I've gotten through more army lists with converting template weapons. I'm currently doing Orks, and I've hit a wall. The Pulsa Rokkit is coming out being so expensive it will be unplayable. I just cannot see anything else to trim though, so I'm going to ask for opinions. This one is a bit complicated, so I'm going to hit it step by step. First the simple parts.

Base cost for a weapon is 2.
Range is variable, being 50cm plus artillery die times 5cm. As the average result of an Artillery Die is 5 ((2+4+6+8+10+0)/6), the average Range will be 75cm, for a multiplier of 1.5.
The base template used is the Small Pulsa 3cm. This has a value of 0.9 (3*3/10).
All possible damage results have the Damages Buildings ability, so *1.5.

Those are the simple parts. The next part is the chart and the results thereon. I'm assuming that Infantry will be targeted approximately 25% (0.25) of the time while everything else 75% (0.75) of the time.

A result of 1 means that it does damage as 2-5, but then the template is removed. Thus it's value is determined as a normal template of this size, but then divided by 6. "Normal for 2-5" means Infantry take an auto hit (no to-hit roll) at -6 TSM. All other targets, including buildings, take a number of hits equal to the 1d6 roll (1 in this case), with no to-hit roll, at -2 TSM, and survivors are pushed out of the area and lose their action. Thus the math for a result of 1 looks like:
Template: 0.9
Auto Hit: *4
TSM vs Infantry -6: *7
Infantry target: *0.25
Die roll 1: 1
TSM vs non-Infantry -2: *3
other targets: *0.75
Push & lose action: *1.5
divided by 6, as this is one of six possible results
or
0.9*(4*7*0.25+1*4*3*0.75)*1.5/6 which equals 2.4

A result of 2 means that Infantry take an auto hit at -6 TSM and all other targets take 2 auto hits at -2 TSM and survivors are pushed. The template then expands to 6cm and remains in play, and the chart is rolled on next turn. The 6cm template normally has a value of 3.6 (6*6/10) but for this I'm subtracting the cost of the smaller template so as to not charge twice for the same area covered. Thus 3.6-0.9=2.7. As all other modifiers are the same as above, except the die roll entry is 2, the math is:
(0.9*(4*7*0.25+2*4*3*0.75)+2.7*(4*7*0.25+2*4*3*0.75))*1.5/6 which equals 22.5

A result of 3 is the exact same as 2, except the die roll entry is 3. Thus the math is:
(0.9*(4*7*0.25+3*4*3*0.75)+2.7*(4*7*0.25+3*4*3*0.75))*1.5/6 which equals 30.6

A result of 4 is the exact same as 2, except the die roll entry is 4. Thus the math is:
(0.9*(4*7*0.25+4*4*3*0.75)+2.7*(4*7*0.25+4*4*3*0.75))*1.5/6 which equals 38.7

A result of 5 is the exact same as 2, except the die roll entry is 5. Thus the math is:
(0.9*(4*7*0.25+5*4*3*0.75)+2.7*(4*7*0.25+5*4*3*0.75))*1.5/6 which equals 46.8

A result of 6 means that everything under the template takes an auto hit at TSM -6, models with a hit location template take 6 auto hits at TSM -2, and all models within 6cm of the edge of the current template take a hit on 3+ at TSM-2. I have to account for this entry being either 3cm or 6cm, as it could have grown to 6cm in a previous turn. For this result, I'm assuming that hit location based targets will account for 10% and all else is 90%. Thus this entry's new modifiers are:
Explodes from 3cm to 9cm: 7.2 (9*9/10-3*3/10)
Explodes from 6cm to 12cm: 10.8 (12*12/10-6*6/10)
Thus the math is:
(0.9*(4*7*0.9+6*4*3*0.1)+2.7*(4*7*0.9+6*4*3*0.1)+7.2*2*3+10.8*2*3)/6 which equals 37.44

Totaling up the chart entries equals 178.44 (2.4 +22.5 +30.6 +38.7 +46.8 +37.44). Remember, each entry is already divided by six, so we do not do that again.

This total is then multiplied by the simple numbers at the beginning. Thus 2 * 1.5 * 1.5 * 178.44 = 802.98 points. Just for the weapon. This seems excessively high, but I cannot find any way to bring it down. If someone can find any errors in my math-logic, please do so.

Admittedly, we are considering dropping the 'Base cost' for template weapons. Doing this would bring it down to 401.49 points. This value is still quite high, but perhaps not unusably so.


The full formula being used for the weapon comes to:
=2*1.5*1.5*((0.9*(4*7*0.25+1*4*3*0.75)/6+(0.9*(4*7*0.25+2*4*3*0.75)+2.7*(4*7*0.25+2*4*3*0.75))*1.5/6+(0.9*(4*7*0.25+3*4*3*0.75)+2.7*(4*7*0.25+3*4*3*0.75))*1.5/6+(0.9*(4*7*0.25+4*4*3*0.75)+2.7*(4*7*0.25+4*4*3*0.75))*1.5/6+(0.9*(4*7*0.25+5*4*3*0.75)+2.7*(4*7*0.25+5*4*3*0.75))*1.5/6+(0.9*(4*7*0.9+6*4*3*0.1)+2.7*(4*7*0.9+6*4*3*0.1)+7.2*2*3+10.8*2*3)/6)

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Net Epic Coordinator

Hi!

These are basically one shot weapons. I did not see any adjustment for that fact in the formula (I hope I did not miss it).

Therefore my suggestion is a steep discount with on the cost because of it. 50% or something like that should bring it down quite a bit if you add it the projected lowering of base cost of all artillery, that could put it around 200 points (although the discount needs not be that steep).

That is the simplest idea I could come up with, hopefully it can work. This is something that could be used for other one shot weapons as well.

Primarch

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Primarch


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OK so I read this last night before bed and tried to walk through it in my head again this morning.

Aside from what Primarch said (one shot weapon) which definitely should be a consideration, it always scatters, is that considered in the calculation?

also the effects from 2-5 are mutually exclusive, should the average value from that be taken instead of the added value? or multiplied by a 4/6 value (2/3 or .667)? or even simpler, divide by 6 again?

Also, does the roll for effect repeat every turn or does it just sit there and block LOS after the initial effect?

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MadMagician
Epic Tyranids

Hi!

Good point on the mandatory scatter. I didn't think of that one.

I think there are several things that could be used to cut cost.

Primarch

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Primarch


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Hmm, Single Shot and Mandatory Scatter. Good points, I did miss those. At the moment, Single Shot weapons apply a multiplier of 0.1 (IE, divide by 10), and Mandatory Scatter I've been putting in as 0.5 (IE divide by 2), so those will bring it down a lot.

The way I see it, while 2-5 is one category on the chart it represents four possible results of the die roll which actually have slightly different effects (number of hits determined by actual die roll) and thus must be accounted for on their own.

Any result of 2 to 5 means that the template remains in play and the chart is rolled on the next (and subsequent) turns until either a 1 or a 6 is rolled.
__________

I have now finished updating all army lists to Tweak 3.2 (except for applying Single Shot and Mandatory Scatter to the Pulsa Rokkit) and will be writing those up to be posted.

I'm thinking that the name "Tweak XX" is a bit off, so I'm planning to change to calling each batch "Version X.Y". However, I'd like opinions on one thing there. I consider the formula to still basically be in Beta, but it is usable, so I'm not sure if it should be "Version 0.32" or "Version 1.32".
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Another change I'm considering is adjusting the Single Shot value from 0.1 to 0.2, as most games don't last 10 turns but most probably get in about 5 turns. Opinions? It's not a change I'd make right away - I'm planning to finish Hit Locations first if possible - but I've noticed most one shot weapons are coming up very low cost, perhaps too low.

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Net Epic Coordinator

What about finding the geometric mean of the per roll costs and multiplying by 5 turns?

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MadMagician
Epic Tyranids

Are you talking about Pulsa Rokkits in specific or Single Shot weapons in general? I'm guessing you mean the former, but not quite sure.

If the former, then no, I'd rather not do that as that would lose accuracy and each entry should be weighed by it's own statistics.

If the latter, then no, as such a weapon can only be fired once over the course of a game.

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Net Epic Coordinator

Sorry that was about the Pulsa Rokkit. I guess I don't see the point of charging it for all 6 possible outcomes.

So my thought is that you take some sort of average or mean of the values of any weapon like this you are capturing the potential damage, not 6x the possible damage simply because it has 6 possible effects.

So your six values based on die rolls are


There are quite a few options here.

First is take the basic average (mean) of the values and use that number

(2.4+22.5+30.6+38.7+46.8+37.44)/6 which is 29.74
Put that into the formula like so :
=2*1.5*1.5*29.74 and your number is 133.83. Is that in like with something like the AMTL Vortex missile?



Now it is clear that the lowest value really skews the average low, so we could also do the think where you toss out the outliers although that is way more complicated, since it uses standard deviation (anything outside X standard deviations is tossed)

First figure out the Mean (which we know from above, how handy!) 29.74

Then calculate the deviations of each data point from the mean, and square the result of each
(2.4-29.74)=-27.34 -29.34^2 = 747.48
(22.5-29.74)=-7.34 -7.34^2 = 53.88
(30.6-29.74)=0.86 0.86^2 = 0.7396
(38.7-29.74)=8.96 8.96^2 = 80.28
(46.8-29.74)=17.06 17.06^2 = 291.04
(37.44-29.74)=7.7 7.7^2 = 59.29

The variance is the mean of these values:

1231.71/6 = 205.25

The Standard Deviation is the square root of the variance or 14.33

If we exclude anythign outside of 1 standard deviation
anything lower than 29.74-14.33 = 15.41
or Higher than 29.74+14.33 = 44.07
is excluded

giving us a mean of 32.31

thus a value =2*1.5*1.5*32.31 equals 145.40



Finally there is the geometric mean which will be lower. it is the nth root of the products of n numbers.

(2.4*22.5*30.6*38.7*46.8*37.44)= some huge number but suffice it to say the 6th root is 21.96

thus a value =2*1.5*1.5*21.96 equals 98.82


You could then multiply it by say 4 or 5 rounds since reasonably you are better than 50/50 for rolling a "1
after the 3rd roll. But that still seems to overvalue it. as very few other weapons get dinged for working in more than one round.

Just my thoughts...

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MadMagician
Epic Tyranids

Hi!

In my experience average game turns is "3". Perhaps that is better number to use than 5.

Primarch

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Primarch


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Sub versioning (X.Y.Z) too deep for something like this is just nonsensical.

Honestly, Versioning seems to be a religious argument, but I would say keep it simple, beta 0.32,.33 up to whatever number you hit before you think it is prime time ready. Then call it 1.0, 1.1. alternatively go Full Google and call it version 32, 33, 34 etc.

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MadMagician
Epic Tyranids

You cannot add up the values for each of the six rolls and divide them by 6 because this is already included in the calculation for each result's value. Notice the "/6" at the end of each calculation segment. Those values already are that die roll's share of the mean average value.

Besides, adding in Single Shot and Must Scatter fixes the problem. Single shot brings it down to ~80, and Scatter brings it to ~40. That is a reasonable value, perhaps even a bit low. So I'm going to go with that.

No, sorry, I cannot "toss the outliers" as if they were irrelevant. They represent the potential of the weapon for that die result, and thus cannot be tossed away like garbage.

You lost me with the 'Standard Deviation' stuff. That's a bit outside of my math skills, so I'm not going to go there.

While I could try to work in the probability of it lasting for each successive turn and adjust the values based on that, that would assume that each Rokkit was fired in the first turn of a game and they cannot all be fired in the same turn, as I recall. Also, as Primarch mentioned, many games don't even last 5 turns. Thus we'd have to figure out how long the game will last as well as what turn it was fired in, and while I'm all for increased accuracy, even I have to draw the line somewhere.

Thanks for bringing up options, even if I'm being unreasonably dismissive of them. I did ask for it.
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Good thoughts on the version issue. The only reason I'd even use the third place is for issues like I'm currently dealing with for Templates. That is, 0.32 (previously known as Tweak3.2) is including the base weapon cost of 2 and 0.325 drops the base weapon cost for template weapons. As the jury is still out pending more information (IE, me posting the lists with values), I'm not sure which one will be used.

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Net Epic Coordinator

sorry there, I didn't mean "throw away" as in not do work. The point was that when you have a dataset where one value is super low, or super high, it is often necessary to set the values aside in order to get a more sensible average.

For example in the set [1,225,230,240,1000] 1 and 1000 skew the data. If the values are set aside for being outside of the range, then you get a nice bell curve.

Now though I see what you are doing with the /6 and it makes sense. I had thought you were using that as a probability value, not a weight!

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MadMagician
Epic Tyranids

Right, many of the revised lists have been posted already, and I'll get the rest up when I can.

In some of them, I've specified this, but in other I forgot, so explaining here.

The first, primary column of values is v0.32. V0.32 has a base weapon cost of 2 for all weapons, including template ones, as well as using the value for the template's size in the calculation. All BP numbers have been removed from all calculations, and To-Hit values added in where needed.

The second column of values, where present, is V0.325. This sub-version removes the base cost of 2 from template weapons, and thus is only relevant for those models and the formations that contain them.

I am posting both versions so that people can look at them, figure out which they think is more balanced in relation to other formations & models, and give opinions on this. Honestly, I expect most people to ignore the balance question and just choose 0.325 as those values are lower, but who knows. [Wait, did I just say that out-loud? ]

As a side note, all of these posts include V0.31 quick-fix to hit location values (dividing v0.3 values by half) so as a warning those will be changing in the near future. While I'm hoping they may go down further, some or all may be increasing.

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Net Epic Coordinator

Hi!

I'm willing to bet your right, since I have been favoring 0.325 myself quite a bit.

Primarch

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Primarch


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Yep they look a bit more reasonable to me. Need to play some games and try these out.

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