MATHS: Impact of proposed change to the Rapid Fire System.

Al_Weeks

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Dec 22, 2014
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Warning this will get a little Maths heavy.

Link to the data set.


TL;DR

Changing the rapid fire mechanics to rolling the ammo dice first and making that number of shots will result in reasonable increase in the chance of scoring at least 1 hit (1 rapid fire dice) and at least 2 hits (2 rapid fire dice).

The opposite effect is seen for more hits, your less likely to score a higher number of hits (2 or 3 on 1 rapid fire dice and 3+ hits on 2 rapid fire dice).

I'm not going to pass judgement yet in whether this is a positive or negative change. I'll let others review the data.


More in depth maths bit:

The data set is a result of a Monte Carlo simulation, which is basically getting the computer to roll dice lots of times and tell me the outcome. It's really good for modelling problems with lots of variables (aka several dice results that influence the final outcome).

Basically I got the computer to roll 10000 times for each scenario in the dataset, I could have done more but it didnt make much difference to the final results (and took longer to run each scenario).

You'll notice that because this is a statistical model some obvious probabilities look a little off. Best example is the old rapid fire method BS4+ chance of scoring 0 hits, this mathematically is 50%, but my simulation came out with 50.27%. Had I ran more runs (say 10 million) you'll see that the Monte Carlo result would get closer to the mathematical result, but I didn't want to wait that long for my scenario runs, and strain my poor PC.


This doesnt matter as 1 it's a very minor difference and 2, the important point of this model is to show the general trend of changing the mechanics, which it does well.

I'm happy to answer any questions and if people would like the data displayed in different ways then I'm happy to try to do that.

I quite enjoyed this analysis.
 
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JawRippa

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First of all, thanks for the analysis. It is nicely laid out.

This is close to what I was expecting. More than +35% chance to hit at least once (compared to not hitting at all) on BS4+ rapid fire (2) and +15% chance to hit at least once for rapid fire (1) is a very powerful boost. It seems to me that rolling to hit for each rapid fire shot would break the game, because pinning stuff would become trivial with common rapid fire weapons. N17+ autogun is basically NCE autoslugger, let that sink in.
This is slightly offset if you disallow aiming + using rapid fire, since it is slightly beneficial to pop 1 shot with aim, than suffer -1/-2 for cover and try to fire full auto at it. With rapid fire (2) you never want to aim though, just spray, you'll hit at least once almost half the time even even with BS6+ (or shooting with BS4+ into full cover).

May I ask you to test my proposed change if you have the time:
  1. rolling 2 firepower dice and doing an ammo check for every ammosymbol. How many shooting actions will it take for a AM4+, AM5+, AM6+ gun to run dry compared to vanilla?
  2. How killiness of a Rapid fire (1) weapon is affected if you roll 2 firepower dice and pick the highest, unless at least 1 ammo symbol was rolled? My napkin math says that it should be roughly the same, but probability of 2 shots is slightly decreased while probability of 3 or 1 shot are slightly increased.
 
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Thorgor

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rolling 2 firepower dice and doing an ammo check for every symbol. How many shooting actions will it take for a AM4+, AM5+, AM6+ gun to run dry compared to vanilla?
You get 10/36 chance to get 1 symbol and 1/36 chances to get 2. So your chances to fail at least 1 check whenever you shoot are 10/36*P+1/36*(1-(1-P)²) against vanilla 1/6*P, where P is the probability for the Ammo check to fail.

Chances to go OoA for each shot fired:
AmVanillaNew
4+8.3%16.0%
5+11.1%21.0%
6+13.9%25.8%

Minimum number of shots we'll be able to fire before having to reload in 80% of games:
AmVanillaNew
4+32
5+21
6+21

Minimum number of shots we'll be able to fire before having to reload in 50% of games:
AmVanillaNew
4+54
5+53
6+53
 
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JawRippa

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Minimum number of shots we'll be able to fire before having to reload in 80% of games:
AmVanillaNew
4+32
5+21
6+21
I'm a bit confused - what does "Minimum number of shots we'll be able to fire before having to reload" mean? 3 shots and Out of ammo for AM4+ seems way too harsh compared to what I was seeing in most of my games.

Warning! Napkin math.
If I understand it correctly, if we are looking for a probability of running out of ammo by turn 1,2,3, etc we need to subtstract the chance that the gun will not run out of ammo after a single shot, raised to power of the number of shots from 1. So for AM6+ it'd be: 1-(0,86)^x, where x is the number of shots.

Number of shotsChance to run out (Vanilla)Chance to run out (New)
114%26%
226%45%
336%59%
445%70%
552%78%
660%84%

So if we have 2 special weapons with really bad ammo check, one of them will have a decent chance of being available even after both have fired 4 times. Meanwhile with alternated take on ammo triggers, you'll probably start having to use back up on one of them after 2-nd shot. From my experience such harsh ammo checks lead to people refusing to take potshots with expensive guns, and only fire those when they sure that the shot will land. Also sidearms becomes a nessesity, while om vanilla you can just ignore those, since 2-3 special weapons will most likely be enough for the entire fight.
 

Thorgor

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I'm a bit confused - what does "Minimum number of shots we'll be able to fire before having to reload" mean? 3 shots and Out of ammo for AM4+ seems way too harsh compared to what I was seeing in most of my games.
It means that, in 80% of games, the weapon won't run out of ammo before at least 3 shots are fired. In other words, in 20% of games (16% to be precise), a weapon with Am 4+ will run out of ammo after the 1st or 2nd shot.
Imo, it's a good measure of what you can reliably count on, the 50% table being a measure of what you can hope will happen.
 

Al_Weeks

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It means that, in 80% of games, the weapon won't run out of ammo before at least 3 shots are fired. In other words, in 20% of games (16% to be precise), a weapon with Am 4+ will run out of ammo after the 1st or 2nd shot.
Imo, it's a good measure of what you can reliably count on, the 50% table being a measure of what you can hope will happen.

Yeah 80% confidence band if a good measure of reliiablitly.

Just to confirm this is you roll 2 firepower dice with every weapon and make an ammo check if either dice results in a ammo symbol (regardless of if the weapon is rapid fire or not?
 

Thorgor

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Just to confirm this is you roll 2 firepower dice with every weapon and make an ammo check if either dice results in a ammo symbol (regardless of if the weapon is rapid fire or not?
Yes. With the caveat that you make 2 ammo checks if you roll a double symbol, but that doesn't change much.
 
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JawRippa

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So, my proposed change for rolling 2 FP for every weapon needs a rework of Rapid Fire trait and Unstable trait. Some people could consider it being too radical and I see where they are comming from.

If I understand it correctly, if we'd decide to keep 1 firepower dice like it is right now, but trigger an ammo check on a roll of 6 (be it for regular shot or improbable shot), it'd have the same effect on ammo check frequency as rolling 2 firepower dice? But with the bonus of not needing to rewrite how rapid fire and unstable traits work.
 

Thorgor

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If I understand it correctly, if we'd decide to keep 1 firepower dice like it is right now, but trigger an ammo check on a roll of 6 (be it for regular shot or improbable shot), it'd have the same effect on ammo check frequency as rolling 2 firepower dice? But with the bonus of not needing to rewrite how rapid fire and unstable traits work.
Yes, the odds will be the same. The difference is that it will happen slightly more often to shots that actually hit the target than to those who miss. I'd rather have it trigger on a natural 1 to hit as it makes more sense (the shot could have 'missed' not because the shooter aim was not true but because the weapon jammed). Also, it feels more natural to have bad things happen on a bad roll (same reason the FW dice has the ammo symbol on 1 hit and not 3).
Depending on how the additional FP dice system was supposed to work for RF2+ weapons, it could also make a difference there.
I largely prefer this solution to rolling an additional FP dice.

Another idea would be to alter the FP so that it has 2 ammo symbol instead of one (if using the official dice, count the 'Ammo + 1hit' result as a '1 hit' and vice versa). That would make ammo rolls slightly more frequent for regular/RF1 weapons (33% instead of 30% with the 2 dice system), and much more frequent for RF2+ weapons.
 

JawRippa

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I'd rather have it trigger on a natural 1 to hit as it makes more sense (the shot could have 'missed' not because the shooter aim was not true but because the weapon jammed). Also, it feels more natural to have bad things happen on a bad roll (same reason the FW dice has the ammo symbol on 1 hit and not 3).
I agree that it feel natural for bad stuff to happen on a natural 1, but I'd prefer it to be on 6's for several reasons:
  1. Same as NCE, so scratches nostalgia itch of some players
  2. It feels better for both players, since both get something bad and good from it. Shooter feels good for landing a hit, target feels good because at least an ammo check was triggered. It is a small thing, but helps in keeping both players invested in the game when things are not going well for one of them.
  3. It makes sense for an improbable shots to land because of extreme ammunition expension.
Edit:
Another idea would be to alter the FP so that it has 2 ammo symbol instead of one (if using the official dice, count the 'Ammo + 1hit' result as a '1 hit' and vice versa). That would make ammo rolls slightly more frequent for regular/RF1 weapons (33% instead of 30% with the 2 dice system), and much more frequent for RF2+ weapons.
I think that triggering an ammo check from some natural to-hit roll would be more elegant. There is only 1 ammo symbol on firepower dice, so it'd always unintuitive to count a side without one as triggering an ammo check.

Edit x2:
I've created a poll regarding backup weapons and ammo checks. I wonder what the results will be.
 
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