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For the random pawn I am on the side of "it depends".
At 20 skill a normal colonist has 99% accuracy, a careful shooter has 99.43% accuracy, and a trigger happy colonist has 98.16% accuracy. At 30 tile range that's 73% chance to hit, 84% chance to hit, and 57% chance to hit respectively. With say a 2/2 weapon it's a 12.5% DPS loss for careful shooter (2.5 aim time, 2.0 cooldown) and a 25% DPS increase for trigger happy (1 aim time, 2 cooldown), 84*0.875=73.5 and 57*1.25=71.25. 20 skill without bionics is around the point where the DPS evens out for all three, after that diminishing returns kick in and careful shooter becomes a hard detriment and trigger happy starts to pull out ahead. Not all weapons have an equal aim time and cooldown though, like the sniper rifle has 210 aim time and 138 cooldown, which means a trigger happy pawn will out DPS a careful shooter at even lower skill than that.
The values at say 30 aiming which you can get from just 20 skill, archotech eyes and marksman command, are 99.650% for no trait, 99.725% for careful shooter, and 99.537% for trigger happy. At 30 tiles again this is 90%, 92%, and 87%, at 40 tiles it's 86%, 89% and 83%. I don't think I have to do the math here for you to realize how much of an impact the aim time difference is at this point with such a tiny difference in accuracy values. Without mods colonists can get up to around 50-60 aiming, so 30 is a pretty low bar. Shooting Specialist also makes a huge difference as you noticed, making careful shooter even worse.
But wait, there's more. Time spent aiming is time spent not being able to move, trigger happy colonists can much more easily kite enemies and stay safe in mobile engagements. Aim time also applies to more than just aiming a gun, the activation time of utility items like jump packs and the cast time of psycasts also use the aim time stat, making careful shooter significantly worse at those things and the trigger happy colonist significantly better. Trigger happy is not only the better stat at ranged DPS, but it's one of the best stats for combat focused melee colonists as well allowing them to have significantly higher mobility in combat using their jump packs (tough, jogger and trigger happy is probably the optimal melee pawn trait loadout (and no, nimble is not good)).
TLDR Careful Shooter is a negative trait and is to be avoided if you are min-maxing. It's questionably useful very early game, if you never have to be mobile in any of your early fighting, but loses all benefits by mid game and becomes a significant penalty later game, and is always just a terrible trait if you also plan to use psycasts or jump packs.
Wiki testing didn't quite include multiple weapons. Besides, pure DPS as a measurement is not exactly that useful in the grand scheme of things, when enemies take damage to various body parts and instakill is a thing.
I figured that if instakill is a thing, consistency of the shots may be more important than pure DPS gain.
And seems I was right.
It is not like all your enemies are centipedes. Vast majority of threats that you face is something human-like.
With this in mind, the notion that Careful Shooter is basically a negative trait is demonstrably false - and both are far clores in effectiveness than I expected.
Yes, there is a point where Trigger-Happy overtakes Careful-Shooter, but it basically requires specialisation and full set of bionic eye replacement - it is more just the question of high skill - you need a fully decked character.
Otherwise, both skills are very much surprisingly similar in effectiveness.
It's the opposite of what you figure though. Consistancy of shots or higher accuracy does not mean more insta kills. Accuracy does not correlate to better body part targeting. The DPS difference between the two is related to number of shots fired over a given period of time and how many of them hit. Trigger happy shoots more shots in the same period of time and of those shots fired more hit than careful shooter is able to put out and hit with. Objectively trigger happy becomes the better trait as soon as chance to hit multiplied by aim time (firing cycle) becomes higher than careful shooters chance to hit multiplied by aim time. There are no hidden factors involved.
Nothing about this is an absolute change in damage per shot, it's a measurement of your average damage output based on how much you're firing and how much you're missing based on your distance from your target.
I can understand the desire to empirically test information, but none of this is meaningful in any way and ignores the pertinent and useful data that is already available.
This is something I need to test still - but this is also something I mentioned when discussing my limited minigun testing - that even though the difference against single target was fairly minor, increased effective rate of fire will matter against hordes, AND against the enemies that are more resistant to damage, like heavily armoured ones, or those that have redundant body parts, like Centipedes - this is where DPS comes into play.
That being said - after reading all the opinions from years before, I was expecting a far bigger difference between the two.
There is are also couple of aspects I would need to test, but I need to figure out a reliable method tha would eliminate RNG - fights with hordes and dispersed crowds.
I suspect that Trigger-Happy will massively pull through in crowds, and that ability to switch targets more quickly will help with dispersed targets.
The point is - DPS matters if the enemy is a healthbar. And rimworld doesn't quite work like that - you can down the enemy through damage to multiple body parts, damage to the brain, neck, heard, liver - these can cause instakill, which negates DPS.
In this scenario - a weapon with low damage per shot but high dps will take longer to kill simply if the high damage but low dps weapon gets lucky.
And Careful Shooter makes these types of weapons more consistent.
Yes, Trigger-Happy will get vastly more shots over time, but also each individual shot is affected by RNG more.
In my testing - especially with legendary charge lances, before application of bionics and shooting specialist, the higher DPS of Trigger Happy didn't matter when Careful Shooters where consistently killing the targets with single shots.
Fact of a matter is - Trigger-Happy offers better DPS, this is not what I'm disputing. I'm also not trying to convince anyone it is not a better over long period of time - it objectively is, unless you are running a body purist colony - it becomes a bit more nuanced in this case.
My question was simple - how much and when Trigger Happy becomes significantly better - and the surprising result is - in short firefights, Trigger Happy is not really better until your pawns are really fully decked.
Trigger Happy gains the edge against hordes and in prolonged firefights where volume of fire has a chance to shine.
Also Urist has a point for the "DPS isn't all" part. Depending of the weapon, careful shooter can give you one or two additional hit on the first salvo which can make the difference to put down the target, allowing you to switch target immediatly when with Tigger-Happy you will have to make one full voley again on the same target, "wasting" DPS. How often it happens seems hard to evaluate.
But of course if a pawn get its accuracy so ridiculously high as described by Astasia there is a point were the positive impact of careful shooter is nothing compared to the drawback.
Misses aren't "wasted DPS" since they are already factored into the DPS numbers. You can say sometimes an alpha shot might miss with a trigger happy, but the difference in accuracy generally means it's more likely to hit than miss, and the trigger happy pawn can line up and fire their second shot long before the careful shooter. Careful shooters can also miss, it's not like they have 100% accuracy. The more colonists you have in your line the more closely to the average DPS numbers your output will be. It's not like if you have 10 careful shooters firing at max range with a sniper you can count on all 10 to hit every time, nor can you assume with trigger happy all 10 will miss. This idea of one lucky instakill with the alpha shot being an advantage only applies in, like I said before, controlled duels. Even then you can say at max sniper range with a single colonist a careful shooter has 10% more chance to hit and that might be a shot that instakills, but more likely it will not instakill and it will require two shots, it's it's more likely the trigger happy pawn will hit both shots and kill the pawn faster than the careful shooter. At moderate skill 30% of the time the trigger happy pawn might miss and the careful shooter hits, and 10% of those times the shot might hit a vital organ and kill the enemy with the first shot. Is that 3% situation really a bonus for careful shooter?
The main weapon where this type of thing might be a factor is the sniper rifle, and I don't think it's really appreciated how large of a difference in firing speeds this is. A sniper rifle has an aim time of 210 ticks and a cooldown of 138 ticks, a total of 348 ticks between shots. A careful shooter is 262.5 aim time and 138 cooldown, a total of 400.5 ticks between shots. Trigger happy has an aim time of 105 tick and a cooldown of 138 ticks, a total of 243 ticks between shots. A trigger happy colonist has finished firing their first round of shots and started aiming their second shot before the careful shooter has finished aiming their first shot. By the time a careful shooter has finished firing their second shot, the trigger happy colonist is aiming their 4th. That's why the small difference in hit chance doesn't make up the difference. And again, the sniper rifle is also the most likely weapon you will be wanting to kite with, and the faster aim time means they can back up and fire their second shot from a safe distance much more quickly.
And to cycle back to something said previously. Enemies do have "hit point bars" and DPS does matter when taking them down. There are actually two hit point bars, one is literally a total hit points where if a pawn takes more than like 200 damage total they die instantly regardless of their injuries (this also applies to colonists). The second, is pain. After something like 60 damage an average pawn will go down. Weapons like chain shotguns and charge rifles can hit this in one burst at high qualities. Weapons like snipers and charge lances become pretty bad in sustained combat because of this (beyond their poor DPS values), since they more likely need two rounds of fire to down an enemy. Snipers have a range advantage which means they are useful for other things, charge lances really don't, they are generally not great weapons to use.
You are correct here.
But, how much of a health bar you have to take down is not exactly consistent, depending on enemy - with mechanoids alone this is pretty massively varied. Smaller mechs tend to go down to vital organ shots, but centipedes and boss mechs have a ton of redundancies built in and can take the beating. And don't get me started on pawns, where we have inconsistent armour values, xenotypes and traits.
Bottom line, combat is more than just a DPS test.
Either way, Careful Shooter pulls higher dps on shooting skills up to ~15 on higher weapon ranges. The closer it gets, obviously Trigger-Happy will start getting the edge.
On skill level of 20, the difference is negligible beyond sniper weapons - which is the thing that surprised me, as I was expecting Trigger Happy to cleanly wipe the floor with Careful Shooter at this stage.
Now, that does not factor in various peculiarities of combat, especially crowds and stray shots hitting, and new target acquisition - in which case I'm fairly certain Trigger-Happy is a definitive way to go.
But for something people tend to call a "terrible trait", Careful Shooter isn't half bad.
Aye, that is something I did not think about, as I'm typically using static defences myself, and overwhelming firepower. And I generally gravitate towards weapons with fairly low aim times to start with, where that careful shooter penalties do not hinder you as much.
Still though, for basic scenario of slugging it out of cover, your basic grunt work, it gets the job done well enough until my colony is basically full of people decked fully with bionics of all sorts, which is where trigger happy blows it right out of the water.
The thing is - what harms Careful Shooter in a long run is a simple fact of diminishing returns of accuracy skill - because everage combat range is rarely bigger than ~30. And you have far more way to improve accuracy than aim time, at least before we factor mods in.
But even with mods, aim time reduction will be always useful, while accuracy increase at one point won't matter any longer.