Showing posts with label Ship Design. Show all posts
Showing posts with label Ship Design. Show all posts

Wednesday, April 11, 2012

Starmada Nova: The Armor Trap

When I first read the Nova rules, I started wondering about armor.  It looked like a nice, straightforward defense, so I ran a little math the next day to see how the shipbuilding numbers work out.  I came to some conclusions that I thought it might be best to keep quiet.  The forums (namely BeowulfJB and a few others) reached similar conclusions recently, so I figured I might as well share here.

In short: the trouble with armor is that it costs the same as buying more hull, but it provides you with very little benefit over just buying more hull.  Having a larger hull provides you with more of those delicious SU, whereas armor actually costs you SU.  As a result, if you want a ship that can take n hits, you're almost certainly better off going with just hull n rather than hull m and armor p such that n = m+p.

There are, however, two possible uses for armor that I can see.  The first has to do with thrust.  A hull n ship has a higher thrust factor than a hull m armor p ship.  How much higher?  Thrust factor scales as hull to the 1.7th power, so thrust t on a hull n requires 2*t*(n)^1.6 SU.  If you look just at the case of a hull n/2 armor n/2, then the armor consumes 30*(n/2)^.7 SUs, though for the same thrust you'll likewise need to use 2*t*(n/2)^1.6.  I did some tables in OOCalc, and I'm having trouble creating useful graphs of my findings since they're in three dimensions and relative, but it is possible to generate an SU savings via armor.  The trouble is that the circumstances must be somewhat extreme; for example, if you really, really want a ship that can take 68 hits and has thrust 8, you can save 222 SU by making it Hull 34 Armor 34 compared to straight 68 hull.  But, for 4, 8, and 12 hits, half-armor-half-hull generates no SU savings for arbitrary thrust.  This is also true of any multiple-of-four number of hits less than 68 for thrusts less than 8.

The other thing armor does is that it lets you ever-so-slightly manipulate the way your systems degrade.  For example, a hull 5 / armor 1 ship can take 3 hits before being damaged, then another 2 to crippled and 1 more to destroy, while a hull 6 ship takes 2 for each step of damage.  Likewise, a hull 4 / armor 4 can take 4 hits before being damaged and 6 to cripple, while a hull 8 takes 3 and 6.  This lets you front-load your damage, and retain fighting effectiveness for slightly longer at the price of a more rapid degradation once you hit damaged or crippled.  However, as you move to larger hull sizes, this effect is diminished; you'll only ever be able to front-load one extra point, which is much more significant on small ships (where armor is basically guaranteed to not generate an SU savings on thrust).  I think this may be a worthwhile use of armor on smaller vessels, though; may have to try it out.  But for like...  a ship that you want to take 16 hits and have thrust 5?  Avoid armor.  You could go hull 14 armor 2 for front-loading (6 to damage, 12 to cripple, 16 to destroy vs 6 to damage, 11 to cripple, 16 to destroy), though it's not clear if that's really advantageous, and but other than that there seems to be little to no advantage to be gained from it in the majority of cases.  Flavor / conversion reasons naturally remain valid.

The really annoying thing is that this is, to some extent, true of ECM and shields as well.  These both have actual advantages, though - ECM can turn long range fire into no fire, and shields can beat the odds if your dice like you.  On expectation, though, both of these will likewise increase your effective hull by some fraction, but use up your SU, generating an effective hull n with less SU and higher potential for thrust than a hull n should have.  I have yet to actually run the numbers on them, though.

Sunday, March 11, 2012

Starmada Sunday: Continuing Damage, Repeating, and Geometric Series


The Homeworld ion frigate - inspiring G-arc inverted range mods repeaters since 1999

So I mentioned in my previous post on ship design that there were a number of other topics I wanted to cover.  A lot of this is going to be rapidly obsoleted by Starmada Nova when it launches, but for those who don't convert (ha), it might be useful.

So, first topic.  Of the weapon traits, Continuing Damage and Repeating get a lot of discussion as being terrifyingly good.  While this is actually true of Continuing Damage, it's only situationally true of Repeating.  To show this, it's necessary to show that the number of hits generated by both of these traits can be modeled as a geometric random variable.  This is is a formalization of the process of flipping a coin until it comes up tails for a coin which has a probability p of landing heads-up, and its output is the number of flips it took to get tails.  Try it a few times and write down how many flips it took each time.  If you do this enough times, and your coin is fair, you'll get an exponential function, where it'll take i flips about 1/(2^i)th of the time (so 1 flip half the time, 2 flips a quarter of the time, and so forth).  If you work out the math with generating functions, the average number of flips it'll take to get heads works out to be 2 for a fair coin.

Continuing Damage's performance is easy to explain under this idiom.  Rather than ending the series when we get heads, we end it when we roll an odd, which happens with the same probability.  Thus, we can expect to get two points of systems damage per die of Continuing Damage, on average.  Further, under the standard interpretation of how Continuing Damage works, we get a hull hit for each point of Continuing Damage; if we roll an odd the first time, then it's a hull hit, and if we got an even initially, then we keep rolling until we get an odd, and hence a hull hit.  Therefore, each point of Continuing Damage is exactly twice as effective as a normal point of damage against starships, as a normal point of damage is guaranteed 1 point of systems damage and gets a point of hull damage half the time.

So, what's the problem with Continuing?  The issue actually isn't, mathematically, that it guts ships without killing their hulls, since it does hull damage on each die, and the ratio of systems damage to hull damage is the same, on average, as with non-continuing damage.  The problem is actually that it's underpriced, at a price multiplier of x1.7.  Since it's twice as effective as normal damage (on average), it should probably be x2, like Double Damage.  It also has the nice property that it scores a hull hit on every die, which is only shared by Extra Hull Damage, which is much more expensive at x3.  It's possible that the community as a whole has misinterpreted the wording on Continuing Damage, but it appears that if Cricket originally intended it to work differently, he has since forgotten.

So, short version: Continuing actually is probably the most reliably cost-supereffective anti-ship weapon trait in the game, scoring x2 hits all the time for x1.7 price, for a 1.18 effectiveness / price multiplier.  Use it if you like blowing up the enemy's ships (and I think most of us probably do), or houserule it to an x2 price multiplier.  For all that Continuing looks like a swingy trait on the surface, it's actually very reliably effective, since it always gets a hull hit.  For bonus points, combine with Catastrophic.

Repeating's a bit harder to analyze.  Here we have a coin that we quit flipping when we miss...  which means that the number of hits we get varies with accuracy, and our probability isn't always 1/2.  Fortunately, the expected number of heads we get before we get tails on a biased coin with probability p of heads is p / (1-p).  We can then work out the expected number of hits per point of RoF based on our accuracy rating:

  • 6+: p = 1/6, so (1/6)/(5/6) = 1/5 hits per repeating RoF, on average.  1.2 times as effective as 6+ Acc without repeating.
  • 5+: p = 1/3, so (1/3)(2/3) = 1/2 hits per RoF, 1.5 times as effective as 5+ non-repeating
  • 4+: p = 1/2, so (1/2)/(1/2) = 1 hit per RoF, 2 times as effective as 4+
  • 3+: p = 2/3, so (2/3)/(1/3) = 2 hits per RoF, 3 times as effective as 3+
  • 2+: p = 5/6, so (5/6)/(1/6) = 5 hits per RoF, 6 times as effective as 2+
So, what this analysis shows is that Repeating is much, much better on highly accurate weapons.  OK, that makes sense.  But when is it cost-effective?  Repeating has a cost multiplier of x3.  This means that with Repeating on a 3+ weapon, you're breaking even.  With repeating on 4+ or higher, you're paying for more than you're getting.  And on 2+, you're getting twice what you paid for; for the price of one 2+ repeater with 6 expected / effective RoF, you could instead get 3 RoF of 2+ weapons, which would be half as effective on average.

Thus, repeating is only broken if you can use it on 2+ weapons...  or if you can make your weapons 2+ during combat by way of range modifiers.  In general, you're going to want to use Inverted Range Mods with these; you want to be obliterating people far away before they obliterate you, ideally during the first round of real firing.  3+ Inverted Range Mods Repeaters and 4+ Inverted Double Range Mods Repeaters are both terrifyingly effective; I've seen them in action, and can attest that they core battleships like nobody's business.  My first win ever was with the Grumm from Hammer and Claw, whose capital ships mount several variants of the aptly-named Eviscerator as their bow weapons.  Range 12-15, Acc 3+, Imp 3-4, Damage 1, Inverted Range Mods, Repeating.  Now, the Grumm only ever being a few of these to battle, and no more than one per ship, so when you score a weapon hit on the Grumm, there's always that chance that you'll get the Eviscerator (and then you celebrate, and the Grumm are sad).  But if you were to build a fleet armed with these as their primary weapons, rather than a few specialists...  Eesh.

On the flip side, if you know your opponent is bringing the good kind of repeaters (3+ or 2+), bring Countermeasures.  That -1 Acc really mitigates Repeating's effectiveness.  Evasive Action can likewise seriously reduce the amount of hurt they can put on you; try to get up to speed, then coast on evasive action through their long-range killzone if you're playing with Newtonian Movement.  Once you get into short range where they're not at 2+, you'll at least be on even footing mathematically.  On the flip side, if your enemy knows you're bringing out the Repeater-cheese, they'll have Countermeasures, so buy Fire Control.  It's worth it (and hey, if they don't have Countermeasures, then it becomes free Directed Damage, which can increase your expected number of hull hits by a factor of 1.5).  Also bring some secondary guns in case they close past your long-range repeaters.  You could also try to maintain a dispersed formation of killzones, so that each ship is in the long-range, high-effectiveness area of another ship's repeaters.  This suffers from the standard problem of dispersed formations, though, namely that the enemy only has to deal with part of your force at a time, and can use his entire force effectively.

So, the verdict on Repeating: it's situationally good, or tactical by my reckoning.  The problem is that getting into that sweet spot is pretty easy; with inverted range mods and long ranges, you can pull it off most games.  Likewise, the payoff when you do is huge, and the penalty for failing to do so is not very severe (even when you take into account the x1.4 cost multiplier for Inverted Range Mods, 3+ repeaters at medium range are still fairly cost-effective).  You only lose at close range.  This is what pushes it into borderline-degenerate territory.  Also: never ever put repeating on 5+ or 6+ weapons.  Generally avoid putting it on 4+, since you'll usually be losing effectiveness if you do.  3+ is fair game, and if you're buying 2+ weapons, Repeating is extremely cost effective.

Saturday, March 3, 2012

Mailbag 3: Starmada Ship Design

Got several hits recently for the search term "starmada ship design".  Initially I kind of ignored them, but upon further reflection I realized that there's actually a lot to say on this topic.  There are several schools of thought, a lot of crunchy math to be done, and plenty of personal experience to draw on.  Plus, if I queue up a bunch of posts about Admiralty Edition, maybe Nova Edition will come out, by the Umbrella Principle (looking at starting an AE Simplest Campaign for the same reason, actually.  Well, that and the fact that I'm kinda jonesing for 'mada...).

So much for motivation.  While reflecting on this topic in the shower, I realized that there are essentially three types of 'traits' in Starmada: AE (well, kind of five, but two are degenerate).  The three interesting ones are Reliable traits, Swingy traits, Tactical traits.  The degenerate types are Awful and Awesome traits.

Swingy traits vs Reliable traits are fairly clear.  A swingy trait can perform strongly, but relies on luck to do so.  Examples of swingy traits include Fire-Linked, Variable RoF (and similar), and high damage ratings.  On average, you'll get exactly what you paid for by expectation, but the actual results vary wildly across games.  Reliable traits include good Acc values (3+, 4+), high RoF, Fire Control (when used to power Directed Damage), and Extra Hull Damage.  These are traits that are always good, and work to mitigate the effects of randomness on the way that you play.  Often you pay a premium for this reduction of randomness, but not necessarily.  An illustrative contrast is between Extra Hull Damage from Core, and Catastrophic from Rules Annex.  Both traits work to increase hull hits per die of damage, but they do it in different ways.  EHD guarantees a hull hit on every die of damage, even if you roll a 1 against an Armor-Plated target.  That's about as reliable as it gets.  Catastrophic works a bit differently.  Whenever you roll a hull hit with a catastrophic weapon, the target instead takes 1d6 hull hits.  Scary, and can lead to instant obliteration of a hull 6 or smaller target from a single die of damage...  but not reliably (only 1 in 12 times, or 1 in 18 against armor-plated targets).  Catastrophic is the poster child for swingy traits.  Another example is Countermeasures versus Armor Plating.  Countermeasures provides a nice, reliable -1 to all weapons fire against you, unless they have Fire Control.  The effectiveness of this actually varies based on the accuracy of their weapons, but it's never completely ineffective.  Armor Plating negates damage rolls of 1.  If your dice like to roll 1s, Armor Plating's great; it can negate huge piles of damage (but you might want to use different dice for firing...).  On the other hand, it's entirely possible to play a game with a fleet where every ship is Armor Plated and have AP negate exactly 0 hits.  It does happen.

Example from play: Matt fielded Catastrophic weapons extensively during our play of Admiralty Edition.  Most of the time, they were scary but not terribly effective, but there was one battle (the Dreadnought Match) where they really came into their own and just tore Alex to pieces.  Their primary value most of the time was really as terror weapons; in trying to stay out of the Catastrophic arcs, you might go places on the map you otherwise wouldn't, or you might split your fleet, and you often ended up staring into his Piercing +2 secondary guns, which were reliably good against targets of all types.  Because you really didn't want to try your luck against Cata...

Tactical traits are a third point on the triangle.  These traits are great if you have a good ability to predict your opponent (to borrow from Sirlin, they're powered by Yomi), and a good way to screw yourself over otherwise.  Cloaking is the canonical example, but dual-mode weapons, slow-firing weapons, and Screens are also tactical.  You almost always pay a premium for tactical traits, which is why you have to use them well for them to be cost-effective.  However, they're a lot of fun, and used wisely can be really, really good.  Arguably the Range-Based Foo traits are also tactical, though the Inverted versions can be used at a profit pretty reliably by 'dancing' at long range.

Example from play: Ah, Cloaking.  I initially started experimenting with Cloaking because by Eldar conversion to Starmada was performing terribly; speed and short-ranged weapons were just not cutting it.  Cloaking, however, gave them a whole new dimension and sent me on a winning streak; I don't recall ever having lost a game with the Cloakdar, though I did draw at least one (I know I did during their first game).  Cloaking let me choose the time, place, and manner of engagement, and let me focus my fire on small parts of the enemy fleet while avoiding retribution from the rest.  Matt and Tim avoided cloaking just based on the amount of work involved, while Jared tried it once but badly mispredicted Matt's movement and ended up right under his guns.

Awful traits are pretty self-explanatory.  They're traits which are just...  bad.  Mathematically, provably bad.  There aren't a whole lot of these in the game, fortunately, since Cricket did a pretty good job with the balance.  The two that I know of, unequivocally, are Anti-Fighter Batteries from the Imperial Starmada Sourcebook and Halves Shields from the Rules Annex.  AFBs are far too expensive for the degree of protection from fighters that they provide.  They're nice, because they can fire in a 360-degree arc, but range 1, 5+ to hit, and RoF 1 are all bad traits for anti-fighter weapons.  You want to hit fighters far away, and you want to hit them a bunch of times.  Further, AFBs boost both your ORAT and your DRAT, whereas a normal anti-fighter weapon would just boost your ORAT.  Since ORATs are usually higher and pricing works on square roots, the DRAT cost of AFBs just isn't worth it.  Halves Shields is the other flavor of bad.  It's actually pretty good...  but Piercing +2, also from the Annex is as good or better against all target classes, for the same price.  Piercing +2 is better against Shields 3, and exactly the same effectiveness against all other shield ratings.  Thus, there is mathematically no reason to ever use Halves Shields if Piercing +2 is available (ie, not banned).

Awesome traits are things which are too damn good not to use if available.  They include traits which are mathematically super-efficient, as well as traits whose only effective counter is those traits themselves.  The contents of this category are naturally contentious.  Generally-conceded traits here are Starship Exclusive and Ammo.  Other candidates for this category include the various shieldbreakers from the Annex, strikers, flotillas, repeating, G-arc weapons, and increased hits.  Personally, I tend to think that Stealth might be a bit too good too, but there is at least a kind of counter for Stealth (namely Inverted Ranged-Based traits).

Example from play: Ammo is disgustingly good.  I don't think we ever played a game where only one side used Ammo and that side didn't win.  My ammo-based disablers crippled Alex in the first round, Jared used ammo'd polecats from Hammer and Claw in his first game and won (one of a very few first-game wins), my 100-point one-shot torpedo boats annihilated Matt's 300ish-point battleship in Planetary Assault, and Jared used a one-shot area-effect shieldbreaker against Matt's short-ranged fleet for a bunch of shield damage in the opening round, which I believe turned into a win.  The trick with Ammo is that it lets you concentrate firepower across time.  For the same SU cost, you can have one weapon with no ammo limits, or five such weapons, each of which can fire exactly once.  Thus, you can get 5 times the firepower in the first round of firing.  This is the so-called "Glitter Fleet" idea you hear about on the forums.  It might be a bit more expensive in terms of CRAT...  but 5x firepower is more than enough to make up for it, and usually to wipe an enemy fleet.  And if it doesn't, you cede.  For bonus points, put Slow-Firing on your one-shot weapons.  No effective penalty for you, but makes 'em cheaper.

So at this point you're probably thinking, "OK, that's nice that you've split traits into five categories, but largely non-useful for me, the ship designer."  Not so!  Your use of these traits determines in large part how your fleet will play.  A fleet running strictly reliable traits will perform consistently, while a fleet full of swingy traits will sometimes win big and sometimes lose terribly.  A fleet with too many tactical traits will overburden the player's ability to guess and micromanage, and will likely lose unless those traits synergize well (Cloaking + Slow-Firing, for example), but one with one 'gimmick' tactical trait can play well and with a distinct style.  Awful traits should be avoided, and awesome traits should either be used universally or banned.

To build a fleet which is mechanically strong, you must understand which traits (and which combinations of traits) are mechanically strong.  To build a fleet that you will enjoy playing, you must know both how you prefer your fleets to 'feel', and how various properties of your ships influence their qualitative performance.  The best way to learn these things is to play fleets which vary across the reliable / swingy / tactical scale and see which you like most.  I tend towards tactical / reliable, while Matt for example likes to use swingy main guns and reliable secondaries.  That sort of thing.

There's a lot more to say on this topic.  In particular, I'd like to make clear the math behind Repeating, varying Acc values, shield-breaking traits and shields in general, range and speed, and damage and degradation (including flotillas).  This may have to become a regular column (until Nova comes out...  guess I'll just start talking about Nova when that happens).