With the introduction of the Z-95, this question is going to be more relevant than ever:
What are the odds of an Assault Missile scoring a hit against a Tie Fighter who has Evaded?
For that matter, what is the expected number of missiles required to kill off a Tie Fighter via Splash Damage alone?
Without a focus, the average damage (which is slightly higher than average hit%) is .44. If a focus is acquired, average damager is 1.04.
I would have thought medians are more appropriate to use, since one doesn't roll averages in this game.
With Assault Missiles, the most important value is the probability to get at least one hit.
With the introduction of the Z-95, this question is going to be more relevant than ever:
What are the odds of an Assault Missile scoring a hit against a Tie Fighter who has Evaded?
For that matter, what is the expected number of missiles required to kill off a Tie Fighter via Splash Damage alone?
4 dice vs 3 dice (no modifiers) has an exact hit distribution that looks like:
0.3833 0.2950 0.2179 0.0885 0.0153
for 0-4 hits. The average damage is 1.0574. With an evade, the average damage is only 0.4407.
If the TIE uses focus for defense instead, then you still only have a 38.33% chance to get 1+ hits, and average damage is 0.5624. (capped at 3 damage)
Now with focus for attack and evade for defense:
63.96% chance of landing 1+ hits, and 1.0361 average damage.
Now with focus for attack and focus for defense:
70.45% chance of landing 1+ hits, and 1.2106 average damage.
That being said, you're much more likely to see focus on TIEs than evades, because if their whole swarm evades, you just focus on one or two TIEs, and the rest can't fire with focus.
My suggestion, shoot it with a Concussion Missile first, then hit it with an Assault Missile second. If the Concussion Missile happens to kill it outright, then well, that's a nice problem to have.
0.1469 0.2262 0.2541 0.1964 0.1114 0.0476 0.0145 0.0027 0.0002
Since the TIE has an evade, everything to the right of 0 damage gets shifted left one, resulting in:
0.3731 0.2541 0.1964 0.1114 0.0476 0.0145 0.0027 0.0002 0
That's a 62.69% chance of landing at least 1 Assault Missile, with an average damage of 1.1761.
If the TIE uses focus as the action, then the exact PDF through 2 Missiles is:
0.3258 0.2776 0.2171 0.1178 0.0459 0.0130 0.0025 0.0003 0.0000
So that's a 67.42% chance of landing at least 1 Assault Missile, with an average damage of 1.2502
Incidentally, the TIE has a 30.17% chance of taking 0-2 damage and still having its focus left.
I think those numbers are all right. Kyros can probably check them.
I also avoided answering your last question completely, because it's complicated and would take longer than a couple minutes to figure out.
Math Wing? Oh man. :-) I remember reading pages and pages of posts about 40k with similar calculations. It is really nuts the data you can come up with. I have a question though. Does it take the fun out of the game for you, or is that part of the fun for you? I only ask as I have been kind of observing playstyles recently; from the hardcore to the casual. It's a curiousity for me.
It's part of the fun for me. Basically, having mathmagicians on my side means I can create in flights of fantasy, then find out its viability.
For instance, this particular thread was inspired by the Z-95 6 ship Swarm vs a Tie Swarm, and the viability thereof.
5 assault missiles look less like overkill than I was initially thinking, if I want a truly commanding alpha-strike.
"Never tell me the odds!"
"Never tell me the odds!"
We're not telling you the odds... We're telling you the chance of it happening. If we were to convert to odds, instead of being 38.33% to get an assault through, it would be 3383:1000 odds =P
It's part of the fun for me. Basically, having mathmagicians on my side means I can create in flights of fantasy, then find out its viability.
For instance, this particular thread was inspired by the Z-95 6 ship Swarm vs a Tie Swarm, and the viability thereof.
5 assault missiles look less like overkill than I was initially thinking, if I want a truly commanding alpha-strike.
is that mine or another?
It's part of the fun for me. Basically, having mathmagicians on my side means I can create in flights of fantasy, then find out its viability.
For instance, this particular thread was inspired by the Z-95 6 ship Swarm vs a Tie Swarm, and the viability thereof.
5 assault missiles look less like overkill than I was initially thinking, if I want a truly commanding alpha-strike.
is that mine or another?
Started with a post formed when Wave 4 was first announced, but I finally got around to it after reading a similar build recently, so if that's yours, have some partial credit.