A Not-So-Brief Summary of the Ship Efficiency Model

This is the documentation for the the X-Wing 2.0 Ship Efficiency Model.
The current version is v1.9, updated April 12, 2021.

Please note this documentation is old and has not been updated since v1.5. Please see the Changes tab in the Ship Efficiency Model spreadsheet to see how the model has changed since then.

What's the Point?

The ship efficiency model is a combination of three things:

• Somewhat-objective facts that rely on meta assumptions, like "How many shots does this ship survive on average?"
• Assumptions based on play experience, like "How good is the StarViper's curved barrel roll compared to a normal barrel roll?"
• Decisions on what to include based on what I think are important and to produce reasonable outcomes, like "Front-loaded damage is better than back-loaded damage" and "The value of repositioning depends on the fraction of lower-initiative ships squared so low-initiative arc-dodgers aren't overvalued".

The objective and data-driven parts of the model provide some grounding for the numbers, but as you can see, the model requires many assumptions and judgement calls. You should not take this model as the literal truth (except when making jokes), but rather as a product of my questionable judgment. If so, why should you care about this big complicated model? Why not just have better players rank the ships?

The advantage of having a model is it's consistent. We don't have time to test out all of the ships, and certainly not enough to give each ship enough tries to figure out if they're good or not. Judging all ships by a consistent metric means we can find some of the overlooked strong ships based on other ships that are strong. We can also find overrated ships if giving those ships high numbers would overvalue other ships. Because the calculations are transparent (albeit complicated), we can also use this model to explain why a ship is strong or weak.

Since I put most of the assumptions up front, they're easy to change. If you disagree with any of the assumptions, you can simply make a copy of the spreadsheet and see what happens if you put in different assumptions. In fact, differences in play-style and in local metas might mean a different set of assumptions are more relevant for you. If you disagree with the inclusion of certain factors or are concerned about the number of free parameters, you can change some numbers to 0 or 1 to remove their effects.

Finally, this model converts ship strength into numbers which helps us answer these questions:

1. In list-building, which non-meta ships have potential and which are so weak they're probably not worth spending time on?
2. For list-building and in-game play, how many times do we need to use a ship's abilities for it to be worth the points?
3. For in-game play, which list is better in the joust? Are there any ships to prioritize killing so it doesn't dominate the end-game?
4. For fun, what are the likely point costs of unreleased ships? What point costs should ships have for them to be balanced?

Please remember you can play your favorite ship even if the model doesn't give it good numbers, and you are not a bad person if you fly the ships with the best numbers. It's not perfect; feel free to disagree with any of its conclusions, and I'd love suggestions on improvements.

Props

Before I go any further, I want to give huge props to Andrew Lauritzen for his X-Wing Probability Calculator. All of the damage tables are built using his Probability Calculator.

Thanks to MajorJuggler for his 1.0 Mathwing project. I used many ideas from his project when building my model, including overkills and the exponent for focus fire situations.

Also, I want to thank Marc de Bruyn for letting me bounce ideas off him and for looking over this for mistakes.

Summary

The goal of this model is to calculate how efficient ships are. Each ship's effectiveness is calculated based on the average number of attacks it takes to kill them (durability) multiplied by their average damage per attack. This is divided by the ship's point cost to calculate its efficiency.

A natural starting point for effectiveness is the ship's average total damage output over its lifespan. To calculate this, we need the ship's average damage per attack and the number of attacks it survives for (durability).


Ships are evaluated in three different scenarios.

• Joust Efficiency is the ship's efficiency in focus-fire situations where repositioning isn't useful (e.g. your other ships will still be in arc).
• Focus Fire with Repositioning (FFwR) efficiency is the ship's efficiency in focus-fire situations where the ship's maneuverability repositioning abilities can let them survive to make more attacks by avoiding arcs.
• 1v1 Efficiency is the ship's efficiency in end-game or isolated situations and includes the bonus for repositioning.

Focus fire situations value multiple ships over one ship: two 3-attack ships with 4 health each are better than one 3-attack ship with 8 health because they attack twice.

I use these three efficiency values to calculate each ship's balanced point cost. I pick a benchmark so the Academy Pilot TIE Fighter and Blue Squadron Escort T-65 X-Wing stay the same points (currently the 69th percentile in each category) and calculate the implied point cost for one point of effectiveness for each scenario. The balanced point cost for a ship is the weighted average across the three scenarios of the point cost per effectiveness times the effectiveness of that ship. To reduce the variability of the 1v1 efficiency, I shrink the difference between the 1v1 point cost and the FFwR point cost by the focus fire exponent.

The model considers:

1. Meta assumptions about the frequency of attack, agility, and initiative values.
2. The ship's agility, shields, and hull, with a discount factor to reduce the value of back-loaded damage compared to front-loaded damage.
3. The ship's attacks and firing arcs, whether the attack requires a token, and whether the ship has difficulty turning around.
4. The ship's actions and other dice modification for offense and defense.
5. The likelihood of the ship having an action based on its size, red maneuvers in the dial, and whether it can turn more than 90 degrees without a red maneuver.
6. The ship's other abilities or upgrades which add to its damage output or durability.
7. The ship's initiative for initiative kills.
8. The ship's maneuver dial, repositioning actions and abilities, and initiative for arc-dodging.
9. A constant points value of blocking modified by the ship's size, initiative, and repositioning actions.

For more details on how these numbers are calculated, you can read the next section.

Like all models, this model is imperfect ignores some features of the game. It's important to know what this model doesn't consider so you can make the appropriate value adjustments yourself.

There are several ways this model can be wrong:

1. Typos and Misunderstandings. If I enter a number wrong or I misunderstood an ability, then the model isn't going to evaluate the ship correctly. Examples: for a while, Countdown and Pure Sabacc were entered as Initiative 1.
2. Incorrect Modeling of Abilities. Special abilities require a special call-out. The model handles some abilities naturally (e.g. additional actions or straight-forward dice mods, repositioning abilities), but others are very tricky. I usually model abilities as triggering a certain number or percentage of times (e.g. based on range). These abilities usually modify the ship's damage dealt, damage taken, or hit points. If I have the wrong chance the ability triggers or the wrong effect when it does, then the model will give incorrect results.
3. Combos and Synergies. The list of base ship chassis is set in stone, but there are a vast number of pilot-upgrade combos. The model can't rate any pilot-upgrade combos unless I add it, and I don't know of every strong combo. Similarly, the model is very limited in considering how well ships work together.
4. Incorrect Meta Assumptions. The model requires assumptions about the distribution of attack, defense, and initiative profiles in the meta. If those assumptions are wrong for the meta you play in, then the model's ratings will be biased.
5. Incorrect "Universal Constants". The model requires assumptions about the value of "universal constants". If these are wrong, then the model will be biased. Examples include the value of critical hits, the value of the coordinate action at different initiative values, the number of extra shots an additional arc gets, percent of shots dodged because a ship with a certain initiative has a certain action on its bar, and how often ships of a certain type loses its action.
6. Simplifying Assumptions. I make some simplifying assumptions to make things easier to model, but these assumptions mean I model a game that is slightly different from the game we actually play. Examples include not modeling the dual-use of focus and calculate tokens and having fixed percentages of times ships spend their action on offense and defense.
7. Foundational Methodology. There may be something wrong with the fundamental way the model is built, i.e. evaluating the ship in a 1v1 situation as its damage per round x number of rounds survived and taking the almost-square root for its focus-fire efficiency.

Here are some other known issues:

Right now, the model doesn't allow for obstructed shots and all attacks received are assumed to have 1 mod. I'd like to improve this in the future, but that requires generating more tables from the probability calculator and requires either a lot of repetitive work or some programming which I need to learn :).

The model doesn't account for the flexibility of focus and calculate tokens. When a token is reserved for offense, it can't be used on defense at all (and vice versa). This should overvalue single-calculate ships with target lock and/or evade, low-agility ships with evade, and ships that have other reasons not to take the focus action. Dealing with this seems really messy (especially with shooting first vs. shooting second) and I'd love suggestions on how to do this.

The value of turrets is a fixed constant, but it should really depend on initiative. For example, a turreted ship that moves last will always have a shot if it has its action, while a turreted ship that moves first is little better than a ship with fixed arcs.

The Jam action isn't modeled at all.

Finally, it only provides a partial measure of squad effectiveness and it's most accurate for squads when all ships have similar damage-to-durability ratios. A squad of ships with different damage-to-durability ratios are much more effective if their tanky ships are shot at first compared to when their glass cannons are shot at first, and you should keep that in mind when list-building and playing the game.

Somewhat Brief Description of the Calculations

The ship's durability starts with its total health divided by the average damage taken per attack for its agility.

• The ship's hull value is reduced for critical hits.
• The ship's total health increased for its potential to absorb overkill damage.
• The ship's durability subtracts the fraction of ships in the meta with higher initiative to reflect lost shots from being initiative-killed.
• Conditional abilities that improve a ship's defenses are added as extra (fractional) shields. This includes defensive abilities that apply to both the ship and its allies: the self-benefit is added as extra shields and the allied benefit is valued with a direct point adjustment (see below).
• The ship's durability is discounted exponentially to reflect early damage being better than damage many turns into the game. This isn't perfect because of focus fire, and I'd love to hear suggestions on better ways to capture this.

The ship's average damage per attack starts with the number of dice it attacks with at each range band and whether it denies the Range 3 bonus.

• Up to two different types of attacks are considered (e.g. the K-Wing's double turret and front-arc Barrage Rockets, the ARC-170's 3-die front arc and 2-die rear arc, and the TIE Advanced's 3-die primary with a Lock and 2-die primary without).
• Bonuses are granted for better firing arcs and extra firing arcs.
• Penalties are applied for front arcs on ships that can't turn around easily.
• Penalties are applied for ion weapons.
• Attacks that require a focus or TL have some probability where the ship doesn't have the token and thus must use a weaker attack.
• Against each type of defense (agility and whether or not it has a focus), the damage is scaled by the average damage that type of defense takes in the meta.
• Conditional abilities that improve a ship's damage output (including torpedoes) are directly added to its effectiveness as extra damage.
• Offensive support abilities are added as extra damage for the ship.

The ship's durability and average damage per attack are both affected by its actions and dice mods.

• The likelihood of ships getting an action depends on its:
• Size
• Maneuverability (reliance on red maneuvers and whether it can turn more than 90 degrees)
• Abilities (e.g. Advanced Sensors)
• Extra firing arcs and the difficulty/linking of the rotate arc action.
• Right now, ships are only allowed to spend one action on defense.
• Ships are assumed to spend some fraction (probably half or more) of their turns reserving their action(s) for offense. They spend one action on defense with the remaining on offense the remaining times.
• The value of defensive actions is based on receiving 2 attacks per round, and reinforce has a chance of being on the wrong side.
• The handling of ships with multiple force or calculate tokens is unfortunately ad-hoc.
• Ships with 1 force get an extra calculate in all attack scenarios and one use of calculate on defense (added to their shields). If they can't use force on offense because they don't have target lock, they get an additional 2 uses of calculate on defense.
• Ships with extra force get 1.5 uses of their special force ability or 1.5 uses on defense per force token.
• Ships with double-calculate get focus/TL when spending their action on offense, 1 calculate on both offense and defense while spending their action on defense, and an extra 3 uses of calculate on defense (added directly to their shields).
• Special cases:
• Luke is assumed to always have calculate on defense, and gets TL+focus when spending his action on offense.
• Leebo always has calculate on offense and defense when he has an action.

The ship's repositioning factor can be interpreted as extra attacks the ship makes because it avoided damage by dodging arcs. This is only included in the FFwR and 1v1 efficiency numbers.

• The ship is only allowed to reposition when it has an action. Pre-maneuver abilities increase the probability that the ship gets an action.
• The value of the extra attacks for repositioning actions are based on the ship's remaining dice mods after spending an action to reposition (most ships won't have any). Ships with blue turns or curved barrel rolls are assumed to have dice mods from linked actions.
• The first component of repositioning depends on initiative for arc-dodging and preventing opponents from arc-dodging. It includes:
• The initiative multiplier is the square of the sum of the fraction of ships with lower initiative and half of the fraction of ships with the same initiative.
• A constant factor for extra shots because your opponent couldn't arc-dodge with perfect information.
• The quality of the ship's reposition actions.
• Whether the ship can change its dial (non-Duchess Ailerons are considered a dial change).
• The second component of repositioning is independent of initiative and rates the ship's general maneuverability. It includes:
• The quality of the ship's reposition actions.
• Whether the ship can cloak.
• The quality of reposition actions are affected by:
• The size of the ship (bigger is better, although the bonus is smaller for barrel rolls).
• Whether the action is red.
• Whether the action can be performed both before or after the maneuver.
• Whether the ship has a better version of the action (e.g. the StarViper's curved barrel roll).
• A bonus multiplier is granted for ships that can reposition twice, with a larger multiplier if it can reposition twice in any order.
• After the factor for repositioning is added, the ship's effectiveness is multiplied by a factor based on the quality of its dial. The number of straight and non-straight maneuvers of each difficulty is totaled and multiplied by a value for each type of maneuver. This is divided by the total value of a benchmark dial and raised to a small exponent to arrive at the multiplier.

Two things adjust the ship's point value before it divides the ship's effectiveness to calculate its efficiency:

• The ship is assigned a flat points value for being a potential blocker, which depends on the ship's size, initiative, and repositioning actions.
• Any abilities not previously accounted for are assigned a points value.

These point values are subtracted from the ship's point cost before it's used for the effectiveness calculations.