The generic X-wings are overcosted by about 2 points, and most of the named pilots also appear to be overcosted. This generally agrees with tournament results. Biggs is the exception, and his ability is almost impossible to mathematically model, but he clearly has a disruptive ability that is one of the best in the game.

Decreasing the cost of the Rookie Pilot to 20 or 19 would allow 5 of them in a list, which is almost certainly why they were initially priced at 21 points during wave 1. However, now that alternatives (B-wing, Z-95) are available, generic X-wings see almost no competitive use.

Most of the named X-wing pilots also appear to be overcosted, which is generally confirmed by tournament results.

Y-wings simply need the turret slot filled to be competitive: their naked jousting efficiency is extremely low, and ordnance is still ineffective for its cost.

The total cost prediction on all of the Y-wings is uncertain due to the turret slot on a 2 attack ship, which is a unique feature. This analysis assumes that the value of placing an Ion Token on a target is an additional 2 points. It is clear, however, that the BTL-A4 modification will make the Ion Cannon turret more cost effective even though it locks the turret to the forward arc. The PS2 "Warthog" Y-wing (Gold+Ion+BTL-A4) at 23 points only has a required efficiency of 127% - 143% (depending on assumptions), which it can easily achieve in a proper control list.

The PS4 Grey Squadron Pilot falls into the "PS4 trap" where +1 cost over the PS2 would have been too little, but +2 cost is too much, so the pilot virtually never sees use.

The A-wings have needed a 2 point cost reduction to be competitive since they were released in wave 2, and they now have that option with the Chaardan Refit. It is assumed that all pilots will take the A-wing Test Pilot if they are able. For calculating the PS1 equivalent cost, the 2nd EPT (when applicable) is counted as 0.5 PS, not the full 1.0 from the first EPT slot, to reflect diminishing returns.

The 15 point Prototype A-wings with Refit have the distinction of being a reasonably cost effective tank / blocker, while also having the boost action.

Even with Refit, Gemmer and Arvel are both overcosted by about a point, and Arvel also needs a base EPT slot and/or a change to his named ability to provide a compelling reason to take him.

Jake's ability to gain a free barrel roll has been valued at 2 points for this analysis, as gaining a free action is normally 3 points, but in this case the action type is restricted. He appears to be the only named pilot that is priced competitively.

Tycho's ability has only been valued at 1, because the ability to perform actions while stressed is less useful when already flying the ship with the most green moves in the game. His cost with Refit appears to be overcosted by 2.

The named YT-1300 pilots are all quite good. The pricing structure of 1 PS = 1 point makes 46 point Han Solo a relative bargain if you are willing to bid up to PS9. On the other extreme, the Outer Rim Smuggler is unfortunately dramatically overcosted.

Note that this math does not consider the non-linear effects of fixed damage reduction per turn, such as the Millennium Falcon Title, C-3P0, or R2-D2 crew. This increases the ship value even further, and partly explains why Fat Falcons dominated the wave 4 meta.

Generic B-wings have essentially replaced the generic X-wings in competitive tournament play. Now B-wing usage is gradually decreasing in favor of the slightly more cost effective Z-95's. The math here indicates that the generic B-wings are probably overcosted by 1 point, but since this only represents 5% of their cost, they are still a viable ship in competitive play.

This analysis assumes that the named B-wing pilot abilities are all quite weak, with the exception of Keyan Farlander. Ten Numb is of course the most overcosted pilot of the bunch. Nera Dantels' ability would be worth more in an alternate universe where ordnance is cost effective.

All of the HWK-290 pilots are nearly impossible to mathematically predict their cost for, because of the native 1 attack, and the difficulty in valuing placing an Ion Token on the enemy target. Roark and Jan appear to be the least overcosted pilots in the entire group.

The generic Z-95 has predictably become the backbone filler ship for Rebel squads, fundamentally and irreversibly changing Rebel squad building.This ship has had at least as much of an impact on the meta as the TIE Phantom, as the cost efficiency of Z-95's have enabled Fat Han lists, which would not have been fully possible with wave 3 ships.

Blount is almost certainly overcosted by a point, as I consider his ability to be worth very little. Crakcen has good cost effectiveness, provided you can keep him alive long enough for his ability to trigger and you can maintain formation around him.

The generic E-wing pilots have an extremely low jousting efficiency that cannot be overcome by their dial and upgrade bar, as indicated by the very high required efficiency numbers for the generic pilots. A fair cost for these ships would be 24 and 26 points at PS1 and PS3.

Etahn needs a point or two shaven off his cost to be more effective in 100 point play, but he can be an effective force multiplier in 300 point epic games.

Corran Horn is the most cost effective E-wing pilot even before considering the synergy that Fire-Control System and R2-D2 provide with his ability. It should not be surprising that he is virtually the only E-wing pilot that sees consistent successful tournament use.

The predicted cost for the YT-2400 is fundamentally uncertain, as a cannon slot on a 2 attack ship with a 360 degree primary arc is a unique feature.

The YT-2400 discussion obviously revolves around the Outrider Title and the Heavy Laser Cannon, which dramatically increases its damage output, with the tradeoff of not being able to fire at range 1. This range 1 "doughnut hole" was not considered for this analysis, so therefore the jousting efficiency and total predicted value for the Outrider + HLC combination is intentionally an optimistic estimate.

The key number in this section is the required efficiency of 205% for 58 Dash. This is easily achievable with 3 actions per round, including the possibility of Boost and Barrel Roll on a large base ship to arc dodge, and the ability to maneuver over obstacles with no ill effect. However if the enemy can get within range 1 of Dash, he can still get burned up very quickly.

The basic TIE Fighter has been the benchmark ship for singe ship cost efficiency since the beginning of the game. The math here agrees with reality that all of the PS6+ named TIE Pilots are very good. It is difficult to place an exact value on Howlrunner's ability, so a better approach is to view the increased efficiency that she provides to ships near her. The PS1 Academy TIE becomes 117% efficient when buffed by her. The 7-TIE Swarm is clearly one of the main central "pillars" in the game, as it is one of the most efficient squads in the game at simply throwing dice at the opponent.

The stock TIE Advanced is clearly overcosted by a wide margin. Vader is easily the best pilot of the group, as he has one of the best abilities in the game.

Analyzing the TIE Advanced Fix requires several different approaches to get a complete picture, since there are several different options.

Analysis #1: Free FCS

The first approach is to give the TIE Advanced a free Fire-Control System. Without an overall point cost reduction, it is still not an effective ship, particularly for the generics.

Analysis #2: Free Accuracy Corrector

The second approach is to give the TIE Advanced a free Accuracy Corrector. This dramatically increases the ship's damage output, while simultaneously allowing its action economy to be used for defense. To simulate the added durability, ships with the "HiD" flag have their durability calculated as if they have focus available to spend on defense 2/3 the time instead of 1/2 the time. This increases the TIE Advanced's durability by about 10%. With a free Accuracy Corrector, the generics have a jousting efficiency right around 100%. Maarek Steele's ability here is valued at zero points because he never gets critical hits. Vader is still obviously the best overall value, simply by valuing his ability at 3 points.

Analysis #3: Advanced Targeting Computer for 1 point, assuming 50% proc rate

A third approach is to give all the ships the Advanced Targeting Computer (ATC) for +1 point. Because the Target Lock is not spent during use, this makes it difficult to exactly calculate, since its effectiveness will largely depend on the tactical situation. The first analysis of ATC will assume that the ship has a 50% chance of having a Target Lock on the target, in addition to its normal 67% chance of having a focus available for attack. I may refine this approach later, but for now it should provide a reasonable estimation of how these ships should perform. With this upgrade, I have increased Maarek Steele's pilot ability to be valued at 2 points, contrasted with being valued at 0.5 points stock, because he will very frequently be getting a critical hit through his opponent. I have excluded Vader from this analysis, because I assume that he will always have a Target Lock on his target, since he is PS9 and gets 2 actions.

Analysis #4: Advanced Targeting Computer for 1 point, assuming 100% proc rate

The final approach is to give each ship ATC for one point, and assume that it kicks in for every shot. This is in addition to the 67% chance for having focus on offense, and so represents how effective a ship is after it gets the Target Lock queued up from a previous round, such as when firing on a high hit point ship. Vader is analyzed here assuming that he will always have target lock and focus available to use on attack. This is slightly different than the "stock" version of Vader, where I analyze his ability by giving him a free TL and then keeping the same focus action economy. However, the ATC TL is not spent during the attack, so Vader will not always need to spend his 2 actions on both TL and focus. Instead, he will sometimes be able to spend his 2nd action on evade instead. To simulate the potential for his added durability, I calculated his value twice: once with standard durability and once with "HiD" durability. Vader's resulting PS1 jousting value is between 24.5 - 25.8 points, which is an exceptional value for a 30 point PS9 pilot with an EPT slot, and corresponds to a PS1 equivalent jousting efficiency of 112% - 118%.

TIE Advanced Fix Summary

Generic Pilots

The generic pilots will be viable with a free Accuracy Corrector, which is almost the identical analysis as performed in this thread . Generic pilots can also work with the Advanced Targeting Computer, but if they can't get the Target Lock queue going they will be better off taking Accuracy Corrector.

Named Pilots (not Vader)

The named pilots will generally be better off with ATC. I believe the best way to evaluate Alozen and Steele with ATC is to use the 50% proc assumption, although if you can manage to get ATC to proc 100% of the time while still having focus available to spend on offense, then you will be doing significantly more damage. Predator is a reasonable upgrade in conjunction with ATC, but since you are only rolling 2 dice most of the time, it is not auto-include.

The Dark Lord Rises

Vader is still by far the best TIE Advanced pilot. Regardless of what fix FFG chose, this was nearly a mathematical certainty unless they simultaneously implemented a universal or generic-specific cost reduction. Vader is extremely good with a free Accuracy Corrector, but Advanced Targeting Computer is so good on him that it is nearly auto-include. Vader + ATC now has one of the highest PS1 equivalent jousting efficiency in the game. Conversly, his required efficiency is only somewhere between 131% - 144%, which should be attainable simply by shooting last at PS9. Almost any other pilot with an efficiency this high has a significant weakness that can be exploited, such as ACD Phantoms that are vulnerable to stress and higher pilot skill. Vader's only weakness is getting blocked during the activation phase to lose his two actions, which is not something that you can simply counter by list building. With this fix, Vader will undoubtedly become a prominent piece in many Imperial lists, and should see consistent and competitive high level tournament play. If anything, this fix could potentially make Vader too powerful, as many Imperial players will now be looking at ways to always incorporate Vader into their list.

The low PS TIE Interceptor was one of the initial motivations for developing the "jousting value" metric, as I wanted a mathematical reason for predicting how well the ship would do. The answer now is the same as the answer then: the low PS TIE Interceptors are paying too much for the boost action. Other than a brief burst in wave 3 which revolved around formation flying with either Swarm Tactics or Stealth Device, low PS TIE Interceptors have almost never seen competitive use. The required efficiency of 122% is simply too large to overcome with a boost action at PS1. Being a glass cannon in a game where target selection is typically dictated by the attacker is also a significant liability.

The PS6 Royal Guard is a good value, but requires the wave 6 AutoThrusters card to offset its weakness to turrets. Soontir Fel, Carnor Jax, and Turr Phennir are all a good value, with Fel obviously being the best in a PS9+ environment, and all three should see more use with AutoThrusters.

The PS3 TIE Interceptor falls into the "PS3 trap" where +1 cost over the PS1 would have been too little, but +2 cost is too much, so the pilot virtually never sees use.

The Firespray's rear arc makes an exact cost prediction difficult, but the values should be within 2 points of reality. I personally believe that the generic Bounty Hunter should cost 31 points. The rear arc is nice, but not good enough to enable the ship to meet its required efficiency of 163%. I find the abilities of the named pilots lacking for their cost. Krassis' ability is nice, but effectively negates the usefulness of having a rear arc. Kath's ability is not reliable unless you spend more points on a sub-par EPT like Marksmanship. Boba's ability is marginal at best, but he is actually the best value of the group if you want a PS8+ pilot.

The TIE Bomber is a viable platform for carrying every kind of ordnance, but unfortunately ordnance is not cost effective. This makes mathematically pricing them almost impossible, as they fundamentally do not have a useful role. The FAQ update for Proximity Mines was a helpful change, but Proton Torpedoes and Concussion Missiles need to do more damage for their cost to make Bombers viable.

The PS4 TIE Bomber falls into the "PS4 trap" where +1 cost over the PS2 would have been too little, but +2 cost is too much, so the pilot virtually never sees use.

If Ordnance was actually useful, then a +1 point cost above the predicted costs here would be completely fair. Even if ordnance were viable, Captain Jonus would still be overcosted by about 1 point, and Major Rhymer by about 4 points.

The Lambda Shuttle has the best jousting efficiency of any generic pilot in the game, but its lack of a K-turn or a even a white turn makes total cost prediction difficult. I would also argue that due to the Shuttle's lack of maneuverability, it gets less of a benefit from bidding to higher PS than any of the other ships in the game. This is not reflected in the predicted point value for the PS6 and PS8 pilots, so I believe that Kagi needs an EPT and/or 1 point cost reduction to be competitively viable, and Jendon needs a 1 point reduction along with a slight boost to his ability.

It is difficult to precisely value the TIE Defender's white K-turn, but the required efficiency provides some insight into the ship's total value. With a jousting efficiency of 76.6%, the Delta Squadron Pilot needs to do 61% more damage than its statline provides. The white K-turn does contribute to the game's highest dial coefficient of 1.23, but this is not nearly sufficient enough to do the required damage, and to overcome a jousting efficiency that is on par with the named YT-1300 pilots. The generic pilots are overcosted by at least 2 points, and possibly as much as 3 as these numbers indicate.

Not included in this analysis is weighting the value of the white K-turn inversely proportional to pilot skill. The PS1 Delta Squadron Pilot sees the biggest gain from the white K-turn, since the other pilots can be blocked.

It should be noted that Vessery can do reasonably well if you build a squad around him so his ability triggers on every shot.

The TIE Phantoms have been evaluated two ways. The first analysis is without Advanced Cloaking Device. This approach uses a fairly low coefficient for the cloak action, since it is only marginally useful without Advanced Cloaking Device. In this context, all of the TIE Phantom pilots appear to be slightly overcosted. Note that Echo's ability has been valued higher with ACD. This does not necessarily conclude that Echo and Whisper are overcosted, because this first analysis ignores ACD. However, a strong argument can be made that because the generics cannot reliably take ACD due to their lower pilot skill, they are both overcosted by one point. This generally agrees with tournament results to date, although a few generic Phantoms did make a brief appearance in the Worlds 2014 Top 32. The Phantom is inherently paying the privilege for having the System Upgrade and Crew slot, regardless if it is filled or not, so its jousting efficiency is expected to be fairly low. Even if the PS3 cost was reduced to 24, its jousting efficiency would still only be 89.6%.

Analyzing the pilot again with ACD is done by adding the cost of ACD (and VI for the named pilots), and assuming that they now have a statline of 4/4/2/2. The resulting jousting values are extremely good, over 100% in all cases. Since this is purely a jousting measurement, this still does not even consider the free decloak maneuver that is performed each round. These numbers clearly quantify why the Phantom + support has become a central pillar in the meta. The most effective way to counter an ACD Phantom is to simply shoot before it, so that it is reduced to a 4/2/2/2 statline.

The VT-49 is a fairly straightforward ship to analyze using the same metrics as the YT-1300. The PS3 Patrol leader appears to be overcosted by quite a few points compared to the named pilots, due to the 1 point = 1 PS cost structure that does not translate well to expensive ships. On the other end, t he abilities for both Kenkirk and Chiraneau can be directly analyzed numerically, and they both appear to be a good value. The VT-49 has three crew slots, which should open up more options in the future as more crew are available. At present, the YT-1300 has access to 3 mechanisms of damage reduction (C-3P0, Millennium Falcon title, and R2-D2 crew), whereas the Imperials only have access to Ysanne Isard, so a "Fat Decimator" dynamic will certainly play differently than a "Fat Falcon" .

Expose has finally found a use on Chiraneau along with Experimental Interface, although this analysis ignores the resulting movement penalty from needing to clear stress.

Another fantastic option is Isard + PtL + Engine Upgrade, which allows a damaged named VT-49 to perform a boost action during the combat phase.

The combinations for different viable crew permutations should only increase with time. With 3 crew slots, and EPTs on all the named pilots, the named Decimators, particularly Kenkirk and Chiraneau, should become a consistent Imperial workhorse.

The Scum Z-95s are all very good. The generics are nearly identical to the Rebel Z-95's, losing one PS in exchange for the illicit upgrade.

Leeachos' ability is underwhelming, but his real value lies in getting access to an EPT slot for only 15 points, making him nearly the Scum equivalent of the Black Squadron Pilot.

Suhlak is easily one of the most cost efficient pilots in the game through wave 6. If you can get his ability to trigger every turn, then he has a mind-boggling efficiency of 122%. Lone Wolf is a natural choice for his EPT, which increases his value even further.

As with the Rebel Y-wings, the total cost prediction is uncertain due to the turret slot on a 2 attack ship, which is a unique feature. This analysis assumes that the value of placing an Ion Token on a target is worth an additional 2 points.

Kavil's ability to gain an extra attack die while firing at targets outside of his arc works well with the Blaster Turret and the R4 Agromech, which gives him a Target Lock after spending his focus to activate the Blaster Turret.

The BTL-A4 Y-wing variant has the same exact values as the Rebel version, given that the Agromech slot is valued here the same as the Astromech slot.

Precisely valuing the HWK-290 pilots is difficult as in the case of the Rebel HWKs, but the named pilots clearly provide the best value.

I'm not sure if the PS1 Scum HWK-290 pilot has been spoiled yet, but I assume it will be 16 points. He probably won't see much use.

I see Torkil Mux's primary use as insurance against ACD TIE Phantoms.

Palob + Blaster Turret provides an exceptional value if he can successfully steal an enemy focus token to spend on activating his blaster turret or modifying its attack rolls. He is the first pilot in the game to have a jousting value near 100% while firing in a 360 degree arc. I fully expect him to be one of the more popular Scum pilots; the only difficulty will be in keeping him alive. When equipped with a blaster turret, he is a glass cannon on the same order as a stock X-wing, as both have 3 attack and almost identical durability.

Palob's opponent will not have any focus or evade tokens because he just stole them for himself, so Opportunist is a perfect upgrade. It essentially gives him 4 attack dice in a 360 degree arc, and this results in almost the exact same jousting efficiency. Finally, the K4 security droid crew can be added, providing him with a free Target Lock each round after performing a green maneuver. This will allow him to fire 4 dice with Target Lock and Focus most rounds, resulting in an jousting efficiency of 108.5%, which is absurdly high for having a turret. The tradeoff is he is an extreme glass cannon at a ratio of 3:1 (vs 1.45:1 with just a blaster turret). In this case it may be worth taking the Moldy Crow title for another 3 points so he can pre-charge focus tokens, and have more tokens available for defense in combat.

Dace Bonearm is fairly straightforward to analyze: equip him with an Ion Cannon Turret, and exactly double his expected damage. This results in a jousting value that is extremely respectable for having a turret, although not as high as Palob's.

Like the Imperial Firesprays, getting an exact predicted value is difficult because of the uncertainty of the rear arc coefficient until we get another ship that also has a rear arc. However, the cost predictions for the PS5 pilot and Emon should be accurate within about a point. Since the printed costs are almost exactly at the predicted costs, both of these pilots appear to be competitive.

Scum Kath Scarlet and Boba Fett however take things to an entirely different level.

For predicting Kath's value I assumed that half of her shots with be out of her rear arc, so her damage will be halfway between 3 attack dice and 4 attack dice, which results in an increase of roughly 23 percent. This was sufficient to increase her jousting efficiency up 96%, which is absolutely fantastic. Note that her required efficiency is still 170%, as she is paying a significant amount of points on the PS bid.

For predicting Boba Fett's ability, I assumed that he will always have 1 enemy at range 1, so he will always reroll 1 die on both offense and defense. In reality this number could be lower or higher, but it is a reasonable starting point. This causes Boba's attack to increase by 30%, and his defense to increase by 25%, resulting in a brute force jousting value of 33 points. Since his PS1 equivalent cost is only 29.3, this means that his jousting efficiency is well above 100%, and with an absolute cost of 39, his required efficiency is still only 134%. Using the same combat coefficients as the rest of the Firesprays, this puts his predicted value at a massive 50 points! Regardless of the specific coefficients that would price the Firespray correctly, it is clear that Scum Boba is the best value for any Firespray in the game. Flying with or against Boba will require particular tactics to either maximize or mitigate his ability.

In many ways the Starviper is similar to the TIE Interceptor. The StarViper has, in my opinion, the most versatile dial and action bar in the game, and this is best utilized on higher PS pilots that can boost after other ships have already moved. The StarViper differs from the TIE Interceptor in that it is only a mild glass cannon, so it should draw less aggro than TIE Interceptors.

Unfortunately, the Generic StarVipers are paying a significant price for their actions and dial, and as a result have a very poor jousting efficiency, which for comparison purposes is only slightly better than the TIE Advanced and E-wing. The PS1 needs to do an additional 41% damage beyond its statline, which it is very unlikely to achieve on a regular basis. The PS1 StarViper could easily cost only 24 points without being overpowered, and at 23 points it would still only have a jousting efficiency of 89.8% and a required efficiency of 121%. These hypothetical 23-point numbers would be almost identical to the PS1 TIE Interceptor, which virtually never sees competitive use. Hypothetically, if the PS1 StarViper were 23 points, then it's more versatile dial and more balanced attack vs defense would give it an advantage over the TIE Interceptor, and you would almost certainly see generic StarVipers being used. However, at 25 points the deficit is too large to overcome, so generic StarViper usage should be low in the long-term.

The named StarViper pilots, by contrast, are a good value. I am valuing Guri's ability to conditionally gain a focus token at 2 points, which incidentally makes this PS5 pilot's expected cost the same as its printed cost, so I expect it to see quite a bit of use. Although Xizor's ability is, in my opinion, not nearly as good, his printed cost is only 1 more, making him a good PS adjusted value.

The M3-A "Skyc" Interceptor has been partially spoiled. The dial is still unknown. More details will follow as the ship is fully spoiled.

Serissu is essentially the Scum version of Biggs, and needs to be paired with glass cannons to be effective. Thankfully, the Scum faction already has several glass cannons, including the HWK pilots Palob and Bonearm, and a generic Skyc pilot equipped with the "Heavy Skyc" title and a Heavy Laser Cannon. With 3 agility but only 3 hull/shields, Hull Upgrade may be a good value.

Cliff notes summary:

• It is highly unlikely that either the PS2 or Ashera will see heavy use. (I am valuing Ashera's ability at only 1 point, because it is easily bypassed.)
• The PS2 stock has a mediocre jousting efficiency.
• The PS2 with HLC also has a mediocre jousting efficiency since the platform has such low durability.
• Adding Hull Upgrade to PS2 + HLC + keeps the jousting efficiency almost identical. This makes Hull Upgrade a good choice (assuming you are willing to buy into the HLC to begin with), to lower its exceptionally high glass cannon ratio.
• The PS2 with the Mangler cannon is not cost effective at all.

The IG-2000 has not been fully spoiled. More details will follow as the ship is fully spoiled.

All we have to go on right now are the jousting values and a guess at what the pilot abilities will be worth. For an initial analysis I assumed a named pilot ability valued at 1. With a jousting efficiency of 95%, the IG-2000 will probably be a competitive option.

Those of you that have followed any of my MathWing type posts might know that I have written several Matlab scripts to make statistical analysis of dice rolls possible for a variety of circumstances. One of the side goals of this project was to use it as inputs to solve the bigger problem of mathematically predicting approximately what a ship's "jousting" value and "total" value should be. In general, FFG has done a good job of balancing the point costs for the ships, although there are a few outliers. Furthermore, extensive play testing is the ultimate way to determine balance between ships, NOT blindly using formulas and equations such as these. So why go through this much trouble? Here's a few reasons:

• Because I can.
• The predicted values all seem to all fall within about 1 point of the community's consensus for each ship, and the predictions also correlate very well with the ships' competitive usage. The results are statistically significant.
• It makes a great starting point for pricing custom ships, if you're into that.
• Knowing a ship's "jousting" value can be helpful when thinking about tactics to get the most out of your squads.
• It could be useful to the community, especially with more feedback and refinement. People occasionally ask for a formula that can be used to value ships, and so far this is the best approach.
• It has a proven historical track record of predicting how effective new ships will be, even without any playtesting. This method has accurately predicted which ships would be most competitive for waves 2, 3, and 4 before the ships were even playable.

• The mathematical predictions for the "jousting" value and efficiency rely on assumptions for the underlying action economy, typical ranges that shots are made at, and frequency of ships that are in the meta. Thankfully the ships in the meta has been tracked, and the action economy and range bins have a relatively small impact on the overall jousting values, so they are still fairly certain. However this is an area for future improvement.
• The cost predictions for the "total" efficiency work best on ships that have no unique capabilities. Thankfully, 8 of the 16 ships through wave 4 should have a very high degree of confidence, so overall the approach should still have utility.
• The game has an element of paper-rock-scissors, so the "total value" does not necessarily predict that one ship is universally better than another. For example, more maneuverability inherently increases a ship's fair value, but it's nearly useless against a turret list.
• If a ship is loaded up with lots of potential upgrades, then you're inherently paying something for that privilege, even if it goes unused. Conversely, ship upgrade slots contribute a relatively small amount to the "total value" since the upgrades themselves are generally self-balancing by their point costs, but there are still many amazing combinations and unique squad ideas.
• The fair point value does NOT consider the opportunity cost associated with target priority, which in this game is generally determined by the attacker. Therefore, mixing glass cannons and tanks together in the same squad generally does not work very well. For example, spending a ton of points on a glass cannon that will likely get killed first (Alpha TIE Interceptors + Targeting Computer), or conversely, spending extra points on very durable units that your opponent simply waits to kill last (A-wing + Stealth) are both generally bad ways to spend points. Again, these factors are not considered in the fair points value, so you still need to consider tactics and specific squad composition to really determine a ship's situational usefulness.

There are at least four ways to predict a ship's value.

• Extensive play testing
• Comparing similar ships and differentially adding or subtracting points for different capabilities
• Converting attack/defense/dial/upgrade/etc parameters into a form that can be used as an input to Lanchester's Square Law
• Combat Salvo Model numerical simulations

Notice that I did not include the linear regression formulas that have previously been attempted. Linear regression formulas that look backwards at existing ship costs and try to figure out a fixed price for each kind of upgrade/dice/etc are fundamentally flawed and were doomed to failure from the start.

A few thoughts on each category:

• Play testing: This is obviously the best method, and technically doesn't belong in this list since it doesn't predict balanced costs, it actually proves what the balanced values are. The main downside is that it requires a large sample size, and therefore cannot be used for discussing upcoming waves (even fully revealed ones), or custom stat ships that people have put together but haven't had much (or any) time to test yet.
• Differential point costing: This is the easiest of the three "theory crafting" methods, and it works OK for comparing ships that are very similar. As the differences between the two ships becomes greater, the margin for error becomes much larger. It also assumes that you can accurately assign point values for the different capabilities, which isn't trivial, but sometimes can be gleaned from looking at the point structure and capabilities of existing ships.
• Lanchester's Square Law: this is the method that I will be discussing here. The difficulty is in figuring out how to accurately quantify all of the various game mechanics to obtain a numerical "combat effectiveness" for each ship. A ship's cost is then proportional to the square root of it's combat effectiveness. This approach has scaling problems when the point squad is low, such as in X-wing, since the assumptions of the continuous time differential equations upon which it is based break down. Thankfully, this is relatively easy to compensate for.
• Salvo Model: this is by far the most difficult method, and takes a fair amount of expertise to generate a reasonable model. Even if there was an ideal simulation, there is still not necessarily a direct link between the results and a points prediction, since a ship's balance is not just based on a single matchup, but rather an aggregate of the entire metagame. I will undoubtedly get around to building such a model eventually, but more for analyzing matchups and less for predicting overall balance.

Lanchester's Square Law states that if you have a large number of ranged combatants that can all fire at each other, the force strength of each side as a function of time can be given as a differential equation, with the result that a force's overall combat strength is:

F = N ² *E

Where F is the force's total combat strength, N is the number of units, and E is the combat effectiveness of each individual unit. Ironically, Lanchester's Square Law is better suited to model X-wing than real-world combat, as most combat in the last century has either been asymmetrical warfare, or is more accurately described by the Salvo Combat Model. Running a Lanchester's "simulation" requires only 3 inputs:

• numerical ratio: number of combatants of the two armies
• efficiency ratio: determined by the damage-rate per unit of the two armies
• time scale

The time scale only changes how fast the simulation reaches its conclusion, and has zero effect on the final ending ratio of forces. Therefore to determine the final state, only the first two ratios matter: numerical ratio, and efficiency advantage.

The first ratio is straightforward: it is the ratio of the number of ships, mathematically represented as A(0)/B(0), where A(t) is the size of army A vs time, and B(t) is the size of army B vs time. The combat effectiveness E determines the ratio of the damage-rate per unit of the two sides. I.e. if the combat effectiveness of squad A is twice that of squad B, then the ratio of the damage-rate per unit is 2:1.

Here is a graphical example from Wikipedia:



What we want to do here instead, is have two different squads with equal force values F but at different ship costs, which yields the equation:

N _A ² * E _A = N _B ² * E _B

If both squads spend the same number of points P, then we have:
N _A = P/C _A
N _B = P/C _B

where C _A and C _B are the costs of each individual ship in squads A and B respectively. If we solve for the cost C _B , we have:

C _B = C _A *(E _B / E _A ) ^0.5

So, the basic premise is that because a squad's power increases proportionally to the number of ships present squared , an individual ship's cost should increase as the square root of its combat effectiveness.

However, this assumes that the number of individual units present is large enough that the changes in the army value over time are small enough that the curve can be approximated as a continuous time equation. In X-wing, we field 2-8 ships per side in a 100 point game, so a single, powerful ship will continue to deal out damage regardless if it has 1 hull left, or 13. Since Lanchester's assumes that damage output goes down linearly as you receive damage, it will artificially undervalue expensive ships.

This is not just related to a ship's hit points, but rather to a ship's total combat effectiveness E, which can occur by increasing its expected durability, expected damage output, or non-jousting efficiency (dial etc). Thankfully, this is easily to numerically determine, and I have done so at a baseline of a 96 point squad. The process is relatively simple and can be easily implemented in Excel. You build a combat "simulator" that calculates two sides continually doing damage to the other side, assuming ideal focus fire onto one ship at a time on each side. To determine how much of an effect expensive ships have at 96 points, I did the following:

• Set side A to have 8 ships (8 TIEs), that each have 3 hull, and 1 attack per unit time.
• Set side B to have [7-1] ships with 1 attack per unit each.
• Adjust the hull points on the side B ships until both squads simultaneously kill each other.
• Repeat steps 2 and 3 for 1 through 7 ships on side B.

For a 96 point squad game, I got a curve with the following data points:

Ship Cost Hull
12 3
13.7 3.855
16 5.142
19.2 7.2
24 10.8
32 18
48 36
96 108

These data points are obviously slightly different than what would be predicted by Lanchester's Square Law. The following formula for ship cost lines up almost identically with the above curve:

value = 12*( E ^{(1 / 1.85)} + (1/150)*(E ^{(1 / 0.8)} - 1) )

where E is the ship's combat power normalized to a PS1 TIE Fighter.

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WARNING

If you are attempting to recreate this work and are using these new curve exponents and coefficients instead of the old ones in the old thread (E ^0.52 ), I strongly recommend you also use the new ship durability values as described further below. The new curve fit makes more expensive ships more valuable compared to the old curve, but this is more than offset by the new durability calculations that has decreased the relative durability of high hit point ships. The net effect of both, generally speaking, is that expensive high hit point ships are now worth slightly less than they were under the old model. Using the new coefficients here, but with the old ship durability calculations will overvalue high hit point ships. The best approach is to compute ship durability based on the probability density function of number of shots required to kill a ship, not simply using average damage numbers , as the latter does not consider the effect of the final "kill shot".

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Now we introduce the technical definition of a ship's jousting power and total power:

P _jousting = {Expected Damage Output} * {Expected Durability}

P _total = P _jousting * {Non-jousting coefficient}

The value is then related to the power by:

jousting value = 12*( P _jousting ^{(1 / 1.85)} + (1/150)*(P _jousting ^{(1 / 0.8)} - 1) )
total value = 12*( P _total ^{(1 / 1.85)} + (1/150)*( P _total ^{(1 / 0.8)} - 1) )

The non-jousting coefficient mathematically represents the increased damage output and/or durability that a ship has above and beyond its basic ( attack / agility / hull / shields ) stat line. For example, ships with 360° turrets have a very good non-jousting coefficient, because they will virtually always have a shot. An important concept is determining how effective a ship needs to be above and beyond its raw "jousting" value to break even with a baseline ship that is 100% "efficient". To repeat from the introduction, the break-even point for the non-jousting coefficient is approximately:

{Non-jousting coefficient} = (1 / jousting efficiency ) ²

For example, if a ship has a jousting efficiency of 80%, then it needs to increase its damage output before it dies by 1 - (1/0.8) ² = 56% beyond what its stat line alone provides.

In order to calculate the average damage that different attacks do relative to 2 dice, the following assumptions were used:

• The attacker has no action 1/3 of the time, and focus 2/3 of the time.
• The defender has focus 1/2 the time.
• The range bins probabilities are [30% 45% 20% 5%] for [R1 R2 R3 R3+obstacle].
• The 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:
[{0 defense dice} {1 defense dice} {2 defense dice} {3 defense dice} {4 defense dice}]:

• low defense meta: [15% 35% 25% 23% 2%]
• "standard" defense meta: [ 7% 30% 30% 25% 8%]
• high defense meta: [ 2% 28% 25% 30% 15%]

These numbers are based on the current wave 4 meta and extrapolating into the anticipated wave 5 meta.

Note: 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.

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

defense meta
low defense normal defense high defense

Basic damage numbers

1 dice: 0.4610 0.4406 0.4242
2 dice: 1.0000 1.0000 1.0000

3 dice: 1.6539 1.7058 1.7511

4 dice: 2.3741 2.5012 2.6161
5 dice ¹ : 3.1304 3.3472 3.5486

1 free reroll on attack (Howlrunner or Predator)

2 dice 1.3222 1.3384 1.3516

3 dice 2.1222 2.2166 2.2994

4 dice 2.9449 3.1363 3.3121

Same action economy as above, plus a free Target Lock

2 dice + TL: 1.4150 1.4360 1.4531

3 dice + TL: 2.3595 2.4745 2.5758

4 dice + TL: 3.3709 3.6095 3.8297

Basic Damage with Wedge ability

2 dice 1.3346 1.3927 1.4369

3 dice 2.0622 2.1959 2.3081

4 dice 2.8257 3.0509 3.2503

Accuracy Corrector with same focus action economy as above

2 dice + AC 1.4508 1.4630 1.4719

3 dice + AC 1.8766 1.9349 1.9849

4 dice + AC 2.4874 2.6177 2.7351

Advanced Targeting Computer (same focus action economy as above)

2 dice, 50% proc 1.4842 1.5215 1.5540

2 dice, 100% proc 1.9685 2.0431 2.1080

2 dice + Preda tor, 50% 1.8477 1.9135 1.9708

2 dice + Predator, 100% 2.3731 2.4885 2.5900

Advanced Targeting Computer with 100% chance of focus and TL (Vader)

2 dice 2.1719 2.2655 2.3471

2 dice + Predator 2.5699 2.7053 2.8246

Rear Admiral Chiraneau with Target Lock instead of focus as his action

3 dice Admiral: 2.0296 2.1155 2.1907

4 dice Admiral: 2.8249 3.0021 3.1642

Secondary weapons
Heavy Laser Cannon ² : 2.2657 2.3750 2.4721

Heavy Laser Cann on ² + TL: 3.2002 3.4130 3.6065

Ion Cannon Turret ³ : 0.8737 0.9247 0.9669

BTL-A4 + Ion Turret ⁴ : 0.6480 0.6950 0.7379

BTL-A4 + Ion Turret ⁵ : 0.8663 0.9295 0.9873

Notes:

1. 5 base attack dice does not exist in the game, this is purely for speculative reference.
2. This assumes that the attacker always has a HLC shot, so the only range bin that changes the number of dice is range 3 + obstacle.
3. This assumes that the attacker always has a range 1-2 unobstructed Ion Cannon shot.
4. If range 3 shot, then zero damage since ion turret is range 1-2. Otherwise, calculate the probability of the attacker and defender each still having a focus after the first attack. These are assumed to be independent to make the calculation simpler. Then calculate the average Ion Cannon Turret damage with these resulting action probabilities.
5. For reference only. Assume that the Ion Cannon Turret always has a shot even if the range bin is range 3. Do not allow for obstruction at range 3+. I.e. the calculation is the same as #3, but with the action economy in #4.

Durability was previously being calculated based on the ship's overall hit points, divided by its average damage intake. This was a good first-order approximation, but I am now using a more accurate method. Durability is now being based on the actual number of shots required to kill a given statline.

The net effect is that high hit point ships see an overall decrease to their durability compared to calculating it only based on average damage numbers. This is because the final "kill shot" never reflects the average damage number, since a ship with 1 hit point doesn't care if it takes 1 damage or 5. Lower hit point ships have more kill shots relative to their health, giving them an effective boost to overall durability. For example, a TIE Defender is slightly less durable than a pair of TIE Fighters, even though the Defender's has 3 shields + 3 hull vs 6 hull on the TIE Fighters.

The probability density function for the likelihood of exactly N number of shots killing the target is computed, so you get the entire curve, and then take the mean. Critical hits that do double damage are explicitly considered in the number of shots required to kill a target. Critical hits that do not do extra damage are weighted as one-third of a hit, resulting in the following two different critical hit weightings:

weighting #1: 2x damage only: 1 + 7/33 + (3/8)*2/33

weighting #2: All critical hits: 1 + 7/33 + (3/8)*2/33 + (1/3)*(33-7-2)/33

The average damage intake using each weighting is then calculated, and the ship's net durability is calculated as:

(mean rounds to destroy) * (avg damage intake w/ weighting #2) / (avg damage intake w/ weighting #1)

All results are then normalized to a x/3/3/0 statline (standard TIE Fighter).

The following action economy and meta assumptions were used:

• The attacker has no action 1/3 of the time, focus 4/9 of the time, target lock 1/9 of the time, and focus + target lock 1/9 of the time.
• The attacker gets 1 reroll 10% of the time (stacking with the above), simulating Howlrunner or Predator on a PS3+ target.
• The defender has focus 1/2 the time.
• The range bins probabilities are [30% 45% 20% 5%] for [R1 R2 R3 R3+obstacle].
• The attacker base attack dice is meta dependent, see below.

The number of attack dice was evaluated in three different "meta" environments:
[{2 attack dice} {3 attack dice} {4 attack dice} {Heavy Laser Cannon}]:

• low attack meta: [45% 45% 5% 5%]
• "standard" attack meta: [35% 45% 10% 10%]
• high attack meta: [30% 40% 15% 15%]

These numbers are based on the current wave 4 meta and extrapolating into the anticipated wave 5 meta. The Heavy Laser Cannon shot will exclude all range effects except for range 3 through an obstacle, which still adds one die. It is assumed that the HLC will still have an alternative shot while in the range 1 bin.

Comments:

• Ships with the "(Hi D)" flag are assumed to have a better defensive action economy, which is simulated by increasing the chance for defensive focus from 50% to 67%.
• The normalized standard deviation is calculated as: (the standard deviation of probability density function of the shots required to kill the ship), divided by (the mean of the shots required to kill the ship).

The jousting efficiency calculated for each ship is the ratio of the ship's absolute jousting value divided by the ship's equivalent PS1 cost. Since some of the ships start at higher than PS1, some adjustment is required to calculate the equivalent PS1 cost. In an ideal world, increasing the PS of your entire squad would cost the same regardless if you had two ships or 8 ships. However, the PS bid cost as a percentage of ship cost can vary significantly between different ships.

The approach taken here is to use the 12 point ships and their cost progression as a baseline. Each additional PS or EPT beyond PS1 as being worth 0.5/12 = 1/24th more. The general formula is:

PS X cost = PS 1 cost * (1 + ( X-1 + EPT)/24) + named ability value

Note: For pilots with 2 EPTs (Green, Jake, Tycho), the 2nd EPT is only valued at 0.5, reflecting diminishing returns.

Conversely, the PS1 equivalent cost of a ship is:

PS 1 equivalent cost = (base cost + upgrades - named ability value) / (1 + ( X-1 + EPT)/24)

The named pilot ability is either directly computed and rolled into the expected damage output and durability, or is assigned a value between 0.5 and 3 points and then added to the final expected pilot cost.

Note that in this model, upgrades become more cost effective on higher PS ships. This generally correlates very well with real world experience, as upgrades like Missiles, Engine Upgrade, and others are all more effective on high PS ships. The basic premise is still that the point cost for increasing your entire squad's PS should, in an ideal world, be independent of how many ships or upgrades you have.

For example, starting at PS1, the projected relative increase in cost for PS 5 with an EPT would be:

1 + (+4 +1)/24 = 1.2083.

Here the +4 accounts for the 4 PS jump from PS1 to PS5, and the +1 accounts for the EPT. Conversely, a 35 point PS5 generic pilot with an EPT would have an equivalent PS1 cost of:

35 / (1 + (4+1)/24) = 29.0

Note that named pilots generally also pay an additional cost for their ability. It will be shown that several of the expensive named pilots like Han Solo and Rear Admiral Chiraneau are actually less expensive than their lower priced equivalent pilots, because the +1 point per PS cost progression that FFG uses costs proportionally less for very expensive ships.

The non-jousting coefficient is broken up into several categories which are multiplied together:

• Dial
• Actions
• Arc
• Upgrade slots

Dial

Actions

Arc

Upgrades

Resulting Coefficients

• December 4, 2014: Initial post.
• December 6, 2014: Changed range 1-2 360 degree arc coefficient from 1.5 to 1.4.
• February 22, 2015: Updated attacker action and reroll economy when calculating expected durability to match actual calculations: 10% chance of reroll, and: [1/3 chance no action | 4/9 chance focus | 1/9 chance TL | 1/9 chance TL+F]