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Usually the best all around "low skill" weapon in the game is considered to be the Heavy SMG though, it's not as accurate but spits out a lot of bullets and does fairly high damage with decent range.
I essentially have all but a few of the very last things researched, but ran into a wall regarding components. Only just recently managed to set up to make my own.
Here's a video that goes over sort of the basic performance of some of the weapons. It doesn't go into niche uses where some of them really shine though, and doesn't cover chain shotguns.
https://www.youtube.com/watch?v=fFjPzn_NNAg
I would like to point out, that regardless of everything I just said, the only guns I personally ever craft are Charge Rifles (or modded equivalent high-end weapons). Until I get high quality charge rifles I just give colonists whatever I find off raiders, and I never really pay attention to their ranged skill since it rises pretty quickly regardless of what you give them.
You want to give bad shooters reliable weapons and good shooters weapons that can make dmg faster.
Sniper rifle is a long cooldown weapon and every shot is crucial.
A rifles and pistols can shoot quite often , I think heavy machinguns are the best for bad shooters.
Shotguns are last line of defense used for stopping power , otherwise other weapons can do more dmg consistently over longer range.
Also Trigger happy want low cooldown weapons and in general are better the more skill you have to compensate for poor aim.
Careful shooter is better on bad pawns.
High skill -> long range weapon
As already said: the skill reduces the penalty per tile. On really low ranges, high skill and low skill pawns are really close together. Shotguns are really reliable on hitting and good if you can make use of the stopping power. SMGs are pretty much the best single target dps weapons on close range. While miniguns can put out a lot of dps, they have a long cd and long warmup which means there is a higher chance the enemy shoots your before you can kill it and also that if you do quick kills, your pawn is standing around longer. SMGs are less situational. There are other useable weapons but you gonna need to find your own playstyle and experiment with those probably.
You seem to have the right idea here already with skill level and range and your OP in general. For the shotgun, you can think of the game simplifying the "spread" into accuracy by what it means in real world: you hit a target reliably. They are not like normal game shotguns with cotton balls on high range and meat grinder of doom on low range. That said, they also have lower than usual armour pen in the game.
Case and point say you have a weapon with 2sec aim and 3 sec cooldown, when you Trigger happy , then you have about 1+3 = 4sec to wait between shots.
If you take a weapons with 1 cooldown and 4 seconds aim = you get 3 sec shooting interval which then leads to maximised dps.
IT sounds like you don't make the distinction between aim time and cooldown , trigger happy does not affect cooldown it affects aim time. Two separate things
Trigger happy is right out BAD on sniper rifles First it defeats the purpose of the weapon lowers it's accuracy and the gain in shots fired is minimal, because of the long cooldown that the weapon has. Sniper rifle is a abusive weapon for picking off enemies before raid happens , hit and run, it has no place on regular battlefield especially when heavy armour rolls in , it is too slow period.
Your example does not prove your point. It proves the point of gimmethegepgun since you your second example has twice the aiming time, which is why there is a big dps increase.
If you wanna compare the effectivesness with low cooldown vs high aim weapons, you have to change that exact stat for your examples. Not both.
E.g.
For the Aim:
3s aim + 2s cd will be reduced from 5s to 3.5s ,which is a 43% increase in dps.
2s aim + 2s cd will be reduced from 4s to 3s, which is a 33% increase in dps.
For the Cd:
2s aim + 3s cd will be reduced from 5s to 4s, which is a 25% increase in dps.
2s aim + 2s cd will be reduced from 4s to 3s, which is a 33% increase in dps.
Edit: Yeah I'm sorry that was mostly nonsense. Burst time is the only thing that puts aim time in front and the ratio is more important.
You see that 1s more aim time has a bigger incease than 1s less cd. Okay it's 50% more aim time vs 33% less cooldown (which is the same multiplier in 2 different directions) and both offer the exact same improvement multiplier.
Here, observe the following charts (made from A17 data, but sniper rifles haven't undergone any massive changes since, nor has the two traits).
Sniper rifle DPS (damage per second) without either Trigger Happy or Careful Shooter:
https://rimworldwiki.com/images/4/48/SniperRifleDPSNoTrait.png
Note maximum DPS is ~4.7 at 15 tiles at 20 skill.
Sniper rifle DPS with Careful Shooter:
https://rimworldwiki.com/images/b/b8/SniperRifleDPSCarefulShooter.png
You'll see the maximum DPS has decreased to ~4.3 at 15 tiles at 20 skill.
Sniper rifle DPS with Trigger Happy:
https://rimworldwiki.com/images/8/80/SniperRifleDPSTriggerHappy.png
Maximum DPS suddenly skyrockets to ~6.0 at 15 tiles at 20 skill.
and
The dps charts show that Trigger happy is inferior to Careful Shooter on sniper rifle
Sniper rifle has already long aim time, in a firefight you make few shots and it's about making those shots count
Making the already Long cooldown weapon less accurate results in poorer performance , in tests you don't have the luxury of being rushed down by meele and your pawns targeting poorly too. So aside from poorer dps the actual combat performance overall is quite bad.