Using Lanchester's Square Law to predict ships' jousting values and fair point values (work in progress)

By MajorJuggler, in X-Wing

Shields block crits first.

Edited for unnecessary rudeness.

Edited by AndOne

Do you even know how to play?

Shields cancel Crits first. Every time. Please read the rules.

Do you even know how to play?

Shields cancel Crits first. Every time. Please read the rules.

Ships can suffer damage from different sources, such
as being hit during combat or by an effect or card
ability. Damage cards track how much damage each
ship has suffered and are used to determine if the ship
has been destroyed (see “Destroying Ships”).
When a ship suffers damage or critical damage,
it suffers them one at a time following these
steps. The ship must suffer all normal damage before
suffering any critical damage.
1. reduce Shields: If there are any shield
tokens remaining on the ship’s card, remove one
of the tokens and skip Step 2. If there are no
shield tokens, proceed to Step 2 below.
2. Damage hull: Deal one Damage card to the
ship based on the type of damage it suffered.
If the ship suffered damage (such as from a
result), place the Damage card facedown next
to the ship’s card. If the ship suffered critical
damage (such as from a result), place the
Damage card faceup next to the ship’s card
(see “Critical Damage” below).
note: If the Damage deck runs out, shuffle the
discard pile to create a new deck.
From page 16 of the rulebook.
Edited by sonova

Do you even know how to play?

Shields cancel Crits first. Every time. Please read the rules.

I believe you're mistaken. Shields absorb hits before crits.

I use howlrunner for my damage boosting. The value of focus is lessened by her presence. ... I value my TIEs being on the table longer where you are leaning more towards taking stuff off the table.

Do you still always take the Evade action once Howlrunner is dead? I ask that because Howlrunner is a priority target for a lot of people so I can't imagine Howlrunner is always around for you.

I use howlrunner for my damage boosting. The value of focus is lessened by her presence. ... I value my TIEs being on the table longer where you are leaning more towards taking stuff off the table.

Do you still always take the Evade action once Howlrunner is dead? I ask that because Howlrunner is a priority target for a lot of people so I can't imagine Howlrunner is always around for you.

Depends on the game state. But evade is usually the go to if there are any arcs on that particular TIE. However if theres only that one arc on multiple TIEs then focus is acceptable for those TIEs.

Is that a change? If not my mind is blown. We've been playing wrong since the beginning.

I need to go home and check my rules now.

If you are correct, my humblest apologies. (I did edit my post for unnecessary rudeness before you responded)

Also theres only 4x 2 damage crits in the deck.

You still have that wrong. There are seven Direct Hit! cards in the 33-card damage deck. There is a 21% chance of drawing a Direct Hit! on a critical hit with a fresh deck.

Sorry, I was off by one.

Is that a change? If not my mind is blown. We've been playing wrong since the beginning.

I need to go home and check my rules now.

If you are correct, my humblest apologies. (I did edit my post for unnecessary rudeness before you responded)

To be fair thats what I thought as well. Until I read the rules myself and found out the filthy space terrorist gypsies were cheating! Which really shouldnt have surprised me!

Edited by sonova

You guys are missing the point with your pedantry. The 'lowly' TIE Fighter is as immune to getting vaporized by any one shot as the Z-95 at range band 2-3. IF you are considering range band 1 shenanigans then the Z-95 is far more vulnerable than the TIE on virtue of having 2 green dice base.

The biggest shake up to the meta which will stem from the Z-95 is not really going to be solely from its cost/durability but also from the fact that it allows the Rebels a low cost missile platform that is also not terrible once it has spent its load. Add munitions fail safe and the options are endless. If all the rebels do is line up 8 Z-95s against 7-8 TIEs they will still lose due to not being able to evade + lack of access to Howlrunner.

Well, our pedantry is correct and we were simply correcting your absolute statement. A TIE with and evade can be one shot with three attack dice. It is true that a Z-95 facing the same result (3 hits, with one of them being a direct hit OR a minor explosion with a "hit" roll, so there are 9 bad cards) is also dead because it doesn't have evade. A TIE without actions is more likely to be one-shot than a Z-95 facing the same number of hits, of course because of its two shields. Two hits that get through are all it takes to kill a TIE w/o evade. A Z-95 requires at least three hits to get through, unless the one hit that does is a proton bomb x2 crit ;)

That said, I agree with you and take evade for exactly the same reasons.

Edited by AlexW

I use howlrunner for my damage boosting. The value of focus is lessened by her presence.

How so? I'd say the opposite: Howlrunner's ability has synergy with focus.

Also, it's worth noting that focus is not only better than evade offensively, it's typically better defensively as well.

Its to do with the mindset that a failure for evasion is punished far more harshly than a failure for missing.

Based on 2 dice math.

Average damage is increased by approximately 0.5 by the focus token

Average damage is increased by approximately 0.34 by Howlrunner

Therefore without the focus the overall loss to average damage is only -0.16 which is an acceptable loss in my mind.

The value of focus increases the more dice you have where the value of Howlrunner is pretty much static, so for something like an interceptor, focus would have greater relative value so its possibly a better choice over evade. However the penalty for failing to evade is also steeper for a squint so that needs to be considered as well.

Edited by sonova

I use howlrunner for my damage boosting. The value of focus is lessened by her presence.

How so? I'd say the opposite: Howlrunner's ability has synergy with focus.

Also, it's worth noting that focus is not only better than evade offensively, it's typically better defensively as well.

I just sent you a PM asking in particular about one shot situations with evade vs focus.

Its to do with the mindset that a failure for evasion is punished far more harshly than a failure for missing.

Based on 2 dice math.

Average damage is increased by approximately 0.5 by the focus token

Average damage is increased by approximately 0.34 by Howlrunner

Therefore without the focus the overall loss to average damage is only -0.16 which is an acceptable loss in my mind.

The value of focus increases the more dice you have where the value of Howlrunner is pretty much static, so for something like an interceptor, focus would have greater relative value so its possibly a better choice over evade. However the penalty for failing to evade is also steeper for a squint so that needs to be considered as well.

Could you explain what you mean about the failure mindset? For me, I feel like the evade does two things that focus doesn't. 1) Make sure I don't get one shotted (or at least highly unlikely) and 2) gives me a chance to avoid more damage than I actually have dice for.

Its to do with the mindset that a failure for evasion is punished far more harshly than a failure for missing.

Based on 2 dice math.

Average damage is increased by approximately 0.5 by the focus token

Average damage is increased by approximately 0.34 by Howlrunner

Therefore without the focus the overall loss to average damage is only -0.16 which is an acceptable loss in my mind.

The value of focus increases the more dice you have where the value of Howlrunner is pretty much static, so for something like an interceptor, focus would have greater relative value so its possibly a better choice over evade. However the penalty for failing to evade is also steeper for a squint so that needs to be considered as well.

Could you explain what you mean about the failure mindset? For me, I feel like the evade does two things that focus doesn't. 1) Make sure I don't get one shotted (or at least highly unlikely) and 2) gives me a chance to avoid more damage than I actually have dice for.

Its to do with the mindset that a failure for evasion is punished far more harshly than a failure for missing.

Based on 2 dice math.

Average damage is increased by approximately 0.5 by the focus token

Average damage is increased by approximately 0.34 by Howlrunner

Therefore without the focus the overall loss to average damage is only -0.16 which is an acceptable loss in my mind.

The value of focus increases the more dice you have where the value of Howlrunner is pretty much static, so for something like an interceptor, focus would have greater relative value so its possibly a better choice over evade. However the penalty for failing to evade is also steeper for a squint so that needs to be considered as well.

Could you explain what you mean about the failure mindset? For me, I feel like the evade does two things that focus doesn't. 1) Make sure I don't get one shotted (or at least highly unlikely) and 2) gives me a chance to avoid more damage than I actually have dice for.

The steep price of failure means the extreme effect of the loss of a ship on a botched evade role. Theoretically a focus token could mitigate more damage over time but it doesnt eliminate the presence and thus the extreme penalty for failure. This is a desirable situation for me because in my mind its harder for a swarm to come back from a points disadvantage where Aminar is of the mind that the time advantage from having a stronger offence is more desirable.

Additionally in an environment where 3 dice ships are the norm, the presence of evade tokens on the table means that they will have to allocate shots inefficiently wasting red dice just to clear those tokens, further 'stretching' the durability of my swarm.

Edited by sonova

Its to do with the mindset that a failure for evasion is punished far more harshly than a failure for missing.

Based on 2 dice math.

Average damage is increased by approximately 0.5 by the focus token

Average damage is increased by approximately 0.34 by Howlrunner

Therefore without the focus the overall loss to average damage is only -0.16 which is an acceptable loss in my mind.

The value of focus increases the more dice you have where the value of Howlrunner is pretty much static, so for something like an interceptor, focus would have greater relative value so its possibly a better choice over evade. However the penalty for failing to evade is also steeper for a squint so that needs to be considered as well.

Could you explain what you mean about the failure mindset? For me, I feel like the evade does two things that focus doesn't. 1) Make sure I don't get one shotted (or at least highly unlikely) and 2) gives me a chance to avoid more damage than I actually have dice for.

The steep price of failure means the extreme effect of the loss of a ship on a botched evade role. Theoretically a focus token could mitigate more damage over time but it doesnt eliminate the presence and thus the extreme penalty for failure. This is a desirable situation for me because in my mind its harder for a swarm to come back from a points disadvantage.

Additionally in an environment where 3 dice ships are the norm, the presence of evade tokens on the table means that they will have to allocate shots inefficiently wasting red dice just to clear those tokens, further 'stretching' the durability of my swarm.

If I evade with everything I still lose a ship in the opening volley but will do less damage. Might be why you worry about a points disadvantage so much.

Its to do with the mindset that a failure for evasion is punished far more harshly than a failure for missing.

Based on 2 dice math.

Average damage is increased by approximately 0.5 by the focus token

Average damage is increased by approximately 0.34 by Howlrunner

Therefore without the focus the overall loss to average damage is only -0.16 which is an acceptable loss in my mind.

The value of focus increases the more dice you have where the value of Howlrunner is pretty much static, so for something like an interceptor, focus would have greater relative value so its possibly a better choice over evade. However the penalty for failing to evade is also steeper for a squint so that needs to be considered as well.

Could you explain what you mean about the failure mindset? For me, I feel like the evade does two things that focus doesn't. 1) Make sure I don't get one shotted (or at least highly unlikely) and 2) gives me a chance to avoid more damage than I actually have dice for.

The steep price of failure means the extreme effect of the loss of a ship on a botched evade role. Theoretically a focus token could mitigate more damage over time but it doesnt eliminate the presence and thus the extreme penalty for failure. This is a desirable situation for me because in my mind its harder for a swarm to come back from a points disadvantage.

Additionally in an environment where 3 dice ships are the norm, the presence of evade tokens on the table means that they will have to allocate shots inefficiently wasting red dice just to clear those tokens, further 'stretching' the durability of my swarm.

I much prefer messing with the threat thresholds of my opponent. If I put a focus on all my academies, offering them optimal offensive power and have Howlrunner as decked out in defense as she can get they're much more likely to try to strip focus tokens than to attack Howlrunner who is the backbone of my fleet. Taking 7 actions to avoid a 1 in 10 chance isn't worth it. If they don't one shot the first tie they'll 2 shot it. Maybe 3. Either way I'll have 12 attack dice with 4-5 focuses and Howlrunner rolls to follow up with(Most likely killing one ship(X-wing) and crippling another, or murdering a B wing and tagging another lightly.

If I evade with everything I still lose a ship in the opening volley but will do less damage. Might be why you worry about a points disadvantage so much.

Yeah I understand where you are coming from. My logic is that faced with a wall of evade tokens my opponent will attempt to strip 1 ship of an evade token and then try to focus it down and I actually dont care if its Howlrunner or not. It should also be noted that I try not to spend evade tokens unless damage is lethal. For example if its 1 normal hit early on in the 'stack' I'd save the evade token for potentially fatal damage later on. This is the important difference between evade and focus defensively. You have 100% control on spending your evade tokens but focus is contingent on your ability to roll eyes.

Mind you this is just an opening gambit. Once the initial joust is over the battle plan transitions into something a lot more flexible. However in a scrum I tend to favor evade on low PS ships because you can never be too sure what will be pointing at your ships.

Edited by sonova

Hobby : a pursuit outside one's regular occupation engaged in especially for relaxation

If doing all the math and crunching gives you that same feeling you are no longer a human, the world has crushed your soul, and and no amount of cool miniatures games will help.

He's onto something! The author of the thread is actually a self-aware artificial intelligence bent on world domination and extermination of the human race, but due to a code bug believes that this can only be achieved through the battle simulator known as "X-wing Miniatures".

Upon attempting to register a squad in a Store Championship, the Tournament Organizers denied access, saying "we don't serve their kind here". The AI has taken to watching the documentary Battlestar Galactica for guidance on how to work around this issue.

See! See! I knew it! Its NOT me! Its THEM!

Thread Necromancy!

I have made some fairly large updates, and wanted to get the predictions "published" before wave 4 is released. The wave 4 rebel ships should be very easy to predict their value for, but the wave 4 Imperial ships... not so much.
Summary for the wave 4 ships:
  • Z-95: It's undeniably an excellent value, and its price point will finally give rebel lists more versatility in filling smaller point gaps. Per point cost, it has more firepower and durability than an X-wing, the mighty B-wing, and even.... a naked TIE Fighter.
  • E-wing: It doesn't look like a very good value, but it should still find its way into some elite 3 ship lists, or Etahn + swarm lists. It's a terrible jouster, so you need some inventive squad builds and flying to make this ship work.
  • TIE Defender: It has a very unique dial, so all mathematical predictions are off. What can be said: its jousting value is just as bad as the TIE Advanced, so this ship needs to repeatedly abuse its white K-turn to be worthwhile. Merely keeping your action isn't enough, you'll need to simultaneously avoid arcs with it as well.
  • TIE Phantom: Mathematical predictions at this point are not very useful, but the jousting value puts a minimum floor on its performance potential. Expect it to be potentially devastating, and meta shifting.
  • A-wing with Refit: Almost as good of an overall value as the Z-95, and its jousting value will be about on par with the B-wing. Lots of people are dreaming about how they can cram tons EPTs onto these ships, but thats not their strength. They're an extremely good jouster with an absurdly good dial, and PS1 blocking. Once Rebels have these highly competitive 12 and 15 point ships, the meta and rebel list building is going to be blown wide open. The diversity of competitive lists and tactics that are going to appear is going to blow your mind.
Major changes are:
  • Scoring the dial coefficients is more regimented than before, and is broken down into various categories.
  • Wave 4 dials have been spoiled, so they are now fully included.
  • The jousting value for each ship now has a range that is meta dependent, rather than returning a singular value.
  • Everything is still relative to a 2/3/3/0 stat line, so ships' jousting efficiency "pivot" around the standard TIE Fighter for any given meta.
  • Critical Hits are now being counted and weighted, and the resulting "value" for shields is now computed mathematically. This resulted in shields being worth around 12% - 15% more than hull, depending on the defender's defense dice and the meta. Previously I had estimated 25%.
  • I'm more explicit about how much confidence the model has for each ship, as I mentioned in an earlier post.
  • Z-95 equivalent PS1 cost has been fixed to be 11.5, not 11.
Updated Limitations
The biggest drawbacks and causes for uncertainty to this approach are estimating the action economy, and in particular estimating how often the defending ship has a focus token. Right now I assume the defender has focus to spend 50% of the time. If this % is actually lower in reality, then it will make lower agility ships relatively more attractive. Conversely, if the % is higher, then it would make higher agility ships relatively more attractive. This issue is largely fixable by getting a large data set, like looking at VASSAL replays and recording the results.

Technical details are in the updated original post, and are quoted in the spoiler tag here.

Combat Effectiveness Coefficients

The combat effectiveness E is a unit's damage output per unit time, multiplied by that unit's durability. To apply this model to X-wing, I have broken this down into the following categories:

  1. Attack
  2. Durability
  3. Dial
  4. Actions
  5. Firing arc
  6. Upgrades

Each of these categories is nominally 1, and then they are all multiplied together.

Since we are using the PS1 TIE Fighter as our baseline, it has a value of 1 in each category.

Attack: 2 attack dice vs. 3 attack dice vs. 4 attack dice

In order to calculate the average damage that 3 or 4 attack dice does relative to 2 dice, the following assumptions were used:

  • attacker has focus 2/3 the time
  • defender has focus 1/2 the time
  • range bins probabilities are [15 23 9 4]/(15+23+9+4) for [R1 R2 R3 R3+asteroid]
  • defender base defense dice is meta dependent, see below

Since we are looking to get an overall aggregate score, I'll treat each of these categories as independent, assign the weighted probability to each, and then calculate the aggregate totals. The base number of defense dice was evaluated in three different "meta" environments [1 dice%, 2 dice%, 3 dice%]:

  • low defense dice meta: [45%, 25%, 30%]
  • "standard" defense dice meta: [30%, 25%, 45%]
  • high defense dice meta: [15%, 25%, 60%]

For a reference on what's currently popular in high level play, see this thread:

http://community.fantasyflightgames.com/index.php?/topic/105107-2014-regionals-results/

Another note while we are here: you don't always need to spend your focus for attack or for defense, so adding up the probability of having focus available for both can certainly be more than 100%. Since we only care about the overall statistical averages, and not conditional probabilities in a specific scenario, we can treat these as independent variables. That being said, please speak up if you have a better method of estimating how often the defender has focus available, since it does affect the result.

I used the ranges at the Worlds 2013 Finals game as a baseline: 15 @ range 1, 23 @ range 2, 9 @ range 3, and 4 @ range 3 through a rock.

This results in the following damage numbers, normalized to 2 attack dice:

defense meta

low defense normal defense high defense

1 dice: 0.4319 0.4189 0.4022

2 dice: 1 1 1

3 dice: 1.7137 1.7590 1.817

4 dice: 2.5129 2.6297 2.779

Also for reference:

2 dice + 1 reroll: 1.3436 1.355 1.3695

3 dice + 1 reroll: 2.2288 2.3125 2.4196

HLC: 2.3935 2.4923 2.6185
Blaster w/ 1 base: 0.2765 0.2670 0.2549
Ion turret w/ 1 base: 0.7407 0.7698 0.8070
Ion turret w/ 2 base: 0.8123 0.8247 0.8406

Durability

In order to calculate the average durability that 1 or 2 base defense dice have relative to 3 dice, the following assumptions were used:

  • attacker action economy:
    • No action: 35%
    • Focus: 30%
    • Target Lock: 25%
    • Focus + Target Lock: 10%
  • defender has focus 1/2 the time
  • range bins probabilities are [15 23 9 4]/(15+23+9+4) for [R1 R2 R3 R3+asteroid]
  • attacker base dice number is meta dependent, see below
  • critical hit values specially weighted, see below.

I do not directly account for a percentage of shots that are affected by Howlrunner. However I wanted to capture some of Howlrunner's reroll ability in how it changes the hit / critical hit ratio, so I shifted some of the focus actions into Target Lock actions. I realize that normally, Target Lock will be taken far less often than focus. I also included some small percentage of shots as having both TL + F to simulate the occasional Rebel PtL, and estimating Howlrunner's reroll affect.

The base number of attack dice was evaluated in three different "meta" environments. I used 5% as a baseline for 4 attack dice once wave 4 comes out, and assume the Phantom will see slightly below average table time. [2 dice%, 3 dice%, 4% dice]:

  • low attack dice meta: [67%, 32%, 1%]
  • "standard" attack dice meta: [33%, 62%, 5%]
  • high attack dice meta: [20%, 70%, 10%]

Critical hits are weighted specially. The are 7 Direct Hit cards, and 2 Minor Explosion cards can be directly computed. The remaining critical hits are treated as being worth an additional 1/3 of a regular hit. None of those other cards do direct damage in the strictest sense, but some of the effects can be very nasty, so I had to put some value on them. That makes the critical hit weighting:

Crit Weighting = 1 + 7/33 + (3/8)*2/33 + (1/3)*(33-7-2)/33 = 1.4773

The damage is then calculated two ways: once with critical hits weighted as above to simulate Hull durability, and again with critical hits weighted as 1 to simulate Shield durability. The results normalized to Hull Durability for 3 defense dice are:

Hull Durability Shield Durability

low attack normal attack high attack low attack normal attack high attack

1 dice: 0.5113 0.5490 0.5647 0.5737 0.6161 0.6336

2 dice: 0.7071 0.7312 0.7411 0.8030 0.8313 0.8427

3 dice: 1 1 1 1.1458 1.1482 1.1490

4 dice: 1.4268 1.3876 1.3717 1.6458 1.6053 1.5886

These results indicate that Shields are worth about 12% to 15% more than Hull, which was far below my earlier estimate of 25%. The meta dependent durability coefficient is therefore:

( Shields*shield_coeffcient + Hull*hull_coefficient ) / 3

Dial

The dial has been broken down into various categories and each category has been given a value. The total dial coefficient is 1 + all the category scores, which are:

Tightest white turn

0: 1 turn

-0.03: red 1 turn

-0.03: large base ship white 1 turn

-0.04: white 2 turn

-0.05: red 1 turn, red 2 turn, white 3 turn

-0.06: red 2 turn, white 3 turn

-0.06: Large ship base white 2 turn

-0.2: large base 3 red turn

slowest straight (-1 for large ship)

+0.025: 1 forward

0: 2 forward

fastest straight (+1 for large ship)

-0.025: 3 straight, red 4 straight

-0.01: 4 straight

0: 5 straight

K-turns

-0.3: no K-turn

-0.02: 1 red K-turn

0: 2 red K-turns

+0.3: 1 white K-turn

stress clear

-0.06: green on 2 straights

-0.05: green on 4 straights

0: green on 2 straights, 1 bank

+0.01: green on 3 straights, 1 bank

+0.05: green on 3 straights, 1 bank, 1 turn

+0.055: green on 4 straights, 1 bank, 1 turn

specialty

0: none

+0.05: red 0

Actions

For actions, I sum together all the values listed as deltas relative to a TIE Fighter: positive points if the ship has the action but the TIE doesn't, and negative points if the ship does not have the action but the TIE does. The reason I add all these actions together first, rather than multiplying them together, is because there are diminishing returns on having many actions on your bar, since you can only perform one per round. This obviously excludes Push the Limit, which I am not analyzing.

I started by estimating how much additional damage Target Lock yields, since this is the only action that can be easily quantifiable in terms of dice rolls. I modified the damage calculator so that instead of the attacker having no action 1/3 the time, and a focus 2/3 the time, the attacker has no action 1/3 the time, focus 5/9 the time, and focus+target lock 1/9 the time. The damage increase, for both 2 and 3 attack ships, is right around 5%. So I gave Target Lock a value of 0.05, and based everything off of that.

Target Lock 0.05

Evade 0.015

Barrel Roll 0.035

Boost = (attack/durabilty)/50

Cloak 0.15

I weighted boost as more useful for glass cannons than tanks, since glass cannons need to use boost to remain out of arc. I only used the "normal" attack/durability meta to calculate the boost coefficients.

So, for example, an X-wing is lacking Evade and Barrel Roll (-0.015 -0.035), but gains Target Lock (+0.5), so its net action value is 1. These values can certainly be fine-tuned, but they are an approximate starting point. Cloak is obviously a complete guess at this point, I'm just guessing that it will be very good. If we ever see (or dream up) a ship that has no focus, then we would need a weight for that as well, but so far all small and large base ships have focus. Again, these coefficients are certainly up for debate. I would love to hear people's thoughts.

Firing Arc

This only affects large base ships that have an innate primary firing arc that is not simply forward facing. Firing arcs help both offensively (closer shots, and more of them), and defensively (getting out of arcs while still being able to fire). I used the following coefficients:

normal arc: 1

360 degree arc: 1.75 (YT-1300)

forward + rear arc: 1.25 (Firespray)

It's obviously difficult to exactly quantify these numbers, with these firing arcs being unique to these ships.

Upgrades

All of the upgrade values are multiplied together, including having multiple crew, which currently only affects the YT-1300 (i.e. 2 crew is worth 1.075^2 not 2*1.075).

Turret: 1 attack ship 1.97 (Turret on 2 attack ship * Ion1 / 1 attack)

Turret: 2 attack ship 1.1

Cannon: 3 attack ship 1.01

System Upgrade 1.05

Crew 1.075

Droid 1.05

Ordnance

value description

1 No ordnance

1.01 1 missile / torpedo with 3 base attack

1.02 1 missile / torpedo with 2 base attack

1.03 1 missile + 1 bomb with 3 base attack

1.04 full loadout with 2 base attack

Cannons are very expensive, just like missiles and torpedoes, so I consider the cannon slot to be basically self-balancing, and only give it a coefficient of 1.01. I was curious about the HLC, so I calculated the net increase in a ship's effectiveness is (2.4506/1.7401)^(1/1.92) = 1.195. That's pretty good, but the problem is that it costs a whopping 7 points, so your ship would have to cost 7/(1.195-1) = 35.8 points at PS1 to break even! When you factor in the increased durability from being able to stay at long range then it helps justify the cost, but in general I still think the high point cost of the cannons themselves make them self-balancing.

  • Edit: March 2, 2014: Updated Worlds 2013 meta with the 16th squad.
  • Edit: March 20, 2014: Updated to include A-wing Chardaan Refit.
  • Edit: March 22, 2014: Updated to include TIE Fighter with Howlrunner reroll, HWK-290 with blaster turret instead of Ion1 + Chewie, and permanently cloaked TIE Phantom.
  • Edit: April 14, 2014: Added the Limitations section.
  • Edit: June 6: several changes:
    • Added meta dependent attack and durability coefficients
    • critical hits explicitly being calculated now to better value shield value
    • maneuver dial broken down into major categories
    • results and ship breakdowns moved into the next post

Numerical Results

All costs and efficiency are based on their equivalent PS1 cost:

X-wing: 20

Y-wing: 17

A-wing: 17

A-wing + refit: 15

ORS: 27

Named YT-1300: 37

B-wing: 21

HWK-290: 15

Z-95: 11.5

E-wing: 27

TIE Fighter: 12

TIE Advanced: 20

TIE Interceptor: 18

Firespray: 31

TIE Bomber: 15

Lambda Shuttle: 20

TIE Defender: 30

TIE Phantom: 23

TIE Phantom + permanent cloaking: 27 (Advanced Cloaking Device, PS bid not included)

min, std. and max columns are to cover various meta environments, which changes the ship's underlying jousting value. TIE Fighters are used as the 100% reference point for all meta.

Degrees of certainty refer to results in the "Total Efficiency" columns. The Jousting columns are all very high certainty.

Very High Degree of Certainty

Jousting Efficiency Total Efficiency

Ship min std. max min std max

TIE Fighter 100.0% 100.0% 100.0% 100.0% 100.0% 100.0%
TIE Fighter + Howl 116.6% 117.1% 117.8% 116.6% 117.1% 117.8%
TIE Advanced 80.6% 80.7% 80.7% 80.9% 81.0% 81.0%
TIE Interceptor 88.3% 89.5% 91.0% 94.5% 95.8% 97.4%
TIE Interceptor + Howl 101.2% 103.2% 105.6% 106.3% 108.3% 110.9%
X-wing 88.9% 91.8% 94.0% 94.1% 97.1% 99.4%
A-wing 85.1% 85.1% 85.1% 89.5% 89.5% 89.5%
B-wing 92.4% 97.2% 100.3% 100.0% 105.2% 108.5%
E-wing 80.2% 81.4% 82.8% 89.2% 90.5% 92.1%
Z-95 104.7% 106.6% 107.3% 108.5% 110.5% 111.2%
A-wing + Refit 96.4% 96.5% 96.5% 98.8% 98.9% 98.9%

High Degree of Certainty

TIE Bomber: requires ordnance to fill a useful role.

Jousting Efficiency Total Efficiency

Ship min std. max min std max

TIE Bomber 95.8% 97.5% 98.2% 96.2% 97.9% 98.6%

Medium Degree of Certainty

Y-wing: turret on a 2 attack ship.

YT-1300: 360 degree primary weapon

Firespray: rear arc

Jousting Efficiency Total Efficiency

Ship min std. max min std max

Y-wing 84.9% 88.1% 89.4% 86.5% 89.8% 91.1%
ORS 60.1% 62.4% 63.3% 82.0% 85.1% 86.3%
Named YT-1300 66.5% 70.0% 72.3% 90.7% 95.4% 98.5%
Firespray 82.3% 84.9% 87.0% 95.2% 98.2% 100.6%

Low Degree of Certainty

HWK-290: turret on a 1 attack ship.

Lambda: No K-turns and no white turns

TIE Defender: white K-turn

TIE Phantom: cloak action

Jousting Efficiency Total Efficiency

Ship min std. max min std max

HWK-290 55.0% 57.2% 58.5% 38.2% 39.7% 40.7%
Lambda 108.1% 113.8% 117.4% 83.6% 87.9% 90.7%
TIE Defender 78.8% 79.9% 81.3% 88.8% 90.0% 91.6%
TIE Phantom 84.6% 88.2% 91.4% 96.4% 100.5% 104.2%
TIE Phantom + cloak 102.3% 105.4% 110.0% 116.6% 120.1% 125.3%
Edited by MajorJuggler

Are you looking at the Cloaking with or without the mods. Because the Stygium Particle Accelerator and Advanced Cloaking Device really changes the game with cloaking.

Are you looking at the Cloaking with or without the mods. Because the Stygium Particle Accelerator and Advanced Cloaking Device really changes the game with cloaking.

He doesn't appear to be using the Particle Generator, but is using the Cloaking Device at peak efficiency.

Are you looking at the Cloaking with or without the mods. Because the Stygium Particle Accelerator and Advanced Cloaking Device really changes the game with cloaking.

Are you looking at the Cloaking with or without the mods. Because the Stygium Particle Accelerator and Advanced Cloaking Device really changes the game with cloaking.

He doesn't appear to be using the Particle Generator, but is using the Cloaking Device at peak efficiency.

Aminar is right, I'm looking at a naked (PS1 equivalent cost) Phantom, and then a PS1 equivalent Phantom with Advanced Cloaking Device that gives it an effective stat line of 4/4/2/2. That obviously doesn't take into account the PS Bid that you will need to make Advanced Cloaking Device worthwhile. Only the jousting numbers are meaningful, since we have no idea how effective the cloaking action will be, although early indications are "very". The Phantom is in the "low certainty" bin for a reason. :)

FYI, I uploaded the new version of the Excel document, and updated the link in the OP, so anyone can download it. This does not include the Matlab scripts that were used to generate the meta-dependent normalized damage numbers and durability. If I can figure out an easy way to implement that in Excel later then I'll wrap that in as well.

https://drive.google.com/file/d/0B4i-dE5epNFzeloyRGVjSlVFNlk/edit?usp=sharing

Edited by MajorJuggler

LSL seems like a nice law but I would suggest something along the lines of this:

1 unit have power 1

2 units have power 3

3 units have power 6

4 units have power 10

This takes into account 100% successful focused fire.

If you have three times the staying power compared to one enemy and the same damage output, you will have an even chance against two such enemies. It takes one time unit to kill the first, and another time unit to kill the second. Meanwhile you will have recieved two time units worth of damage during the first exchange and one time unit during the second exchange. So you dealt two time units of damage and recieved three in total.

If you add one enemy you will take 3+2+1 units worth of damage over three time units before you kill your opponents and therefore needs to have six times the staying power or lets say double the fire power and three times the staying power do deal with them.

In X-wing this means that a ship that cost half as much as another might do a decent job in a fight 2 against 1, but will do a great job 4 against 2 or 6 against 3. The real power comparisons would be

2 ships vs 1 ship, 3 power vs 1 power (3 : 1)

4 ships vs 2 ship, 10 power vs 3 power (3.3 : 1)

6 ships vs 3 ships, 21 power vs 6 power (3.5 : 1)

My simulator also confirms this to some degree.

SO are the costly ships in X-wing based on LSL with 1,4,9,16 progression, this suggestion 1,3,6,10 progression or straight up 1,2,3,4 progression?

MJ you said that the cost scaling was off on the larger ships, could this be the reason? I must admit I haven't had the time to go through all the info in your math threads, but this was my first reflection. :-)

In principle you have the right idea, but remember that you have a 100 point cap. So your example here of one ship having 3x the durability of two otherwise identical ships, translated to a 100 point limit, would be comparing a 100 point ship to 2 50 point ships. But we don't have a 50 point ship, let alone a 100 point one.

If you were to decrease the point cost to 12 and 24 so it was 8v4, then you would need more than 3x the durability to break even. The discontinuities in the curve become less, and it becomes closer to the continous time solution which results in the square root ratio.

I will analytically solve for this later, but for now the empirical calculations and corrected curved I use are pretty good until the ship value gets up well past 30 points.