Necromunda combat stats

[Eldarin]

Indeed, in much more detail than I was considering

I was just thinking of the case of a draw - if you should settle for it or go for the win.

Interesting analysis though. The more fundamental question is is it worth bothering with a parry at all?

 

[enyoss]

Interesting analysis though. The more fundamental question is is it worth bothering with a parry at all?

I think it is, although it does depend on the fighter.

For poor fighters, I think the parry is always worthwhile, although mostly you don't get the option of using a strategy - as you pointed out you'll probably only ever get to parry when you're already losing.

For good fighters the parry itself is less powerful, apart from its capability to nullify the parry advantage of weak fighters.

It's certainly never a disadvantage to have the option to parry - the more options you have in combat, even if you don't exercise them, the better your fighter.

I can't remember right now whether the option to parry is more valuable than +1WS, but I'll show some plots in an upcoming post which does give the answer.

 

[Eldarin]

The WS is more powerful, if I remember correctly, but I meant is it worth 15 points for a sword?

Say 65 points without vs 80 points with.

 

[enyoss]

I would say yes. For the extra insurance it offers on the variance or your combat score difference, it's definitely worth 15 points.

I think it's probably worth more actually, especially as from mid-campaign onwards 15 credits for anything is affordable. Just look at the situational junk most players throw their money at from the rare trade post (I've even seen people buying Grav Chutes in the past...).

 

[Eldarin]

Oh, I agree practically everything on rare trade is costed horribly and swords are less bad than most.

However, would I take 5 guys with an autopistol or 4 guys with an autopistol and a sword?

 

[enyoss]

Weapon skillz pay the bills, but playaz use their initiative...

Ok, so it's (finally!) time we looked at the relative importance of Weaponskill and Initiative on our (neglected) fighter's combat score.

This one is easy really – we've already done the work! Everything we need is already in the curves shown before... we just need a little bit of explanation on how to dig the information out.

Impact of Initiative

Firstly, we'll start by showing the same plot as before with a slight modification to represent that our protagonist, Fighter1, has a higher initiative than his opponent:

What happened here? Well, simply put, we shift the dashed line going up from +1 on the x-axis, which denotes the score at which Fighter1 wins, over one place to the left so it now goes up from 0 on the x-axis. That is, when the combat score is drawn (equal to zero), Fighter1 wins.

That's it.

For example, let's assume our fighters both have A1, so we're looking at the black curves. If they both have the same initiative, if we look where the black dotted and black solid lines cross the dashed lines at x = -1 and x = +1 we see they will each win around 42% of the time (and they therefore draw the remaining 16% of the time).

But now that Fighter1 has the higher initiative there is no such thing as a draw – he wins such occurrences with a single hit. So looking where the solid-circle black curve crosses our purple dashed line, we now see that Fighter1 will win around 58% of the time. His win-zone now just starts at x = 0.

(Note that the percent chances for all win-loss-draws, when you add them up, should come to 100%, despite what X-factor contestants might assure us regarding their capacity for 110).

So having a higher initiative than your opponent boosts your win rate by around half as much again (i.e. 1.5 * 42% = 58%... almost)! This doesn't just hold when you both have A1, it's also true when both fighters have A2 or A3. In fact, you get a similar size boost whenever your fighters have similar WS no matter how many attacks each one has. The boost is biggest when both fighters have A3, when a higher initiative than your opponent takes your win rate from 40% to 60%.

I think the size of this win-rate boost which is just down to high initiative is underestimated by most players. To be honest, I think it barely registers on most people's radar, when most of the time it's more valuable than an extra attack (assuming it's an extra attack over A2 that is). Looking back at the figure above, we see that going from A2 to A3 for Fighter1 takes us from 55% to 60% win rate. But if we have A2 and high initiative, that takes us from 55% to 70% win rate. Most people probably wouldn't get the relative importance of those two characteristics correct.

Also, I think this highlights a major flaw with the current rules for massive weapons, more so even than the associated inability to parry or loss of an extra attack. That is, if you halve your initiative when deciding who wins draws, unless you have I5+ you are effectively reducing yourself to I2 in combat, gifting a significant advantage to the legion of I3+ opponents you will face. In my view, which I like to think is pretty well informed by the nuts and bolts of the core combat mechanics, this is pretty harsh.

And just how legion are those I3 opponents versus I5+? Well, of course, I had to answer that question as well. It took a pretty cool little modelling project (the only modelling I've done so far, given that everything else here is just raw probabilities... I'll show the results in my next post along with some validation from real campaign gangs) but I found that I3/I4/I5/I6 gangers crop up in a (very rough) ratio of 75/20/5/0 during a campaign.

That's right, of all the gangers in a campaign only around 5% of them will have an initiative high enough to claw back even a lowly a draw if armed with a massive weapon. The other 90-95% of ganger level fighters are just surrendering a lot of combats they shouldn't be.

I plan on turning my attention to that in the Community Edition thread at some point.


Impact of Weaponskill

This one is very similar to what we did for Initiative. This time though, instead of just moving one of the dashed lines, we shift both of them to the left by an amount equal to the combat bonus enjoyed by Fighter1:

In the example shown, it could be that Fighter1 has +4WS over Fighter2, or he could just have +3WS and have charged that turn. All that matters is that Fighter1 has an extra +4 combat score bonus to add to his score, above any bonuses that Fighter2 is getting.

For example, if Fighter1 has A1, looking at the solid black curve and seeing where it crosses the relevant black and purple vertical lines, we go from a win rate of 42% to a whopping 89% when we have +4WS. I'd buy that for a dollar.

Also, although not exactly obvious from this busy plot, one other thing can be extracted from this figure immediately. That is, +1WS is always better than having higher initiative than your opponent (all else being equal).

Why? Well, imagine a Fighter1 with +1WS advantage. That means we just shift the vertical dashed lines one point to the left. This means the Fighter1 win-zone now starts at 0 on the x-axis – this is the same starting point as that given in the previous figure for a Fighter1 with high initiative. That is, both indicate that the win zone for Fighter1 is now traced up from 0 on the x-axis rather than +1.

It gets even better for our +1WS Fighter1 though – he can still steal the probability which is reserved for draws, i.e. he can push the vertical line denoting his win zone even further to the left, so it would now go up from -1 on the x-axis! And if he has lower initiative than his opponent? Well, in that case the Fighter2 dashed line would move back one point to the right (indicating that he has now turned draws into wins and expanded his win-zone on the left), and we just end up with the exact same situation as the first plot in this post.

To summarize all that:

• A fighter with +1WS is better in combat than a fighter with +1I.
  
  
• A fighter with +1WS and low initiative is exactly the same in combat as a fighter with just high initiative.

• A fighter with A2 and high initiative is better in combat than a fighter with A3+ and low initiative.

• Players often underestimate the value of initiative in combat, giving high initiative fighters the element of surprise.

• (Here, low initiative would be less than 3, and high initiative would be 5 or more)

So there you have it. A complete framework for figuring out the exact combat value for fighters with any number of attacks (up to 3 anyway), and any WS or I advances. I'll also post up all the curves for any combination of Fighter1 and Fighter2 attacks for reference.

Next up? Well, now we've got a framework for finding out our exact probabilities of winning combat, we can develop our parry and combat skill strategies...

 

[Eldarin]

This is nice work, I'm pleased that it's agreeing with my figures so I've got a bit more faith in my own!

In mine I only worked out chance to win, so parry was always if drawn - I imagine yours will have more detail, so I look forward to reading.

I also look forward to the discussion moving to the CE thread

 

[Mamutera]

Hey, I enjoy every second of your analisys.

In another thread I proposed to make Combat Master skill more powerful to help CC strategies. A lot of people complained about CC being too double edged. My proposal was that Combat Master could reduce opponent's attack skill to 1 to make the charge more reliable. Considering your data, do you think it would be too overpowered?

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[Eldarin]

Does that not just duplicate body slam without the required strength test?

 

[Mamutera]

Body slam limits opponent's WS to 1, which at this point I should be able to compare to limit A to 1 but I need to look up the graphs. I am not sure what you mean by duplicate, if you mean the use or effect then my ansmwer is the skills involved belong to different skill lists, making CC more reliable to almost all houses (combat skills) and helps a little bit goliaths if convined with body slam (muscle skills). Ok maybe the two skills stack is too powerful.

 

[Eldarin]

Ah, no, I just read attack skill as weapon skill. Ignore me

 

[enyoss]

Mmm. Limiting A to just one is quite valuable but it does step on the toes of the massive weapon, making that even more limited use than it is already.

That ability is actually about the only saving grace of the massive weapon in my view.

I'm really not sure what to do about Combat Master. As it is it can be very powerful for the right fighter but is just too situational to elicit anything other than a resigned sigh when you roll it up.

 

[Eldarin]

It's probably an inappropriate place to discuss it - but I'd just change it to allow them to follow up and fight an extra hth combat.

Same kind of ethos of multiple opponents - but in a less almost-never-useful way

 

[Mamutera]

Mmm. Limiting A to just one is quite valuable but it does step on the toes of the massive weapon, making that even more limited use than it is already.

That ability is actually about the only saving grace of the massive weapon in my view.

I'm really not sure what to do about Combat Master. As it is it can be very powerful for the right fighter but is just too situational to elicit anything other than a resigned sigh when you roll it up.

I see your concerns about Massive Weapons. Maybe the solution could be to rollback to ORB where combat draws are automatically lost, but instead of giving +2 force it could give +3. This way massive weapons would take gangers one strength increase away from being able to use high impact weapon rule (NCE) which would be cool. Fluff wise it would justify the word "massive".

This way Combat Master could reduce opponents A to 1 and be more useful while rolling a 1 on the skill list would be exiting. Well I guess we can discuss all these topics when you bring up the massive weapons problem in the Community Thread.

 

[enyoss]

I see your concerns about Massive Weapons. Maybe the solution could be to rollback to ORB where combat draws are automatically lost, but instead of giving +2 force it could give +3. This way massive weapons would take gangers one strength increase away from being able to use high impact weapon rule (NCE) which would be cool. Fluff wise it would justify the word "massive".

This way Combat Master could reduce opponents A to 1 and be more useful while rolling a 1 on the skill list would be exiting. Well I guess we can discuss all these topics when you bring up the massive weapons problem in the Community Thread.

Yeah, probably best to discuss it in its own thread, as I think there is plenty to discuss! For what it's worth, I do have a couple of my own ideas surrounding Combat Master and how to make it more characterful and useful. One is that it allows you to choose which result to keep when rerolling one of your opponents (e.g. through Parry or Deflect) or your own dice (e.g. through Counter Attack). Maybe doing that for as many rerolled dice as you have attacks? I think it would then be the best skill on the table though!

 

[enyoss]

Unlucky number sevens...

We've all been there. The juve or ganger who just keeps getting 7's on the advance table.

You self-consciously laugh about deploying your meanest fighter when you place him on the table, to the politest of smiles from your opponent. But the joke is on you. He's a lemon, and everyone in the campaign knows it. While his fellow juves have flown the nest and grown into lethal brawlers and snipers, there he is, at the back, still on heavy meatshield duty as his experience clocks over to the 30s, 40s, 50s, as out of place in his role as a 17 year old at Legoland.

You live in perpetual fear of a successful leadership challenge, though you secretly court the uprising so your leader can put him out of his misery once and for all.

Such is the curse of the serial 7-roller.

At least, so I thought until recently. Then I started looking at these combat probabilities, and I'm starting to view the humble 7-roller in a different light.

As discussed in my last update, I think the importance of initiative in combat is undervalued by players. I don't want to speak for or about the community (but I'm going to do it anyway), but I think this is due to two factors:

a) Players just don't appreciate the potential impact it can have on combat.

b) I think players probably don't appreciate how common, or uncommon, initiative advances are. Even if you understand the impact of initiative on combat, it's hard to read much into that if you don't then know how common initiative advances are (e.g. I know that high initiative helps a lot in combat but I have a fighter with I4... what does that mean for me?).

For (a), I hope my last update started to redress that a bit. When I start talking about parrying strategies a bit more in a moment it will become even more clear (hint: parrying shifts a lot of a the probability from loses to draws for a fighter, which doesn't actually help you a lot if your opponent's initiative is higher than your own).

As for (b), well that's where I'm going now.

Without going into too much detail, here is my approach:
- Given my fighter has an advance, I know the probability that she will get an Initiative advance (it's the 1/6 chance of rolling a 7 on 2D6, followed by a 50:50 chance of getting Initiative over Ld, so a 1/12 chance overall). There is a caveat to this (see below) but it's a good approximation.
- But... that's just for one fighter, and assumes she has just the one advance. What if she has many advances?
- So... we have to model the probability that our fighter has 0-N advances. That is, how many fighters in our campaign have 0 advances, how many have 1, how many have 2 etc.
- But... for the same amount of experience gained, juves advance faster than gangers. What do we do about that then?
- But... gangs have a mix of gangers and juves, so how do we blend this all together?

So that's what I'm going to do here.

This differs from what I've done so far in this thread in one major way: this will be a model. So far, everything has been exact - it has been a pure combinatoric analysis of all possible outcomes in a combat (from 6^2 = 36 outcomes for two A1 fighters facing off, up to 6^8 = 1679616 outcomes for two A4 fighters). This time though, we need to make some assumptions. While there's no guarantee the results are 'correct', I've tried to quantify uncertainties to give conservative estimates, and will validate against real campaign data.

Anyway, the assumptions:

- Assumption 1. No advance leakage. This is the caveat I mentioned before. What does it mean? Well, advance leakage happens when you cap out one characteristic and any further advances to that characteristic 'leak' over into the other characterstic advance it is grouped with. In this case, if we have capped out our Ld we will be forced to increase Initiative instead. This means the probability of getting an Initiative advance isn't exactly 1/12, but when you do the full mathematics it comes out so close it doesn't really matter.

- Assumption 2. Distribution of advances. That is, how many fighers have 0 advances, how many have 1 etc.. I'm going to model this in 4 ways.
1) The first assumes a uniform distribution, so we have equal numbers of fighters with 1 advance, 2 advances etc.
2) The second assumes a modified normal distribution, so we have more fighters with a few advances compared to those with none or many.
3) The third assumes that we are in the early stages of a campaign and all fighters have one and only one advance.
4) The fourth assumes that we are in the late stages of a campaign and all fighters have reached 101 experience (i.e. 6 advances for fighter who started off as a ganger, and 10 for a juve). These last two assumptions will help quantify our uncertainty and give conservative estimates.

- Assumption 3. Distribution of gangers and juves. That is, in our campaign, how many fighters started out as gangers compared with how many started out as juves. For simplicity I'm going to assume 2 gangers to 1 juve, although the results don't change much if you go 3:1 or even 1:1.

- Assumption 4. No injuries, we're just interested in advances here. Any appeals to include partially deafened injuries will fall on deaf ears.

- Assumption 5. No heavies or leaders. I am only interested in your unwashed masses of gangers. Leaders have their own niche and skill benefits which set them apart, so we'll leave them out. As for heavies, my main motivation here is combat effectiveness, and we all know that chasing down that heavy into combat like a lion catching a tubby panicking gazelle is probably going to be worth it despite any feeble high initiative protests he might make.

- Assumption 6. We assume that fighters here don't have advances above 101 experience.

So, putting all that together, we get the following distribution of Initiative advances for fighters in a campaign.

What means what on the figure?

- The blue points show what percentage of the gangers in our campaign fall into the 0/+1/+2/+3 initiative advance groups.
- The green shows the same, but for juves. Note that juves are more likely to have more initiative advances than gangers at any point in a campaign.
- The red combines the two in a ratio 2G:1J, to get overall percentages for any generic fighter in a campaign, no matter what level they were hired at.
- For each of the above, the circles show numbers calculated when we assume fighters are equally likely to have any number of advances. The squares show numbers calculated when we assume fighters are more likely to have a few advances, and less likely to have lots or none.
- The grey area marks out the extreme ranges. "Early" gives numbers calculated when all fighters have just one advance. "Late" gives numbers calculated when all fighters in the campaign have reached 101 experience (but no higher! I told you it was a model). Roughly speaking, these mark out how high or low we could ever expect the number of fighters with 0/+1/+2/+3 initiative advances to go over the course of a campaign.
- The dashed line shows a mid-campaign rule of thumb which is fit to the data.
- The yellow triangles show actual data from two mature campaigns I'm currently playing in. There are a mix of gang ratings included, but gangs who have played only one game are excluded (they would unfairly bias the results towards zero advances). As I'm ignoring injuries, I just counted the number of initiative advances for a fighter even if they were partially deafened. In case anyone was interested, the campaigns have a total of 141 fighters which went into getting these numbers.

I was actually pretty impressed with myself (that happens a lot, mainly because I have to congratulate myself for performing everyday tasks most people can do without thinking, but this time I actually earned it) that the model predicts the real campaign data pretty well. Ok, it's mainly driven by that 1/12 probability I had no control over, but we couldn't get these results without making those assumptions as well.

Anyway, looking at the rule of thumb, roughly speaking 70% of our fighters will have no initiative advance at all, 25% will have +1I, 5% will have +2I, and an insignificant number will have +3I.

Put another way, seeing as everyone starts out with I3, this means that if my fighter has Initiative 4 he will probably win around 70% of his drawn combats, draw 25%, and only expect to lose around 5%.

In the very early stages of a campaign this would become 90/10/0/0, and in the late stages 55/35/10/0.

Still, one thing becomes clear. If you have I5 in a campaign, at any stage, you can be quite confident that you will win around 90%-95% of any drawn combats you encounter. Not bad, eh? And if you have I6 then relax in the knowledge that there are probably only a couple of other fighters out there who can challenge your supremacy.

On the other hand, if you have I2 you might as well take a massive weapon - parrying and getting more drawn outcomes probably isn't going to end too well for you anyway. Cling to that axe with both hands and hope for the best.

Anyway, I couldn't have predicted those results (I actually thought there would be far more I4 fighters in both the model and the campaigns I'm playing in), so I'm hoping at least some players will also find it useful.

 

[TakUnderhand]

Thank you! This stuff is pure gold.
My high I gangers are losing their basic weapons and getting two pistols, right now!

 

[spafe]

That sa very interesting and useful write up about Int advances..., I've always found them useful, and liked getting a smattering of them across my gangs but never realized they were so good in combat too, I love them just for the ability to safely go up higher and escape pinning better!

 

[enyoss]

Thanks for all the encouraging comments . There's been quite a bit of recent activity on some other threads surrounding combat outcomes (including @sebwiers nifty simulation tool) including rules tweaking etc., so hopefully this might add something to that discussion.

In the meantime, although I've already discussed it a few posts back, I added the following parrying strategy to the others I listed a while back:

Escher-max Strategy

A modification to the regular Escher strategy which optimally maximizes the difference you win by. As it doesn't optimize our number one priority of simply winning, I'm not calling it 'optimal', ergo the 'max'. Suitable for the same kind of fighter who would use the Escher strategy.
- Always parry an opponent's 6
- Always parry an opponent's 5
- Parry an opponent's 4 if he has no 4's on his other dice, otherwise do not parry
- Never parry a 3 or lower

 

[enyoss]

The story so far...

Before showing the results for various parrying, deflect, and counter attack strategies, I thought it might be a good idea to summarize everything which has come up so far.

Plus, there are currently quite a few H2H rules discussions going on elsewhere on the forum, so if a summary is ever going to be of any use it's probably now.

So, the following plot shows all possible combat win/lose outcomes for combats involving knives, clubs, or massive weapons (i.e. not swords or chains), and where neither side has any combat skills (apart from Combat master, which still works within this framework). That's right - up to A3 for each fighter, this covers all possible outcomes within that remit, including any charge bonuses, WS advantages, massive weapons, initiative bonuses, the lot. I didn't bother to show A4 as it doesn't really add much – A4 combat nerds are pretty rare, and if you use the A3 curves you'll get a pretty similar result anyway.

How to interpret the plot? Let's assume fighters who are identical to begin with, apart from the number of attack dice they roll. Your fighter is Fighter1 - root for him.

First, look up the curve which corresponds to the number of attack dice your fighters are rolling. In multiple combats, only consider the two fighters who are actually fighting. We'll factor the other fighters in in a moment.

Then, look up from x=+1 on the x-axis (dark grey dashed line). The value of the curve here is the probability that your fighter wins, i.e. P(Fighter1 wins).

Then look up from 0 on the x-axis (the other dark grey dashed line). The value of the curve here is the probability that your fighter wins or draws, i.e. P(Fighter1 wins or draws).

Then:
1) P(Fighter1 wins) we already have
2) P(draw) = Probability of a draw = P(Fighter1 wins or draws) – P(Fighter1 wins)
3) P(Fighter2 wins) = 1 – P(Fighter1 wins or draws)

So, there you have it - the exact probability that each fighter will win, or that the combat will end in a draw. Well, for identical fighters at least.

For fighters who aren't identical? We talked about it a bit already, but seeing as this is a summary here we go again...

1. Calculate any bonuses your fighter has over the other fighter, e.g. WS advantages, charging bonuses. For example, if Fighter1 has WS4 versus Fighter2's WS3, and Fighter1 also charges, they would have a +2 bonus.
   
   For the number of bonus points you have, let's say N, instead of looking up from x = +1 to find your win probability we move to the left and look up from x = 1 – N instead (if N < 0, i.e. Fighter2 has the bonus, we move to the right instead... oh dear for Fighter1). Same story for calculating the probability of winning or drawing: just move to the left and look up from x = 0 - N instead of x = 0. Once you've done this, just recalculate the win/draw probabilities for each fighter as before but with these adjusted inputs.
   
   
2. If either fighter has higher initiative than their opponent, they add P(draw) to their winning probability and there are no draws at all.
   
   
3. For multiple combats, take all bonus attack dice into account when selecting which curve to look at, and just add any multiple combat WS bonuses to those calculated in step (1) above. If it rears its head, Combat Master can just be factored in when doing this. Also, if a massive weapon reduces one fighter's attacks then take this into account when selecting your curve.

If using this for gang planning or rules evaluation, rather than in the heat of battle, then it becomes impossible to know exactly who will win draws etc., but the following rules of thumb usually work:

1. If your fighter has I4, then assume you will have highest initiative and win draws 70% of the time, i.e. as a rough guide add 0.7 * P(draw) to P(Fighter1 wins), and the remaining 0.3 * P(draw) becomes the corrected P(draw).
   
   
2. If your fighter has I5+, then assume you will always have highest initiative and win draws – add P(draw) to P(Fighter1 wins), and set the corrected P(draw) to zero.
   
   
3. If your fighter has a massive weapon and I4 or lower, then assume you will always lose draws. No matter what your initiative, assume you will never win draws outright.

When written down like that it sounds more complicated than it actually is. But if you work through an example or two it just becomes second nature.

In any case, those are the numbers for all possible combats involving no exceptional rules. I think it's quite nice that one figure can show all that. The following two plots expand on that a bit and give equivalent numbers for combats where Fighter1 has a chain, and combats where Fighter1 has the Feint combat skill (or Fighter2 has those benefits... just swap the win/loss probabilities if that's the case):




The clamour from the community for those plots was hardly deafening, but there you go. Producing similar plots for parry, deflect and counter attack is also pretty straightforward once you know what strategy to use for those skills (and make no mistake - the strategy you use for those can really matter), although thanks to those same strategies it's impossible to factor in all possible WS and Initiative bonuses on the same plot like we did above. I'll just make plots for the most common cases, which should cover 90% of the stuff we could ever care about.

Anyway, now those summaries are up, it's time for a proper treatment of those Parry, Deflect and Counter Attack strategies...

UPDATE: Actually, what the hell, you can actually do this for the Escher family of parry/deflect strategies and still incorporate all those WS, Initiative and other bonuses just like before. So here are results for the best of that family of strategies - the "Escher-Max" parry, and the "Escher-Max" deflect. This should give you some indication of how much the strategy you choose can impact your outcome. Happy Valentines day my lovelies: