Need help with Math Wing

By Siddhi, in X-Wing

Arrrgh, my brain is starting to melt! With the german Nationals coming up I can't stop figuring out new squads! I've been playing X-Wing for quite some time now but I'm struggling with a question that I can't really answer myself: what is better - a ship with 4 HP and 3 evade dice or a ship with 5 HP and 2 evade dice? I mean which ship lives longer?

My feeling tells me to go for the 5 HP ship but I'm sure somebody out there has already calculated that back and forth and has some hard evidence from statistical analysis. Unfortunately I'm rubbish with math. Can somebody sooth my overheating brain with an answer?

4Hp 3 evades is more survivable, except against 4 attack dice ships with focus and /orTL and 3 attack dices with focus and TL when it has no focus/evade for defense.

Edited by Icareane

Maths.

Posted Today, 11:08 AM

Maths.

Yeah sorry, I'm german. Can't really pronounce th followed by s anyway. :)

@Icareane: Thanks for the answer!

It's a tough call, because it depends a bit on what you are facing, and position and tokens...

Quick guide is to consider defense a lock. And attack a key to that lock, equal attack has a good chance of getting through given the dice... .5 attack to .375 defense. So an hlc is a good way to hit a stealthed interceptor with its 4agi. From this perspective a 4hp agi 3 ship will last longer than a 5hp agi 2 ship against 2 attack, but that story changes against 3 and 4 attack.

You can use expected hits as a quick and dirty guide... Say unfocused, multiply agi dice by expectation value

3 agi x .375 = 1.125 evades, expect to prevent that much damage per attack on average.

2 agi x .375 = .75 evades

Now let's assume 3 attack focused which is 2.25 hits (same method, 3 x.75) .. Subtract your expected evades.... So for 3 agi, 4hp, it's 1.125 damage per attack, divide into hp... You to survive about 3.5 attacks.... 2 agi 5 hp... Is more like 3.3 attacks... So they are close.. When you add in focus on defense, lack of focus for attack, or an evade token or 2 att, things change, but vs your 3 attack, there is slight advantage to the higher agi here, but we don't have half attacks, so it's about a wash...

Edited by Ravncat

Posted Today, 11:08 AM

Maths.

Yeah sorry, I'm german. Can't really pronounce th followed by s anyway. :)

@Icareane: Thanks for the answer!

Just a little joke don't worry about it :)

As I'd usually calculate it (against an attacker with 3 dice and focus or TL, with no defensive tokens), 4 total hit points on 3 Agility is exactly equal to 5 hp on 2 Agility. That means that in typical play, where you at least sometimes use an action for defense, the ship with 3 Agility has an edge.

Posted Today, 11:08 AM

Maths.

Yeah sorry, I'm german. Can't really pronounce th followed by s anyway. :)

@Icareane: Thanks for the answer!

lol! Well, that explains it then. As a german I was taught Oxford english in school so I should have written "maths" but by reading mostly english-language novels by american authors and watching lots of american movies or playing american video games my english has been corrupted, so I wrote "math". :)

Actually I just forgot to add the s; I work with a lot of british people and speak english almost every day at work. Those guys keep making fun of me though when I try to pronounce "months" or "maths" correctly, so I just might stick to "math" from now. Anyway, thanks for clearing all that up and helping me with the Math(s)-Wing too! Maybe I'll be able to get a full night's sleep again now instead of tossing around restlessly while mumbling hit probability calculations in Galactic Basic all night. :D

All results taken from http://www.xwingdice.com

Attacker is always considered to use a focus. Expected damages are,

Against 3 evade, no defensive focus:

<2 attack dice> = 0.61 damage (simple) 0.65 damage (crit damage included)

<3 attack dice> = 1.22 damage (simple) 1.28 damage (crit damage included)

<3 attack dice> = 1.91 damage (simple) 2.01 damage (crit damage included)

Against 2 evade, no defensive focus:

<2 attack dice> = 0.85 damage (simple) 0.89 damage (crit damage included)

<3 attack dice> = 1.53 damage (simple) 1.61 damage (crit damage included)

<3 attack dice> = 2.26 damage (simple) 2.37 damage (crit damage included)

To get the proper expectation of the number of attacks a ship will survive, take the HPs and divide the number of expected damage:

5 hull, 2 evade:

<2> = 5.6 - 5.9 attacks

<3> = 3.1 - 3.3 attacks

<4> = 2.1 - 2.2 attacks

4 hull, 3 evade:

<2> = 6.2 - 6.6 attacks

<3> = 3.1 - 3.3 attacks

<4> = 1.7 - 1.8 attacks

So what this means is:

-Vorpal Sword is right, the only difference is in his analysis the number of attack dice is only 3.

-Icareane is right, where he says "except where the number of attack dice is 4."

-Ravncat is right, especially when he implies it's complicated when you consider the number of action possibilities and the fact that fractional attacks don't exist.

-It depends on what you expect to be facing.

-This took all of 2 minutes to do, so you can run the numbers quickly with more complicated scenarios if you desire just using the site I hyperlinked. (You can also determine more accurately the amount that shields will help, since shields take only "simple damage" while hull takes "crit damage")

Edited by Sparklelord

...my english has been corrupted, so I wrote "math".

For some reason you mis-spelled "corrected" as "corrupted". :D

Siddhi, on 21 Aug 2014 - 3:41 PM, said:snapback.png

...my english has been corrupted, so I wrote "math".

For some reason you mis-spelled "corrected" as "corrupted". :D

That probably depends on the point of view, which would be the two sides of the Atlantic Ocean in this case. ;)

Don't confuse me further please - I'm just a poor German who's already struggling with his english here. Can't see why it's mouse and mice but not house and hice for instance. Sometimes I think you native english-speakers just make all that up on the go to confuse foreigners. :D

Edit: By the way - how do you all get the user names into the headline of quotes? Can't figure it out.

Edited by Siddhi

Don't confuse me further please - I'm just a poor German who's already struggling with his english here.

Nah, don't worry about it. Speaking seriously, your English is excellent, and no native English speaker is likely to mistake your meaning even if you mix American usage with British/European usage.

Can't see why it's mouse and mice but not house and hice for instance. Sometimes I think you native english-speakers just make all that up on the go to confuse foreigners. :D

When I was a kid, I insisted that there was no way that the plural of "goose" is "geese", but the the plural of "moose" is "moose". So I went around for about a year talking about "meese", which my parents found hilarious but my teachers less so. (It didn't help that I was being taught French at the same time, where the plural is fairly regular: orignal, orignaux.)

The problem is that English is full of inconvenient loanwords and mutations. We get both "house" and "mouse" from German, which of course you know, but the current linguistic theory (which I learned about a decade ago, so this may be out of date) is that in the 14th or 15th century, the plural of mouse mutated from something like "mussiz" to "missiz" to "mis". For whatever reason, "house" didn't see the same mutation, so they have different plurals.

Alternately, it's possible that there is no standardized written English, and we just make it up on the go to confuse foreigners. From the outside, I agree there's no way you'd be able to tell the difference. :P

Edit: By the way - how do you all get the user names into the headline of quotes? Can't figure it out.

I usually post using the markup/BBCode interface, so I just copy the header (which looks something like [_quote name="Siddhi" post="1216672" timestamp="1408630478"_]) to the top of the next paragraph I'm quoting. I'm not sure how you'd do it in the normal editor.

Arrrgh, my brain is starting to melt! With the german Nationals coming up I can't stop figuring out new squads!

OK, so maybe we can help each other out! I am trying to collect Nationals data, and I need to get in contact with the TO who will be running the event in Germany this weekend. Do you have the email of the tournament organizer, or at least the email of the store that it will be at? The Nationals thread is here:

http://community.fantasyflightgames.com/index.php?/topic/110928-2014-nationals-results/

I've been playing X-Wing for quite some time now but I'm struggling with a question that I can't really answer myself: what is better - a ship with 4 HP and 3 evade dice or a ship with 5 HP and 2 evade dice? I mean which ship lives longer?

My feeling tells me to go for the 5 HP ship but I'm sure somebody out there has already calculated that back and forth and has some hard evidence from statistical analysis. Unfortunately I'm rubbish with math. Can somebody sooth my overheating brain with an answer?

So, it turns out that I have done exactly this kind of analysis already, from a macro meta perspective. The original thread is here:

http://community.fantasyflightgames.com/index.php?/topic/100360-using-lanchesters-square-law-to-predict-ships-jousting-values-and-fair-point-values-work-in-progress/

What I do, is calculate the average damage received, as a function of how many agility dice you have, from a variety of different kinds of attacks (2 dice, 3 dice, different ranges), and different action economies available on both the attacker and defender (75% chance of focus on attack, 50% chance of focus on defense). The resulting durability for various numbers of defense dice, normalized to 3 defense dice as a "standard" is:

0 defense dice: 0.4278

1 defense dice: 0.549

2 defense dice: 0.7312

3 defense dice: 1

4 defense dice: 1.3876

These numbers are all based on wave 3 meta (which affects what's attacking you, and how often), but these results should still be pretty close.
So:
4 hull behind 3 defense dice = 1*4 = 4 (normalized) durability
5 hull behind 2 defense dice = 0.73*5 = 3.65 (normalized) durability
So the 4 HP ship is on average more durable. (It is still possible that you can roll all blanks, or roll all evades, so the ship with more defense dice will generally have a higher standard deviation.) But it gets more complicated, because then you need to consider the effects of shields. Shields are generally worth around 15% more than hull. So here are some sample numbers for a few ships:
E-wing: 1*(2 + 3*1.15) = 5.45
B-wing: 0.55*(3 + 5*1.15) = 4.812
A-wing: 1*(2 + 1.15*2) = 4.3
X-wing: 0.73*(3 + 2*1.15) = 3.87
Z-95: 0.73*(2 + 2*1.15) = 3.14
TIE Fighter = 3*1 = 3
That being said, this does not address whether or not the ship cost is justified by its durability, attack power, dial, and upgrade potential. That's a whole other can of worms.
Hope that helps.
Edited by MajorJuggler

@Vorpal Sword:

Thank you for saying that! :) I've had English in school since 5th grade and after school I started reading novels in English because I didn't want to forget everything. All that reading actually helped to further improve my English and for the last few years I've also had a lot of practice at work on a daily basis. Unfortunately it's the only other language I really speak besides German.

From all the languages that have their origins in Latin English is probably the hardest to learn. There's quite some Saxon words mixed up in there like "window" which originally meant something like the "wind-eye" in the wall (eye being Auge in german). Funnily a window is called a "Fenster" in German from the latin "fenestra". Probably because we've had more Romans running around here than there were in Britain. What is even more interesting is that a lot of Latin words actually have their roots in old indian Sanskrit, e.g. "frater" which is "brathara" in Sanskrit or "brother" in English. The numbers sound very similar too e.g. two, three, four - dvi, tri, catur. Sorry for the smart-ass mode which was triggered by the interesting bits of information you've shared. I just think it's fascinating to be able to follow the migrations of peoples over thousands of years by analyzing (or "analysing"? ;) ) their language.

I think I'm going to use "meese" just to annoy my english colleagues. I guess you're from Canada then? Since you've learned French and there's that talking about meese I mean. :D

@MajorJuggler:

Thanks a lot for sharing your analysis!

I'll send you a PM with the email address of the organizer. The event is scheduled for next Sunday and it'll be happening in a castle actually, not a store. Not really fitting for Star Wars but kind of cool anyway. Don't expect too much input from the organizers though since they're notorious for being fairly unorganized and late with everything. I'm sure there will be results and squad lists to be found in the german forums afterwards and of course I can forward that information to you then.

evade dice are an illusion. no matter what the math says you are going to roll not enough evades on 6 dice when it is most important. Fly something that lets you stay out of arc (like Echo) and you will be a happy pilot.

I think I'm going to use "meese" just to annoy my english colleagues. I guess you're from Canada then? Since you've learned French and there's that talking about meese I mean. :D

I'm from Alaska, actually, but my French teacher was Quebecois.

He didn't succeed particularly well, though; I know just about enough French to order a meal and get a hotel room, but I can't hold a conversation or read a newspaper. My Spanish is better but still not great--so if you speak, read, and write both German and English that means you're one ahead of me (and about one and a half ahead of most Americans...)

The event is scheduled for next Sunday and it'll be happening in a castle actually, not a store.

OK. Your mission is to bring a camera and get some awesome pictures! We all need to see X-wingery in a castle!

@Sid I can safely say your English far exceeds my French and German, I have no skill for picking up new languages, I know two English and bad English :)

There will certainly be pictures of the german X-Wing Castle Nationals! I'm afraid the castle is a youth hostel nowadays, so it might not look quite as sinister and medieval as one might hope for but it sure beats some run-of-the-mill gaming store.

Thanks for all the praise about my English - you guys are very kind! :)