
3. Again, have you just divided average hits (incorrect figure of 1.99) by required hits (2)? The actual chance of at least 1 kill is 0.6667. Just because you average enough hits to make a kill does not make that result certain. Sure, if you have an infinite number of Lunars shooting at an infinite number of escorts, you should end up with 1 kill per Lunar. But 1 lunar vs 1 escort is far more likely, and that escort will only end up dead 2/3 of the time.
4. Yup, we agree with your average hits for the closing eldar escort.
5. Once again, this is completely wrong. "1.16 chance of a kill". What you mean is "1.16 Eldar escort deaths on average." You again seem to have divided the average hits by the required hits to get a certainty greater than 1, which is impossible. the chance of at least 1 kill is 0.79.
So I hope this post makes it clear exactly where Sigoroth and I are having our sticking points with regard to your math.
But ignoring the math and going back to the point your post was trying to make: eldar escorts are indeed more vulnerable than equivalent swords. However, in MSM they are far less likely to be in range, and MMS have shields.