(boiler plate stuff, background in the "spoiler" tab below)

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%