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Fighting the Lizardmen - Leadership Rolls 
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Warrior

Joined: Mon Mar 29, 2004 2:22 pm
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Mightypeon wrote:
Some Additions:
1: All examples assumed onmarked Saurus Warriors.


True, but it's the same numbers for spear + shield + quetzl, which is another probable case. So saying that the probability results aren't valid based on just that is a bit off base.

Quote:
In my experience, the marking of Quetzl is the most propable.
The stats are signifcantly tweaked as the LZM Chance to pass armour saves agasint CoKs doubles.


Well, it moves from the 4+ (assuming hand weapon and shield) to 3+ base saves - which in the case of a charge moves the base probability to wound from .37 to .30. The chance to make armor saves doesn't double ... the entire analysis is based on first turn results only.

Quote:
In addition, some posters had very strange situations which do not happen in a normal battle field (unless you are playing CoS).

For instance?

Quote:
A) The CoKs in the Flank situation: This is rare. The only way this is goign to happen is by breaking the LzM flanks, these flanks tend to be protected by Skink+ Kroxigor formations.


Sorry, I disagree. I've blown through Salamanders to get to the flanks and rear, skinks, etc. You can also hold up a unit of Saurus with Black Guard, or frankly any charging unit to allow you to move to the flanks. Sure, a good player will guard them as best they can, but it's not that hard to get a flank charge off on a slow opponent with fewer units.

Quote:
I will just present some averages:
{snip}
.
.
.
Inregards to a Hydra banner, if you have a Battle standart I have a Scar vet who has 4 S7 attacks.

Somehow I thought you were a Lizardman player from the tone ... ;) The responses I've had from other players here have been far more positive even when making negative (but constructive) feedback.

Quote:
In addition, You Battle standart bearer is a significantly softer target that the reast of the unit, so that I will get an additional dealt wound agasint him.


I'll refrain from making a response to this ... someone else can point out the obvious to you. Or not.

Quote:
Taking your own characters into account while not considering the significantly stronger LZM ones is self illusion.


And when was this done exactly? I stated at least once (if you had bothered to read the thread) that characters and magic items weren't being considered in the probability analysis - only the individual units. Part of the reason was because I predicted a response just like the one you are making. :) I find the "my character can beat up your character" type of discussion rather uninteresting and rather pre-schoolish.

I think this will be my last response to negative posts from the Lizardman community players since there doesn't seem to be any point in discussion. I think anyone who did a critical analysis of the post would realize that I was pointing out that a block of Saurus was a unit to respect in the upcoming campaign and needed to be handled with careful tactics -- with an analysis to the probability of success for a given case. If you are missing that point, there's not much that I can do about it.


Tue Apr 27, 2004 5:45 pm
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Slave (off the Altar)
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Just some data :)

For the example of Mightypeon described above, the chances for wounds caused by DE look as follows (as usual, in %).

Not less than 1 Wounds : 98.89
Not less than 2 Wounds : 93.17
Not less than 3 Wounds : 79.31
Not less than 4 Wounds : 58.35
Not less than 5 Wounds : 36.16
Not less than 6 Wounds : 18.67
Not less than 7 Wounds : 8.01
Not less than 8 Wounds : 2.85
Not less than 9 Wounds : 0.85
Not less than 10 Wounds : 0.21
Not less than 11 Wounds : 0.04
Not less than 12 Wounds : 0.01

Note that this table takes into account ALL attackers - Knights, CO, Riders and steeds. BUT I'm not 100% sure how the blessing of Quetzl works; the calculation was made with the assumption of Lizzzie basic armour save increased to 3+. If it is wrong - please let me know

As it is, the table basically means that there is a good chance that all charging DE together will cause 3 wounds, and a decent (but far from guaranteed) chance that sauri would suffer 4 wounds. The rest is less likely.
Chances for causing above 12 wounds are next to zero, so I didn't post them.


May Hoeth guide our ways...
SeekingOne

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Wed Apr 28, 2004 12:55 am
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Slave (off the Altar)

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*LMAO*

Heh, a few things to start off with. First, I am a University student, majoring in Physics, with a minor in Math (concentration in stats). This thread absolutely tickles my fancy. I came into the thread thinking some sweeping comments would be made about Ld tests, and breaking them in combat. Low and behold, I find stats. The exact same stats I did while in the shower a week ago:) Oh, and my numbers line up perfectly.

I haven't really taken the stats I do to the extremes presented here, mainly due to time constraints, and nothing else. I have often wondered the probabilities behind my attacks, and knowing when I get lucky. I k,now when I get lucky, usually, and my stats are more sound than anyone elses (that I speak with). To all the ppl who say stats are irrelevent in WH. True, we are dealing with such small scales that predictability isn't one of the high points. However, it adds to the realism. We know that (in war) he can likely run over someone if we are mounts and they don't have a pike. But maybe they just got a pep speach, and really want to die. It happens, although you should run through them like a knife through hot butter, you don't. That's what this is all about. Taking the randomness of RL and putting it in a game. That being said, you still know when you should be able to kill someone, and that's what we are doing.

Zedar -> (From Belgariad perhaps?) Thank you! I have, for no long been puttiung up with ppl who tell me that states are crap. Thank you for doing them anyway! I wasn't all that interested in the Ld, since I've done it all myself anyway, but it was cool to know I was right:) In regards to the stats with the breakage. THANK YOU! I played a game Vs lizzies last knight, I forces 4 break test on a Ld of 4, he passed them all, and we ended up drawing =/ All of your mistakes, that were more obvious, have been corrected by know, so kudos for keeping us informed, and keepign up with the topic. I also wish to thank you for leaving out charcters. Although it makes things interesting, sometimes interesting isn' t way to go. I like your algorithm, and your way of explaining things, however, there are those of us who are indeed intested in more particulars, such as myself. I want to know a little more depth, and I am definately not scared by formulas or words. (And btw, I would like to see you collapse Schrodinger's wave eq'n :)) I find these stats VERY useful, especially the thouroughness with which they were (eventually) done. It is very interesting, indeed, to note the benefit of a flank over the rear. This is even more noticable in a unit 24 stron (6x4). Rears are not always better :) Thank you, also, for dealing with (Mighty) useless posts apropriately. You report is a non-biased as I wish to see it:)

SeekingOne -> I think that I may appreciate your method a little more over Zedars, though I think that, as of yet, it is slightly lacking rigourousness. I hate (and love) Bernoulli for what he did to (and for) us. But that's beside the point. You did indeed calculate the blessing properly, as it gives +1 to thier scaly skin (in effect a 5+ base, as opposed to 6+).

I wish to thank both of you for the calculation of the champion, for I rarely feel justified taking him. Very expensive point cost, though in this casr, with the attacks being so powerful, and frontage being limited, it is worth it. However, there are often times when the % of attacks the champion adds in not wirth the % in point increase (warriors, corsairs). I will likely post a little more later, but as of yet, this is all I really wanted to say :)

Thanks one again!

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Wed Apr 28, 2004 1:39 pm
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Warrior

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Lucius,

Thanks for the kind response. It's Zader though, not Zedar. ;) I think that most of the details of how I've made are in the various posts in the thread, but if you have any particulars I'd be glad to answer them. I would like to point out though that the formula SeekingOne gave is mathematically identical to the alogrithm I'm using - in fact, I'll probably wind up replacing that section of my code with it. I'm glad he pointed it out since it's something that I had forgotten back when I was in school 14 years ago. I'll leave it to him to give you the proof, since I still haven't started looking for any of my old textbooks. ;)

The next step after calculating the individual probabilities is just combining them together; whether it's just the riders and mounts or vs. the opponent. Again, I'm just doing this by alogrithm - calculating the individual probabilities for all the possible outcomes and then adding/subtracting the CR modifiers. I can post code snippets if anyone is interested. Unfortunately my work schedule has been a bit hectic, so I haven't had a chance to look at further refinements to the code other than for a few specific cases - like adding the modifiers for S. Musk, Killing Blow, Poisons, etc. I still need to add code to handle multiple attackers from the same or different directions - I might get that done this weekend. (I think this would be useful for modeling MSU/MSE). I still might look at tying things into database files and doing HTML output so folks can model combats as they like, but that's for the future.


Wed Apr 28, 2004 4:23 pm
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Trainee Warrior

Joined: Tue Feb 03, 2004 6:22 pm
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1: I would like to excuse myself if I sounded offensive.

2:@ Zader The response in regards to the hydra banner/ characters was not aimed at you but at the persons who brought up this matter.
Furtherly I have to admitt that reading the entire post in one stroke can lead to situations where one starts to confuse posters.


@ Saurus with Spears: Someone did a very extenisve statisical analysis about Spear Saurus warriors, it showed that they are inferior to HW+Shield in almost all cases. I just dont remember the site...
They are rarely seen in the current Lizard ruleset which is the first one that favors the hand weapon wielding Saurus by the way.
In an attempt to simplify this matter: Agasint most enemies Speer Saurus warriors lose one Warrior more in hand to hand, as Saurus warriors almost always strike last (unless they charge, where they cant use their spears) they only get 3 additional hth attacks, in exchange for a +1 CR boon for the enemy because the foe has killed an additional Saurus. These 3 bonus attacks would have to kill one foe in order to get only even with the cheaper HW+ shield Saurus.

You can propably leave Spaer Saurusses out for the Calculations.


Wed Apr 28, 2004 5:09 pm
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Slave (off the Altar)

Joined: Mon Sep 01, 2003 2:12 am
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I have a hard time believing that Saurus, if taken 6 wide (which I know was not done here, but then again, CoK don't hit the front) that they cannot do a little better. You are getting 6 "additional" attacks. So, for the 'one more' that would be killed statistically, you would be getting 5 additional attacks. Seems to me like, at str 4, this could do enough damage. Now, I am not arguing the validity of spears, nor am I trying to nay-say you Mighty. It's just... odd. And thank you for apologizing.

Zader -> Figured you just had a spoonerism stuck in there. Yes, I undestand both metheds are equivalent, but there are not identical. Lagragnian and Newtonian mechanics are similar, just one is WAY more useful, and adaptable. 14 years outa school eh? I'll probably be back in school in 14 years:) Another thing that this proves though, is that sometimes a whole swack of points is worth that back rank!

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Thu Apr 29, 2004 11:28 am
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Warrior

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Lucius wrote:
I have a hard time believing that Saurus, if taken 6 wide (which I know was not done here, but then again, CoK don't hit the front) that they cannot do a little better. You are getting 6 "additional" attacks. So, for the 'one more' that would be killed statistically, you would be getting 5 additional attacks. Seems to me like, at str 4, this could do enough damage. Now, I am not arguing the validity of spears, nor am I trying to nay-say you Mighty. It's just...


Edit: Oops, I missed the spear part when I ran the below numbers ... the comparison at the end is just flank charge and rear charge against the expanded 6 wide frontage. I'll run the numbers for the spear case later today.

Quote:
Yes, I undestand both metheds are equivalent, but there are not identical.


Well, on the last point, I'm going to have to say that you are arguing semantics. ;) The Bernoulli Trials aren't an approximation, it's the exact binomial probability distribution. If you have a textbook handy you can probably find the proof reduction somewhere - I'm at work so I don't have anything handy. I am, admittedly, doing things the long way at the moment - but the formula SeekingOne gave does provide exact results for the individual distributions. If anything it's more accurate than my method since it's less subject to rounding errors. I'll be switching to it for at least the individual probability distributions when I can ... been a long week at work this week.

Quote:
Another thing that this proves though, is that sometimes a whole swack of points is worth that back rank!


The 6 wide frontage in comparison to the 5 wide frontage appears to be that the additional number of probable attacks back shifts the case of being charged to the rear slightly to the favor of the Saurus defenders when compared to the flank attack case. While there are additional attacks, the heavy armor save of the Cold One Knights keeps the probability of a wound being delivered back at only .1111 per attack. The probability shift of the additional attacks are also counterbalanced by the additional -1 CR that they are starting with due compared to the flank attack case. So the final result is that in the case of the 6 wide frontage, the defenders have a slight advantage over the flank attack case, but the difference is relatively trivial for this particular case. I think the advantage however would be considerably different if they were attacked by our lightly armored infantry units ...

Here are the numbers:

rear:
Code:
=====================================================
...Attack is to the rear, +2 to CR.  (2)
...Attacker has standard, +1 to CR. (3)
...Defender has standard, -1 to CR. (2)
...Attacker has 2 Ranks, 1 modifier to CR. (3)
...Defender attacked to the rear or flank, no rank bonus.
...see table below for outnumber bonus
=====================================================
Combat Results table (includes CR modifiers)
=====================================================
0 CR result -> (...Defender Outnumbers, -1 to CR)  2.31%
1 CR result -> (...Defender Outnumbers, -1 to CR)  6.05%
2 CR result -> (...Defender Outnumbers, -1 to CR) 12.13%
3 CR result -> (...Defender Outnumbers, -1 to CR) 18.55%
4 CR result -> (...Defender Outnumbers, -1 to CR) 21.47%
5 CR result -> (...Defender Outnumbers, -1 to CR) 18.62%
7 CR result -> (US is tied, no outnumber bonus) 11.98%
9 CR result -> (...Attacker Outnumbers, +1 to CR)  5.61%
10 CR result -> (...Attacker Outnumbers, +1 to CR)  1.99%
=====================================================

flank:
Code:
=====================================================
...Attack is to the flank, +1 to CR.  (1)
...Attacker has standard, +1 to CR. (2)
...Defender has standard, -1 to CR. (1)
...Attacker has 2 Ranks, 1 modifier to CR. (2)
...Defender attacked to the rear or flank, no rank bonus.
...see table below for outnumber bonus
=====================================================
Combat Results table (includes CR modifiers)
=====================================================
0 CR result -> (...Defender Outnumbers, -1 to CR)  3.49%
1 CR result -> (...Defender Outnumbers, -1 to CR)  8.93%
2 CR result -> (...Defender Outnumbers, -1 to CR) 16.51%
3 CR result -> (...Defender Outnumbers, -1 to CR) 22.19%
4 CR result -> (...Defender Outnumbers, -1 to CR) 21.22%
6 CR result -> (US is tied, no outnumber bonus) 16.95%
8 CR result -> (...Attacker Outnumbers, +1 to CR)  7.09%
9 CR result -> (...Attacker Outnumbers, +1 to CR)  1.99%
=====================================================

front:
Code:
=====================================================
...Attacker has standard, +1 to CR. (1)
...Defender has standard, -1 to CR. (0)
...Attacker has 2 Ranks, 1 modifier to CR. (1)
...Defender has 4 Ranks, 3 modifier to CR. (-2)
...see table below for outnumber bonus
=====================================================
Combat Results table (includes CR modifiers)
=====================================================
-5 CR result -> (...Defender Outnumbers, -1 to CR)  2.31%
-4 CR result -> (...Defender Outnumbers, -1 to CR)  6.05%
-3 CR result -> (...Defender Outnumbers, -1 to CR) 12.13%
-2 CR result -> (...Defender Outnumbers, -1 to CR) 18.55%
-1 CR result -> (...Defender Outnumbers, -1 to CR) 21.47%
0 CR result -> (...Defender Outnumbers, -1 to CR) 18.62%
2 CR result -> (US is tied, no outnumber bonus) 11.98%
4 CR result -> (...Attacker Outnumbers, +1 to CR)  5.61%
5 CR result -> (...Attacker Outnumbers, +1 to CR)  1.99%
=====================================================


Thu Apr 29, 2004 12:35 pm
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Trainee Warrior

Joined: Tue Feb 03, 2004 6:22 pm
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@ Lucius The point is, with Spear Saurus you would get only 4 additional attacks (6 attacks for the 6 Saurus in the 2. rank, -2 attacks for one saurus morethat died on the charge). These 4 attacks have to make one kill to get even with normal Saurus warriors, they would have to kill 2 in order to surpass them.
If an enemy is so weak that he cant take advandatge of the weaker armour, well the Saurus are not goign to need spears for this.

4 attacks on WS3 will only hit two times (If Saurus are fighting Enemies with WS2 chances are high that they wont need spears anyway), they will propapbly wound on a 3 and the enemy is goign to have some kind of save.
Against decent enemies the spears wont cut it.

The big difference between Saurus Spears and other Spears is that a Saurus on the front has 2 attacks a Saurus in the rear only one.
Combined with their low Ini the loss of armour hurts them more than other Spearman.


To Saurus formations:
The most common ones are 6x3 5x4 and 6x4.
I wont talk about the propabilities, but more on the reasons for a LzM player to field the specified formations:
6x3 Pros: 12 attacks, wide frontage, wide front charge arc, relativly cheap.
Contra:only +2 to CR.
This is acutally my favorite ones, the wide forntage is nice as it is a bit more difficult to get into the flank. The fact that I save 24 points compared to 5x4 and 72 points compared to 6x4 is the main bonus however.
In combat efficensy this formation has two good points agasint the 5x4 one.
First: you get +2 attacks, second it takes 3 kills to take your first rank away as opposed to 2 for the 5x4 folks. In some cases, the 2 bonus attacks score another casulty which makes them even in CR while beeign superior in the movement battle.

In addiiton the 24 points are just enough to get me another Dispell dice (blessing of Tepoc) immunity to psychology (Tlaxcotl) or moving freely through woods (Huanchi).

The 5x4 fomration is so standartised that I wont talk about it. It is 48 points cheaper than 6x4 though.

6x4: It is nice but I dont like it for cost reasons. In contrast to 6x3 you pay 72 points for +1 CR by ranks and a better chance of outnumbering the enemy. 72 points may not sound much, yet it is the equivalent of: 12 not Scouting Skinks or 10 Scouting Skinks or a Sallie or 1.5 Kroxiogrs or 2 Cold one Riders or 2 Terradons.


Thu Apr 29, 2004 3:27 pm
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Slave (off the Altar)
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@ Lucius
Thanks for your appreciation :)

@Zader
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Hey, it certainly beats working right? :)


Yes, it surely does :)


May Hoeth guide our ways...
SeekingOne

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Fri Apr 30, 2004 8:20 am
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