MajorJuggler

MathWing: Comprehensive ship jousting values and more

287 posts in this topic

-------------------------------------- SCUM  SHIPS  ------------------------------------
----------------------------------------- wave 6 ---------------------------------------
------------------------------------------- Z-95s --------------------------------------
Commentary

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.

                                Cost          |      | PS1 Jousting Efficiency |
Ship name                actual|predict|  PS1 |  JV  | std   |     range       | req eff
PS1 Z-95                    12 | 11.9  | 12   | 12   | 100%  | 99.3%  - 100.4% | 100%
PS3 Z-95                    13 | 12.9  | 12   | 12   | 100%  | 99.3%  - 100.4% | 115.8%
Kaa’to Leeachos0.5          15 | 14.9  | 12   | 12   | 100%  | 99.3%  - 100.4% | 150.3%
N’dru Suhlak2               17 | 17.4  | 11.6 | 12   | 103.3%| 102.6% - 103.8% | 188.5%
Suhlak w/ ability*          17 | 20.6  | 13.2 | 16.1 | 122.3%| 119.4% - 124.6% | 110.6%
Suhlak + Lone Wolf**        19 | 26    | 15.2 | 21   | 138.1%| 134.5% - 141.4% | 83.6%

*  Assuming Suhlak's ability always trigger
** Assuming Suhlak's ability and Lone Wolf both always trigger
 
------------------------------------------ Y-wing --------------------------------------
Commentary

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.

                                Cost          |      | PS1 Jousting Efficiency |
Ship name                actual|predict|  PS1 |  JV  | std   |     range       | req eff
PS2 Y-wing                  18 | 15    | 17.3 | 14.4 | 83.5% | 82.3%  - 84.2%  | 149.7%
PS4 Y-wing                  20 | 16.2  | 17.8 | 14.4 | 81.1% | 80%    - 81.9%  | 181.1%
Drea Renthal1               22 | 17.8  | 18   | 14.4 | 80.1% | 79%    - 80.9%  | 215.3%
Kavil0                      24 | 18.6  | 18.6 | 14.4 | 77.6% | 76.5%  - 78.3%  | 252.2%
Kavil* + Blaster + R4       30 | 34.4  | 23.2 | 23.4 | 100.6% | 96.6% -  103.9% | 156.9%
PS2 BTL-A4 + Ion3           23 | 22.9  | 19.2 | 20.2 | 105%  | 102.3% - 107%   | 127%
PS2 BTL-A4 + Ion3(no R3)    23 | 21.6  | 19.2 | 18.9 | 98.2% | 95.9%  - 100%   | 143.4%

 
* Ion Cannon Turret considered as additional 3 point value, which increases jousting efficiency.
* BTL-A4: calculated 2 ways. 1st: assuming Ion always gets a shot
                             2nd: no Ion shot 25% of the time
 
* Approximating Kavil's ability plus R4 plus Blaster Turret as simply having 4 attack per turn. In reality, if Kavil loses his action he cannot fire the Blaster Turret. The combat coefficient also assumes the standard coefficient for a 360 degree arc, but he cannot use his ability in his front arc.
 
------------------------------------------ HWK-290 -------------------------------------
commentary

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.


                                Cost          |      | PS1 Jousting Efficiency |
Ship name                actual|predict|  PS1 |  JV  | std   |     range       | req eff
PS1 HWK-290 + Ion3          21 | 17.5  | 18   | 12.6 | 69.9% | 67.3%  - 72%    | 253.9%
Torkil Mux3 + Ion3          24 | 21.7  | 16.6 | 12.6 | 75.7% | 72.9%  - 78%    | 323.1%
Palob2 + Blaster Turret     24 | 25.6  | 18.2 | 17   | 93.1% | 91.4% -  94.5%  | 187.8%

Palob2 + Bla + Opp.         28 | 30.6  | 22.3 | 21.3 | 95.5% | 92.3% -  98.1%  | 164.2%

Palob2 + Bla + Opp. + K4    31 | 36.4  | 24.9 | 26.7 | 107.2%| 102.5% - 111.3% | 131.3%

Dace Bonearm + Ion3         28 | 30.4  | 19.4 | 18.4 | 95.1% | 91.6%  - 98%    | 213.4%

 
Ion Cannon Turret considered as additional 3 point value, which increases jousting efficiency.
 
Palob: Assuming he always steals a focus token, and spent on activating blaster turret. His ability is then valued at +2 for removing an enemy focus token.

 
---------------------------------------- Firesprays ------------------------------------
Commentary

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.

                                Cost          |      | PS1 Jousting Efficiency  | req

Ship name                actual|predict|  PS1 |  JV  | std    |     range       | eff
PS5 Firespray              35  |  34.6 | 29   | 25.2 | 86.9%  | 85.1% -  88.4%  | 181%
Emon Azzameen1             36  |  35.6 | 29   | 25.2 | 86.9%  | 85.1% -  88.4%  | 190.2%
Scum Kath Scarlet*         38  |  41.6 | 29.4 | 28.3 | 96.1%  | 93.4% -  98.3%  | 169.9%
Scum Boba Fett*            39  |  50.2 | 29.3 | 33   | 112.9% | 109.8% - 115.9% | 134.6%

 
Scum Kath: assuming rear arc shot 50% of the time
Scum Boba: assuming 1 reroll on offense and defense

 
----------------------------------------- StarViper ------------------------------------
commentary

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.

                                Cost          |      | PS1 Jousting Efficiency |
Ship name                actual|predict|  PS1 |  JV  | std   |     range       | req eff
PS1 StarViper               25 | 22.7  | 25   | 20.7 | 82.6% | 81.1%  - 84%    | 141.2%
PS3 StarViper               27 | 24.8  | 24.9 | 20.7 | 82.9% | 81.3%  - 84.3%  | 162.3%
Guri2                       30 | 30    | 23.2 | 20.7 | 89.1% | 87.5%  - 90.7%  | 196.2%
Prince Xizor1               31 | 31.1  | 23.2 | 20.7 | 88.9% | 87.3%  - 90.5%  | 207.9%

------------------------------------- M3-A Interceptor ---------------------------------
Commentary


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. 

                                Cost          |      | PS1 Jousting Efficiency  | req
Ship name                actual|predict| PS1  |  JV  | std    |     range       | eff
PS2 M3-A                    14 | ????  | 13.4 | 12.2 | 90.8%  | 90.7% -  90.9%  | 128.6%
Ashera1                     18 | ????  | 14.1 | 12.2 | 86.7%  | 86.6% -  86.8%  | 203%
Serissu3                    20 | ????  | 12.8 | 12.2 | 95.7%  | 95.6% -  95.8%  | 245.7%
PS2 + Ion3                  19 | ????  | 15.4 | 11.7 | 76.1%  | 73.7% -  78.1%  | 242.1%
PS2 + Ion3+ Hull            22 | ????  | 18.2 | 13.3 | 72.9%  | 70.6% -  74.9%  | 249.7%
PS2 + Mangler               20 | ????  | 19.2 | 15.8 | 82%    | 81% -    83%    | 154.4%
PS2 + Mangler + Hull        23 | ????  | 22.1 | 17.9 | 81.2%  | 80.1% -  82.2%  | 157.2%
PS2 + HLC                   23 | ????  | 22.1 | 19.6 | 88.9%  | 86.5% -  91%    | 133.3%
PS2 + HLC + Hull            26 | ????  | 25   | 22.4 | 89.6%  | 87.1% -  91.8%  | 131.4%
PS2 + HLC + Serissu         23 | ????  | 22.1 | 22.8 | 103.4% | 100% -   106.8% | 101.5%
PS2 + HLC + Serissu + Hull  26 | ????  | 25   | 26   | 104.3% | 100.8% - 107.8% | 99.8%
 
Ion effect: valued at additional 3 points
Mangler: not considering the effect of a free hit to crit.
HLC: assumes always has an HLC shot
PS2 + HLC + Serissu: assumes always gets 1 defensive reroll
 
------------------------------------------ IG-2000 -------------------------------------

commentary

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.

                                Cost          |      | PS1 Jousting Efficiency |
Ship name                actual|predict|  PS1 |  JV  | std   |     range       | req eff
IG-881                      36 | ????  | 28   | 26.6 | 94.9% | 93%    - 96.9%  | 172.3%

Edited by MajorJuggler

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Underlying Methodology

 

Motivation

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.

 

 Limitations

  • 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.

 
Different methods for valuing ships

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

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 = N2*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:
 
Damagerace.JPG
 
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:
 
NA2 * EA = NB2 * EB

If both squads spend the same number of points P, then we have:
NA = P/CA
NB = P/CB
 
where CA and CB are the costs of each individual ship in squads A and B respectively. If we solve for the cost CB, we have:
 
CB =  CA*(EB/ EA)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.

 

------------------------------------------------------------------------------------------------------------------------------------

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 (E0.52), 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".

------------------------------------------------------------------------------------------------------------------------------------

 

Now we introduce the technical definition of  a ship's jousting power and total power:
 
Pjousting = {Expected Damage Output} * {Expected Durability}
 
Ptotal = Pjousting  * {Non-jousting coefficient}
 
The value is then related to the power by:
 
jousting value = 12*( Pjousting(1 / 1.85) + (1/150)*(Pjousting(1 / 0.8) - 1) )
total value       = 12*(     Ptotal(1 / 1.85) + (1/150)*(    Ptotal(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.

 
Calculating Expected Damage Output

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 dice1:                 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 + Predator,  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 Cannon2:     2.2657        2.3750         2.4721

Heavy Laser Cannon2+ TL: 3.2002        3.4130         3.6065

Ion Cannon Turret3     0.8737        0.9247         0.9669

BTL-A4 + Ion Turret4:    0.6480        0.6950         0.7379

BTL-A4 + Ion Turret5:    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.

 

Calculating Expected Durability

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.

 

----------------------------------------------------------------------------------
                                Ship Durability
----------------------------------------------------------------------------------
                   | normalized durability |    normalized std dev |
                   |    vs attack meta     |      vs attack meta   |
ship               |  low  |  std  | high  |  low  |  std  | high  |
IG-2000            | 2.506 | 2.482 | 2.464 | 0.384 | 0.382 | 0.381 |
YT-2400 (Hi D)     | 2.408 | 2.411 | 2.412 | 0.323 | 0.322 | 0.32  |
YT-2400            | 2.257 | 2.271 | 2.279 | 0.319 | 0.317 | 0.315 |
Firespray          | 2.232 | 2.248 | 2.258 | 0.32  | 0.318 | 0.316 |
Named YT-1300      | 2.141 | 2.192 | 2.226 | 0.252 | 0.251 | 0.25  |
VT-49              | 2.006 | 2.085 | 2.139 | 0.197 | 0.197 | 0.197 |
TIE Defender       | 1.925 | 1.91  | 1.898 | 0.437 | 0.435 | 0.433 |
ACD TIE Phantom    | 1.855 | 1.817 | 1.791 | 0.553 | 0.552 | 0.55  |
Lambda Shuttle     | 1.693 | 1.734 | 1.761 | 0.283 | 0.282 | 0.281 |
TIE Advanced (Hi D)| 1.796 | 1.772 | 1.754 | 0.482 | 0.479 | 0.477 |
ORS YT-1300        | 1.677 | 1.718 | 1.746 | 0.284 | 0.283 | 0.281 |
E-wing             | 1.652 | 1.639 | 1.629 | 0.472 | 0.47  | 0.467 |
TIE Advanced       | 1.617 | 1.607 | 1.6   | 0.475 | 0.472 | 0.469 |
StarViper          | 1.581 | 1.573 | 1.568 | 0.478 | 0.475 | 0.471 |
B-wing             | 1.395 | 1.429 | 1.452 | 0.311 | 0.31  | 0.309 |
Y-wing             | 1.362 | 1.397 | 1.422 | 0.314 | 0.313 | 0.311 |
TIE Bomber         | 1.34  | 1.357 | 1.369 | 0.407 | 0.403 | 0.401 |
A-wing             | 1.343 | 1.336 | 1.33  | 0.522 | 0.519 | 0.516 |
X-wing             | 1.188 | 1.202 | 1.21  | 0.435 | 0.431 | 0.428 |
HWK-290            | 1.164 | 1.178 | 1.189 | 0.438 | 0.434 | 0.43  |
Scyk               | 1.033 | 1.031 | 1.028 | 0.593 | 0.589 | 0.585 |
TIE Fighter        | 1     | 1     | 1     | 0.595 | 0.59  | 0.586 |
Z-95               | 0.988 | 1     | 1.008 | 0.478 | 0.475 | 0.472 |

 

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).

 

 

Calculating PS1 Equivalent Cost

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.

 
Calculating the Non-Jousting Coefficient

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

  • Dial
  • Actions
  • Arc
  • Upgrade slots

Dial


The dial is 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:
 

--------------------------------- Dial Coefficients ------------------------------
Note: green equivalent to white except for stress relief section
--------------------------- Small base ship tightest turn ------------------------
White 1, 2, 3 turns:   0
White 1, 2 turns:      -0.01
White 2, Red 1 turns:  -0.03
White 2, 3:            -0.04
White 2, Red 3:        -0.04
White 2:               -0.06
Red 1, 2, White 3:     -0.07
Red 2, White 3:        -0.075
--------------------------- Large base ship tightest turn ------------------------
White 1, 2, 3:         -0.01
White 1, 2:            -0.02
White 2, 3:            -0.05
White 2:               -0.06
Red 2:                 -0.1
----------------- Slowest forward move (+1 for large base ships) ----------------
White 1:               0.04
White 2:               0.04
----------------- Fastest forward move (+1 for large base ships) ----------------
White 5:               0
White 4:               -0.01
Red 4, White 3:        -0.02
---------------------------------- Fastest bank ---------------------------------
Large ship White 3:    0.02
Large ship Red 3:      0.01
Small ship White 3:    0
Small ship Red 3:      -0.01
------------------------------- K-turns / S-Loops -------------------------------
One White K-turn:      0.35
One pair Red S-Loops:  0.1
Two Red K-turns:       0
One Red K-turns:       -0.02
None + turret:         -0.1
None, no turret:       -0.25
--------------------------- Stress Clear (all green) ----------------------------
1 turn, 1 bank, 4 straights: 0.055
1 turn, 1 bank, 3 straights: 0.05
2 bank, 3 straights:         0.02
1 bank, 3 straights:         0.01
1 bank, 2 straights:         0
4 straights:                 -0.05
3 straights:                 -0.055
2 straights:                 -0.06
----------------------------------- Specialty -----------------------------------
None:  0
Red 0: 0.1
----------------------------- Net Dial Coefficients -----------------------------
------------ Imperials ------------
TIE Fighter:           1
TIE Fighter:           0.94
TIE Interceptor:       1.05
Firespray:             0.97
TIE Bomber:            0.945
Lambda:                0.75
TIE Defender:          1.23
VT49:                  0.87
------------ Rebels ------------
X-wing:                0.97
Y-wing:                0.89
A-wing:                1.055
YT-1300:               0.98
B-wing:                0.96
HWK-290:               0.7
HWK-290 (with turret): 0.85
E-wing:                1.01
Z-95:                  0.97
YT-2400:               0.99
------------ Scum ------------
StarViper:             1.13

 
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 analysis excludes upgrades like Push the Limit that change the action economy.
 

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.

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+target lock 1/9 of the time, and focus the remaining 5/9 of 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:        0.02
Small Ship Barrel Roll: 0.05

Large Ship Barrel Roll: 0.06

Cloak (no ACD): 0.05

Cloak (with ACD): 0.20

Small Ship Boost:         ( normalized attack / normalized durability )/ 50 + (PS + EPT - 1)/150

Large Ship Boost: 1.5* (( normalized attack / normalized durability )/ 50 + (PS + EPT - 1)/150)

 
Boost is comprised of two components. The first component is weighted higher for glass cannons than tanks, since glass cannons need to use boost to remain out of arc. The second component is proportional to the Pilot Skill and existence of an EPT slot, since boost is most useful when moving after other ships have executed their maneuver.

 
Arc

  • Forward firing arc:           1.00
  • Auxiliary rear firing arc:    1.125 (mathematically equivalent to dodging 1 out of 8 arcs)
  • 360 degree range 1-3 arc:  1.50   (mathematically equivalent to dodging 1 out of 3 arcs)
  • 360 degree range 1-2 arc:  1.40


 
Upgrades

All upgrade coefficients apply for the baseline ship with no upgrades attached. Specifc builds that fill the upgrade slots (or intentionally leave others blank), such as 58 Dash, sets the corresponding coefficient to 1, since the value of the addition is explicitly computed.

 

Turret Slot

  • Turret slot on 1 attack ship: 1.5. HWK-290.
  • Turret slot on 2 attack ship: 1.1. Y-wing.

Cannon Slot

  • No cannon: 1.00.
  • Cannon on 3 attack ship: 1.01.
  • Cannon on 2 attack ship with turret: 1.1.

Droid slot: 1.03

System Upgrade slot

  • System Upgrade on 3 attack ship: 1.06. Lambda Shuttle, TIE Phantom, B-wing, E-wing.

Crew Slots

  • 1 + (# crew slots)*0.075

Ordnance

Note: Ordnance coefficients are extremely low because ordnance as a general rule is overcosted.

  • No Ordnance: 1.00: TIE Fighter, TIE Interceptor, Lambda Shuttle, VT-49, TIE Phantom, HWK-290.
  • Missile / Torpedo on 3 attack ship: 1.002. TIE Defender, X-wing, YT-1300, B-wing, E-wing.
  • Missile / Torpedo on 2 attack ship: 1.005. TIE Advanced, Y-wing, A-wing, YT-2400.
  • Missile / Torpedo / Bomb on 3 attack ship + 1.02. Firespray.
  • Full loadout on 2 attack ship: 1.03. TIE Bomber.

Illicit Upgrade slot

  • 1.03: Scum Z-95, Scum Firespray.


 
Resulting Coefficients

--------------- Net Combat Coefficients for total point prediction --------------
-------------- Rebels --------------
X-wing:                  0.981
Y-wing:                  0.993
Y-wing + Ion Turret:     1.354
Y-wing + BTL-A4:         0.903
A-wing (vs PS):          1.076 1.083 1.09  1.097 1.104 1.111 1.119 1.126 1.133
A-wing + Refit (vs PS):  1.071 1.078 1.085 1.092 1.099 1.106 1.113 1.12  1.127
YT-1300:                 1.66
B-wing:                  1.061
HWK-290 + Ion:           1.343
HWK-290 + Ion + Chewie:  1.249
E-wing:                  1.16
Z-95:                    0.955
YT-2400:                 1.835
Outrider + HLC:          1.66
54 Dash:                 1.544
58 Dash:                 1.711
------------ Imperials ------------
TIE Fighter:             1
TIE Advanced:            0.992
TIE Interceptor (vs PS): 1.086 1.093 1.1 1.107 1.114 1.121 1.128 1.135 1.142
TIE Firespray:           1.228
TIE Bomber:              1.003
Lambda Shuttle:          0.846
TIE Defender:            1.282
TIE Phantom (no ACD):    1.185
TIE Phantom (with ACD):  1.354
VT49:                    1.567
-------------- Scum ---------------
Scum Z-95:                0.984
Scum Y-wing:              0.984
Scum Y-wing:              0.993
Scum Y-wing + Ion Turret: 1.354
Scum Y-wing + BTL-A4:     0.903
Scum HWK-290 + Turret:    1.384
Scum FireSpray:           1.265
StarViper (vs PS):        1.191 1.198 1.206 1.213 1.221 1.229 1.236 1.244 1.251

 

Changelog

  • 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]
Edited by MajorJuggler

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hmm.  Those HWK values make me really skeptical.  

 

Its also interesting to note that these values don't seem to be to me as easily understandable for how they play out in the game.  its hard to tell how much is a strong, workable required efficiency versus one that isn't.  

 

Also, you made some comments about Kenkirk and Chiraneau, but not Oicunn.  What does your math say about him?  I'm noting in my test games that I get about 2 smash hits in a game.  sometimes 1 sometimes 3, rarely 4.  so average about 2.  

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Also if FFG is adamant about not banning or errata-ing powerful builds, does that not mean that our meta will simply become the only ships that can achieve a maximal cost-effective efficiency on par with your very very very high values for Falcon and ACD Phantom?  

 

I think that means it will lead to general power creep and escalation.  Otherwise, how does a new release (which they want to be well received) have any place against the cost efficiency we see already?  

 

Second, do you really expect the developers to allow more crew that leads to Fat Decimator builds?  I'm not sure I think this is even a good idea.  Playing against a Fat build is really annoying and frustrating.  It's also come to note that the 75 minute time frame for a tournament match has become hard enough to get to in a Falcon game that a significant number of games will go to time and a win by MOV.  

The_Brown_Bomber likes this

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Based on your analysis:

 

The best Rebel pilots in the game (based on std efficiency):

Airen Cracken (106.7%)

PS2 Z-95 (104.2%)

PS4 Z-95 (103.8%)

Biggs (102.2%)

PS2 Y-Wing + BTL-A4 + Ion (100.4%)

 

The best Imperial pilots in the game (based on std efficiency):

PS1 TIE Fighter buffed by Howlrunner (117.4%)

Howlrunner (114.3%)

Captain Kagi (110.4%)

Echo + VI + ACD (110.2%)

PS2 Shuttle (108.1%)

 

The best Scum pilots in the game (based on std efficiency; information incomplete):

Boba Fett (112.9%)

Palob + Blaster Turret + R4 + Opportunist (108.5%)

N'dru Suhlak (107.5%)

Kavil + Blaster Turret + R4 (102.9%)

Serissu (M-3A) (101.7%)

 

It seems the Scum has some good pilots for the smaller number of available ships. I suppose that's to put it on equal footing with the other factions out of the gate and apply some learning from the development lessons of the game.

 

I'm intrigued by the findings that Darth Vader, Ten Numb, and the PS3 Phantom have identical std joust values. Does this suggest they have equal utility in the game?

 

The lowest overall std joust is the basic Rebel PS2 HWK at 54.5%. The highest required efficiency is Jan Ors + Ion Turret at 482.9%.

 

Interesting- thanks.

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Is there anywhere an actual spreadsheet of this could be placed, and subsequently downloaded for easier viewing, manipulation, etc.?

 

And let's make sure we get this "linked to" within the pinned post we have.

 

Thanks for the work.

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Based on your analysis:

 

The best Rebel pilots in the game (based on std efficiency):

Airen Cracken (106.7%)

PS2 Z-95 (104.2%)

PS4 Z-95 (103.8%)

Biggs (102.2%)

PS2 Y-Wing + BTL-A4 + Ion (100.4%)

 

 

Muahahahahha. Three of my favorite ships right there in the list.

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Thanks for the updates on the numbers.  

 

I've always wondered about something with the E-wings.  This pure jousting number has them pretty low in the scale, and that seems to correlate well with their usage in competitive play - while you occasionally see a super-Corran or even more occasionally an Etahn, you never see a Knave or Blackmoon.  

 

So, did the designers really over-cost something like the E-wing so much?  I can only assume the additional points for the E-wing go into their upgrades and what one can do with those.   In particular, R2-D2 seems quite potent on an E-wing, as it has the agility to take a few hits then regenerate more easily than something like an X-wing.  

 

So, all this leads to my question: would you be able to run the numbers on an E-wing which costs four more points (for R2-D2) but has two more shields (a rough guess on an average number of shields R2-D2 might regenerate during a fight)?  Actually, it would be even more interesting, if possible, to see the relative effects of R2-D2 on the E-wing: if R2-D2 regenerates 1 shield, the jousting efficiency is X, if he regenerates 2 shields the jousting efficiency is Y, etc.  

 

Thanks!

Edited by category

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Wow, what the eff?  

(ha....ha....ha???     ok, ok, i know that was pretty bad)

 

No seriously, loving the data thus far.  Good average assumptions, and some concrete numbers to help identify the most quantifiable values possible.  Plus it helps to have a history of what people have been running so far, to sort of double check your findings.

 

I will definitely be checking back to this thread as new ships and 'fixes' come out.

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Thank you for taking the time and effort to compile and post your revisions!  

 

A slight note on the Tie Defender dial.  While it does have a white K-Turn, it also has not a single bank or hard turn that is a green maneuver.  Clearing stress can be very challenging on a T/D.  Furthermore, the ship has only Hard 3 white, all other turns are there (which is awesome) but they are red, which is a problem with the just mentioned difficulty of clearing stress.

 

Vessery's ability is nice, but I have never seen or heard of a game where he was able to use the free target lock ability more than a few times (certainly not every turn).  You can kill the ship that holds the target lock, or Vessery can kill the ship in his attack, thus your other imperial ship has now wasted a target lock action.  

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hmm.  Those HWK values make me really skeptical.  

 

Its also interesting to note that these values don't seem to be to me as easily understandable for how they play out in the game.  its hard to tell how much is a strong, workable required efficiency versus one that isn't.  

 

Also, you made some comments about Kenkirk and Chiraneau, but not Oicunn.  What does your math say about him?  I'm noting in my test games that I get about 2 smash hits in a game.  sometimes 1 sometimes 3, rarely 4.  so average about 2.  

 

Which HWK values? The ones in orange are colored for a reason. The jousting values however are correct given the assumptions.

 

The lower the required efficiency, the better (all else being equal). For example, a required efficiency of 150% means that the ship needs to do 50% more damage than what would be simply predicted by its jousting value. That gives you an idea on how well you need to fly the ship, or just get lucky.

 

Edit: Re Oicunn: it is hard to put an exact value on his ability, unlike Kenkirk and Admiral which directly translate to increased jousting value. So I just gave him a pilot ability value of 2. If you think it should be more or less, then adjust the final predicted point value by the difference.

 

Also if FFG is adamant about not banning or errata-ing powerful builds, does that not mean that our meta will simply become the only ships that can achieve a maximal cost-effective efficiency on par with your very very very high values for Falcon and ACD Phantom?  

 

I think that means it will lead to general power creep and escalation.  Otherwise, how does a new release (which they want to be well received) have any place against the cost efficiency we see already?  

 

Second, do you really expect the developers to allow more crew that leads to Fat Decimator builds?  I'm not sure I think this is even a good idea.  Playing against a Fat build is really annoying and frustrating.  It's also come to note that the 75 minute time frame for a tournament match has become hard enough to get to in a Falcon game that a significant number of games will go to time and a win by MOV.  

 

The meta has already become one where only the most efficient ships are used, especially with the generic pilots. This merely quantifies the underlying reason why. It doesn't have to mean that we get power creep though, that would require them releasing new ships that make the generic TIE Fighter and Z-95 obsolete.

 

re: Decimator crew: Dangit Jim, I'm a math guy, not a prophet! :P  We'll just have to find out. 3 crew slots provide a lot of flexibility, and it is paying for that flexibility.

 

 

My poor disnumerate brain, this is why I like pretty pictures.

 

It's in my backlog, but no ETA.

 

Can we have this thread pinned please? It's really useful and if Juggler updates it it will stay useful for the time being!

 

No need to have it pinned. It is linked in my pinned Index thread.

 

 

Is there anywhere an actual spreadsheet of this could be placed, and subsequently downloaded for easier viewing, manipulation, etc.?

 

And let's make sure we get this "linked to" within the pinned post we have.

 

Thanks for the work.

 

Generating a spreadsheet it also in my backlog, but no ETA.

 

It's already linked to in the pinned thread.  :)

 

 

Based on your analysis:

 

The best Rebel pilots in the game (based on std efficiency):

Airen Cracken (106.7%)

PS2 Z-95 (104.2%)

PS4 Z-95 (103.8%)

Biggs (102.2%)

PS2 Y-Wing + BTL-A4 + Ion (100.4%)

 

The best Imperial pilots in the game (based on std efficiency):

PS1 TIE Fighter buffed by Howlrunner (117.4%)

Howlrunner (114.3%)

Captain Kagi (110.4%)

Echo + VI + ACD (110.2%)

PS2 Shuttle (108.1%)

 

The best Scum pilots in the game (based on std efficiency; information incomplete):

Boba Fett (112.9%)

Palob + Blaster Turret + R4 + Opportunist (108.5%)

N'dru Suhlak (107.5%)

Kavil + Blaster Turret + R4 (102.9%)

Serissu (M-3A) (101.7%)

 

It seems the Scum has some good pilots for the smaller number of available ships. I suppose that's to put it on equal footing with the other factions out of the gate and apply some learning from the development lessons of the game.

 

I'm intrigued by the findings that Darth Vader, Ten Numb, and the PS3 Phantom have identical std joust values. Does this suggest they have equal utility in the game?

 

The lowest overall std joust is the basic Rebel PS2 HWK at 54.5%. The highest required efficiency is Jan Ors + Ion Turret at 482.9%.

 

Interesting- thanks.

 

 

Bear in mind that the jousting efficiency assumes that you are willing to spend a certain % of your points to bid the pilot up to its current PS and EPT. And almost all of the high PS ships now in play have some way of adjusting their position other than dial reveal, so you should be less willing to spend the points on Cracken and Kagi than other pilots like Fat Han + Engine, or Soontir.

 

Otherwise everything is as expected. Serissu's value is highly squad and formation dependent, so your mileage may vary.

 

Jousting values don't tell you the entire utility of a ship, it just says how good it is at throwing dice for its PS adjusted cost.

 

A naked HWK with only 1 attack is obviously going to have the lowest value. It's more included as reference and to be a completionist, since nobody would ever field the ship that way. And Jan + Ion's absolute jousting value (JV) is basically the same as a TIE Fighter, but she costs twice as much. So yeah, she obviously has a lot of work to do to pay back that investment. This is why many people prefer Blaster Turret, which I will go back later and add numbers for.

 

Thanks for the updates on the numbers.  

 

I've always wondered about something with the E-wings.  This pure jousting number has them pretty low in the scale, and that seems to correlate well with their usage in competitive play - while you occasionally see a super-Corran or even more occasionally an Etahn, you never see a Knave or Blackmoon.  

 

So, did the designers really over-cost something like the E-wing so much?  I can only assume the additional points for the E-wing go into their upgrades and what one can do with those.   In particular, R2-D2 seems quite potent on an E-wing, as it has the agility to take a few hits then regenerate more easily than something like an X-wing.  

 

So, all this leads to my question: would you be able to run the numbers on an E-wing which costs four more points (for R2-D2) but has two more shields (a rough guess on an average number of shields R2-D2 might regenerate during a fight)?  Actually, it would be even more interesting, if possible, to see the relative effects of R2-D2 on the E-wing: if R2-D2 regenerates 1 shield, the jousting efficiency is X, if he regenerates 2 shields the jousting efficiency is Y, etc.  

 

Thanks!

 

Done. I simulated it with regenerating 3 shields on the PS1, so 31 points for a 3/3/2/6 stat line. The absolute jousting value is still only 26.1, but it costs 31. The break even point (at least for 100% jousting efficiency) is to regenerate about 5-6 shields. And you are restricted to only green moves most of the time, so if you miss shots because you can't turn around, then it is even higher. If Knave + R2-D2 was viable, people would have been running it by now. This explains why. Note - the numbers for Corran will obviously be different, his threshold is far lower, especially coupled with FCS + double-tap, and PtL turtle.

 

----------------------------------------- E-wings --------------------------------------
                                Cost          |      | PS1 Jousting Efficiency |
Ship name                actual|predict|  PS1 |  JV  | std   |     range       | req eff
PS1 E-wing                  27 | 22.9  | 27   | 21.1 | 78.3% | 76.7%  - 79.7%  | 155.8%
PS3 E-wing                  29 | 24.8  | 26.8 | 21.1 | 78.9% | 77.3%  - 80.4%  | 177.2%
Etahn Abaht1                32 | 28.7  | 25.5 | 21.1 | 82.9% | 81.2%  - 84.5%  | 211.3%
Corran Horn3                35 | 33.6  | 23.3 | 21.1 | 90.9% | 89%    - 92.6%  | 248.2%
PS1 + R2-D2, 3 regen        31 | 28.4  | 31   | 26.5 | 85.6% | 84.2%  - 93.4%  | 132.2%
 
PS1 E-wing + R2-D2: assumes 3 shields regenerated, so net 3/3/2/6 stat line.
 
 

 

Thank you for taking the time and effort to compile and post your revisions!  

 

A slight note on the Tie Defender dial.  While it does have a white K-Turn, it also has not a single bank or hard turn that is a green maneuver.  Clearing stress can be very challenging on a T/D.  Furthermore, the ship has only Hard 3 white, all other turns are there (which is awesome) but they are red, which is a problem with the just mentioned difficulty of clearing stress.

 

Vessery's ability is nice, but I have never seen or heard of a game where he was able to use the free target lock ability more than a few times (certainly not every turn).  You can kill the ship that holds the target lock, or Vessery can kill the ship in his attack, thus your other imperial ship has now wasted a target lock action.  

 

I agree about the TIE Defender dial. If anything, the dial coefficient that I give it is gracious. It's all documented in the 2nd post. The thing is, if I were to argue the other side and try to value the white K-turn even more, it would be mathematically equivalent to saying that the dial is almost as good as having a 360 degree turret, which is clearly not the case. So there is absolutely no way that the Defender is priced correctly, it's just a question of how overcosted it is.

 

And yes, Vessery is tricky. You need a squad something like this:

 

(97)

Vessery

Whisper + VI + ACD + FCS

Lambda + FCS

Edited by MajorJuggler

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Thanks for the updates on the numbers.  

 

I've always wondered about something with the E-wings.  This pure jousting number has them pretty low in the scale, and that seems to correlate well with their usage in competitive play - while you occasionally see a super-Corran or even more occasionally an Etahn, you never see a Knave or Blackmoon.  

 

So, did the designers really over-cost something like the E-wing so much?  I can only assume the additional points for the E-wing go into their upgrades and what one can do with those.   In particular, R2-D2 seems quite potent on an E-wing, as it has the agility to take a few hits then regenerate more easily than something like an X-wing.  

 

So, all this leads to my question: would you be able to run the numbers on an E-wing which costs four more points (for R2-D2) but has two more shields (a rough guess on an average number of shields R2-D2 might regenerate during a fight)?  Actually, it would be even more interesting, if possible, to see the relative effects of R2-D2 on the E-wing: if R2-D2 regenerates 1 shield, the jousting efficiency is X, if he regenerates 2 shields the jousting efficiency is Y, etc.  

 

Thanks!

 

Done. I simulated it with regenerating 3 shields on the PS1, so 31 points for a 3/3/2/6 stat line. The absolute jousting value is still only 26.1, but it costs 31. The break even point (at least for 100% jousting efficiency) is to regenerate about 5-6 shields. And you are restricted to only green moves most of the time, so if you miss shots because you can't turn around, then it is even higher. If Knave + R2-D2 was viable, people would have been running it by now. This explains why. Note - the numbers for Corran will obviously be different, his threshold is far lower, especially coupled with FCS + double-tap, and PtL turtle.

 

----------------------------------------- E-wings --------------------------------------
                                Cost          |      | PS1 Jousting Efficiency |
Ship name                actual|predict|  PS1 |  JV  | std   |     range       | req eff
PS1 E-wing                  27 | 22.9  | 27   | 21.1 | 78.3% | 76.7%  - 79.7%  | 155.8%
PS3 E-wing                  29 | 24.8  | 26.8 | 21.1 | 78.9% | 77.3%  - 80.4%  | 177.2%
Etahn Abaht1                32 | 28.7  | 25.5 | 21.1 | 82.9% | 81.2%  - 84.5%  | 211.3%
Corran Horn3                35 | 33.6  | 23.3 | 21.1 | 90.9% | 89%    - 92.6%  | 248.2%
PS1 + R2-D2, 3 regen        31 | 28.4  | 31   | 26.5 | 85.6% | 84.2%  - 93.4%  | 132.2%
 
PS1 E-wing + R2-D2: assumes 3 shields regenerated, so net 3/3/2/6 stat line.

 

 

 
 
Thanks!  I'm surprised the shield regen doesn't increase it's jousting efficiency that much, but it is what it is.  

 

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Thanks!  I'm surprised the shield regen doesn't increase it's jousting efficiency that much, but it is what it is.  

 

The problem is that now you are spending 31 points on a single ship that has low attack power for its cost, so it needs to make up for it with more durability.

 

 

Off-the cuff math:

 

At 3/3/2/3 it has a JV of 21.1. With R2-D2 it has a cost of 31.

 

So you need to increase JV from 21.1 to 31, that requires a net increase in durability of roughly:

 

(31/21.1)^2 = 2.16

 

(Note the squared relationship). So the total hull+shields needs to be roughly:

 

5 * 2.16 ~= 10.8.

 

So R2-D2 needs to regen about 5 times. 

Edited by MajorJuggler

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Thank you for taking the time and effort to compile and post your revisions!  

 

A slight note on the Tie Defender dial.  While it does have a white K-Turn, it also has not a single bank or hard turn that is a green maneuver.  Clearing stress can be very challenging on a T/D.  Furthermore, the ship has only Hard 3 white, all other turns are there (which is awesome) but they are red, which is a problem with the just mentioned difficulty of clearing stress.

 

Vessery's ability is nice, but I have never seen or heard of a game where he was able to use the free target lock ability more than a few times (certainly not every turn).  You can kill the ship that holds the target lock, or Vessery can kill the ship in his attack, thus your other imperial ship has now wasted a target lock action.  

 

Vessery seemed to do pretty well in Flight 1. Hothie fought him in his final match, so he did pretty respectable. 

 

Also if FFG is adamant about not banning or errata-ing powerful builds, does that not mean that our meta will simply become the only ships that can achieve a maximal cost-effective efficiency on par with your very very very high values for Falcon and ACD Phantom?  

 

I think that means it will lead to general power creep and escalation.  Otherwise, how does a new release (which they want to be well received) have any place against the cost efficiency we see already?  

 

Second, do you really expect the developers to allow more crew that leads to Fat Decimator builds?  I'm not sure I think this is even a good idea.  Playing against a Fat build is really annoying and frustrating.  It's also come to note that the 75 minute time frame for a tournament match has become hard enough to get to in a Falcon game that a significant number of games will go to time and a win by MOV.  

 

It is interesting data, no doubt. Probably pretty useful, though I do disagree with a lot of the point costs. But if you are only interested in the top tier, then you would be asking these types of questions, math or no. That is the constant question for games that have continual expansions. And the game is much more than the top tier. 

 

It is also important not to take it as gospel. You cannot mathematically predict a player's preferred style. A Firespray with HLC's effectiveness depends heavily on the player, so it's effectiveness will vary on the player. 

 

I mean it is good data, and I do respect the work. But I don't think it completely has the dna of the game. 

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