Current Game, and Balancing Ship Modules

[Maze1125]

The augments do indeed stack, or rather, they each apply individually, so for instance, 2 scrap recovery arms will both give you the bonus scrap, equaling double the bonus scrap. But % chance effects don't combine. So for instance, (2x 15% chance to block 1 hull damage) is very different than (30% chance to block 1 hull damage). To be specific, the 30% chance is much better.

That's not necessarily true.
If the "2x 15% chance to block 1 hull damage" has a chance to block 2 hull damage from weapons that do 2 at once, then the mean protection of each case, vs. weapons like that, is identical.
Further, even if it only ever can block 1 damage, it's still only a difference between 27.75% and 30%. Which, although still worth considering, isn't much of a difference.

[angelocire]

That depends on what your hope is. It's a 15% chance to block ONE damage, because each roll taken individually is 15%. If you're hoping for BOTH augments to apply, and thus block 2 damage, the chance is lower, because now you're talking about permutations.

I don't know where you got ~27% from, but I honestly would like to hear. It's entirely possible that I'm calculating this all wrong.

Each preceding roll doesn't affect the chance of the following roll, meaning each one taken by itself is 15%.
i.e. If you roll a die, rolling it multiple times doesn't make your chance of landing on a given side higher than 1/6.

Let me try to work this out "on paper" here, to show you my reasoning. Please correct me, becuase I'm not too great when it comes to this.

Let's reduce this from 15% to 10%, to make the numbers nice and round.
1/10 chance to succeed.
Do that twice, hoping to get a the same number twice in a row.
This means that out of 10^2 possible combinatons/permutations (1-1,1-2,1-3,1-4,....2-1,2-2,2-3,...etc.), only 1 is the permutation you want. Which is 1/100. Which is a 1% chance.

So increase this accordingly, and you get 1.5% chance to succeed on BOTH checks if it's a 15% chance to succeed on one.

[Gorlom]

In all this talk about the hull augmentation are you considering that there is a dodge chance involved in the equation as well? Dodge is quite random as that's a % as well. considering that your 100% certain x points blocked every y seconds seems a bit overpowered to me.

Sequential probabilities is calculated as 1-(1-x)*(1-x) Ie with your 2 times 10% chance to block hull damage you would take the chance not to block damage the first time (90%) multiply it by the the chance to not block damage the second time (also 90%). 0.9*0.9= 0.81 That means there's a 81% chance that that no damage will be blocked. 1-0.81 = 0.19
There is 19% chance that at least 1 point will be blocked with 2 chances to block. (if you use 15% instead of 10 you get maze's 27.75% instead of 19)

To get the chance of both hull damages being blocked you just multiply the chance to block (0.1 in your example 0.15 in FTL) with itself. You get 0.01 (1%) in your example and 0.0225 (2.25%) in FTL.


With your admission about your proficiency of mathematical probability the weirdness in your posts in this particular thread finally makes sense to me. You're intelligent enough to understand probability, but you don't quite seem to have a firm handle on it and seem to overthink or misunderstand certain aspects of it.

If you roll a die, rolling it multiple times doesn't make your chance of landing on a given side higher than 1/6.

Technically correct for each individual roll. But the more times you roll the probability that one of those rolls land on a given side will increase. That's why loot in WoW or Diablo3 or any other MMORPG can have dropchances of 1% for certain items (or even 0.01% for the extra rare loot, I believe that some mounts had this drop chance..) without people ever whining about them being impossible to get. (Well some people whine.. but it isn't justified and ignored by everyone else)

[Chris Woods]

You just multiply to get the chance of both events happening. If 2+ incoming damage hits a ship with 2 mods that say '15% chance to reduce damage to hull by 1' the chance you reduce it by 2 is 0.15 * 0.15 or 2.25%.

The chance only one activates is the chance the first activates but the second doesn't (.15 * (1 - .15)) plus the chance that the second activates but the first doesn't ((1 - .15) * .15) which is 2 * (.15 * (1 - .15)) or 25.5%.

You can add these together to get 'the chance anything activates at all' (.0225 + .255) which is 27.75%. (Another easy way to get this is "1 minus the chance neither work" which is (1 - ((1 - .15) * (1 - .15))) or 27.75%)

EDIT: Or read the post above mine. :/ Seconds late!

Chris Woods

[angelocire]

So it's 27.75% chance to block 1 damage with 2 rolls, and 1.5% chance to block on both rolls, assuming you could block 2 damage.

That still seems underpowered in terms of chance-to-block vs. using 2/3 augment slots.
Essentially the repair arm wipes the floor with it.

Also, I understand that if you just keep rolling a die you statistically will roll any given number eventually, but that analogy doesn't really work well in this case because half of the time your battles won't have very many shots hitting your hull/systems(as opposed to WoW where you kill the same animal 1000 times), so 1.5% chance is really wasteful. Sure, if your goal is to EVENTUALLY block 2 damage as some kind of personal achievement, then yeah, it will happen at some point, but as far as being practical goes it fails.

[Gorlom]

2.25% chance to block 2. You came up with that 1.5% chance from erroneously scaling back up after having used 10% to block in an example. For it to be 1.5% to block 2 points you would need to have 10% chance on one roll and 15% on the other or 12.2474..% (square root of 0.015) chance on each roll.


I think you underestimate chance augments and overvalue the scrap recovery arm (not overestimate but rather put more value in getting additional scrap over other things) compared to others (well me at least). Are you playing on normal or on easy btw? (Just curious on which amount of scrap drop you judge it's usefulness on.)


For instance you say that the repair arm is much more useful? It doesn't do anything in the fight. It doesn't help prevent you from dying in a fight, it just helps restore you after one is concluded.
If the (non boss) enemy jumps away I don't think you would get any hull repairs since you don't get any scrap.


Furthermore I don't see the point in having all the augments to be "equal", the game is based on randomness after all. It's not possible to always get those augments you want. It adds a bit of spice if some augments are more desirable, whether it's generally more desirable or only desirable for certain specific playstyles.

[angelocire]

I actually realized the fallacy of the 1.5% when I was eating dinner earlier. 15^2 permutations is 1/225, or 2.25%.

I think that the majority of comments on the forums discussing augments have brought up the usefulness of scrap recovery arms both in normal and easy.

[Maze1125]

The problem with the scrap-arm vs. defensive modules is the rushed nature of the main game.

The scrap-arm makes each battle more dangerous but you get a higher reward, while defensive modules make each battle safer but without the extra reward the scrap-arm would give.
Now, if you had as long as you wanted to explore each sector then the safer option would be able to fight more battles and so, if they needed more scrap, they could use the defence they have to go out and claim it when the ship with the scrap-arm might have been too damaged.

So the scrap-arm would be the faster but more dangerous option, while a defence module would be a slower but safer option.
But with the rushed nature of the game, the slow option isn't available causing the defensive modules to lose out in the balance game.

I actually realized the fallacy of the 1.5% when I was eating dinner earlier. 15^2 permutations is 1/225, or 2.25%.

Actually, 1/225 is less than 1%, not 2.25%.
You need to stop thinking in terms of permutations. We don't have multiple options each with the same chance, we have two options with differing probabilities.
The probability of a module blocking a point of damage is 0.15, so to probability of two modules both blocking a point of damage in the same attack is 0.15*0.15 = 0.0225 = 2.25%

[Gorlom]

I think that the majority of comments on the forums discussing augments have brought up the usefulness of scrap recovery arms both in normal and easy.

Nicely done. You dodged that question beautifully



Well the scrap recovery, drone recovery, repair and weapon preigniter are all inactive during combat. (the weapon preigniter gives you one shot with each weapon at the start of combat, but is useless for the remainder after that. For that reason it is not considered active for the purpose of this discussion.) Since they are only used once per jump they use a clump benefit as opposed to the spread out benefit of augments that are still active during combat.
Because you get the benefit all at once you notice it more then the other augments benefits. But has anyone (except for the devs) actually done the math on all the augments? Has anyone theorycrafter for all the different ship setups or only for one general one?

Take the weapon preigniter for example. It is widely praised and seen as one of the most desirable augments.
It's active counterpart is the weapon autoloader which as far as I know is 15% faster reload times. The preigniter is essentially 1 extra shot per weapon per combat. The weapon autoloader is one extra shot per 7 (well 6.66666 repeating. approximately 7) shots without it. On weapon with 10seconds reload time that is 8 shots per 1 min 10seconds. on weapons with 20 that time is 2 min 20 seconds. on 6 seconds that's 42 seconds. (And this is all assuming there is no one at the weapons control. If there is the autoloader becomes even better)
In any battle that exceeds the magical number of 7 times your longest reload time the autoloader is better then then the preigniter (in the sense that it allows you to shoot more)
That being said you're unlikely to get the benefit from the longer reload time weapons in short battles against easy opponents. But what about the boss?

For that matter how much use is the scrap recovery arm once you have reached the boss?

[Maze1125]

There's more to the preigniter than you describe there.
With the igniter you can free immediately with all your weapons, potentially disabling their weapons before they even have a chance to fire them, which can then cascade into their destruction without them even firing a shot.
Without the preigniter, they could well get that first shot and disable your weapons first, causing that same cascade to happen to you. Sure, most battles don't go as decisively as I describe there, but that first bit of damage done to a ship immediately puts that ship at a disadvantage.

The value of the preigniter isn't that it gives an extra shot, but that that shot is always the first shot.