The value of Murderous Prowess

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Daeron
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The value of Murderous Prowess

Post by Daeron »

The value of Murderous prowess

Some words and opinions have been flying around about the value of Murderous prowess. I'd like to contribute to the discussion by working out some numbers on the value of this rule. We are given the rule, whether we like it or not, but it might be fun to see the impact of it on our troops.
I begin with a simplistic, linear calculation that expresses the damage increase in a direct percentage.


Damage increase from Murderous Prowess

Mundane attacks
We reroll only 1's. We get the following chart:

Wound roll . Regular . . . MP . . . Increase
. . . 2+ . . . 83,3% . . . 97,2% . . . 13,9%
. . . 3+ . . . 66,7% . . . 77,8% . . . 11,1%
. . . 4+ . . . 50,0% . . . 58,3% . . . 8,3%
. . . 5+ . . . 33,3% . . . 38,9% . . . 5,6%
. . . 6+ . . . 16,7% . . . 19,4% . . . 2,8%

The damage increase ranges from nearly 14% when we roll 2+ to wound, to a little less than 3% when we need 6+ to wound. Against a regular T3 trooper, we can expect a good 8% increase or more. It's an interesting damage amplification, but it's unfortunate that it doesn't help us much against those tougher matchups.

Killing Blow

The reroll of 1's increases our chance to score a killing blow. The chance to wound doesn't impact this bonus at all. (it's all or nothing).
- Killing blow chance: 16.7% (1/6)
- Killing blow chance with Murderous Prowess: 19.4% (almost 1/5)
- Increase: 2.8%.

There are rumors about a 5+ Killing Blow rule, so I'll add those numbers too:
- Killing blow chance: 33.3% (1/3)
- Killing blow chance with Murderous Prowess: 38.9% (almost 2/5)
- Increase: 5.6%

Every increase on a killing blow is welcome, but it's not the kind of increase that will define a game. To model this, we work out the chance on X killing blows, with 10 hits.

Image

Is it enough to make killing blow a workable strategy? Let's see how many hits we need to get at least 1 killing blow:

Image

Unfortunately, it's not enough to make killing blow a reliable strategy. It remains a gamble. But the gamble is also on the recieving end of the stick: an opponent certainly won't welcome this increased chance on a killing blow per hit.


Poison

Poison negates the need to wound and not benefit from the murderous prowess rule. Still, let's look at the impact. I look at numbers with or without reroll, different to hit and to wound values. The table is a little daunting, but I'll make some observations below.

Reroll Hit . hit . wound . . Poison . Poison+MP . Difference
. Yes! . . . 3+ . . . 3+ . . . 66,7% . . . 74,1% . . . 7,4%
. Yes! . . . 3+ . . . 4+ . . . 55,6% . . . 61,1% . . . 5,6%
. Yes! . . . 3+ . . . 5+ . . . 44,4% . . . 48,1% . . . 3,7%
. Yes! . . . 3+ . . . 6+ . . . 33,3% . . . 35,2% . . . 1,9%
. Yes! . . . 4+ . . . 3+ . . . 58,3% . . . 63,9% . . . 5,6%
. Yes! . . . 4+ . . . 4+ . . . 50,0% . . . 54,2% . . . 4,2%
. Yes! . . . 4+ . . . 5+ . . . 41,7% . . . 44,4% . . . 2,8%
. Yes! . . . 4+ . . . 6+ . . . 33,3% . . . 34,7% . . . 1,4%
. Nope . . . 3+ . . . 3+ . . . 50,0% . . . 55,6% . . . 5,6%
. Nope . . . 3+ . . . 4+ . . . 41,7% . . . 45,8% . . . 4,2%
. Nope . . . 3+ . . . 5+ . . . 33,3% . . . 36,1% . . . 2,8%
. Nope . . . 3+ . . . 6+ . . . 25,0% . . . 26,4% . . . 1,4%
. Nope . . . 4+ . . . 3+ . . . 38,9% . . . 42,6% . . . 3,7%
. Nope . . . 4+ . . . 4+ . . . 33,3% . . . 36,1% . . . 2,8%
. Nope . . . 4+ . . . 5+ . . . 27,8% . . . 29,6% . . . 1,9%
. Nope . . . 4+ . . . 6+ . . . 22,2% . . . 23,1% . . . 0,9%


Murderous prowess helps, but it's not a game changer. It helps us mostly against opponents against which we already have good rolls, for having a higher strength, rerolls to hit and so on.


Final observations and remarks

Murderous Prowess is a nice little help, but it doesn't score impressive numbers "where we need the help the most". We can assume that murderous prowess is a little extra that might save us in a fluff roll, but it's unlikely to impact the dynamics of the army considerably. My guess is that Games Workshop wanted to increase the elite feeling of the army by increasing the point cost, and was forced to give us a little extra push in return. Or perhaps it was the opposite.

One important observation though, is that the benefit of murderous prowess increases against opponents for which we already have good rolls. It seems to work like an amplifier. If you let your unit fight a bad matchup, it will remain a pretty bad matchup. If you fight a good matchup, then this rule will increase the weight in your favor.
This encourages good matchups, achieved through strategy or magical enhancements. The Dark Elf army seems to sport a fair few options to buff units, and this rule would work in tandem with such a playstyle.
I love me a bowl of numbers to crunch for breakfast. If you need anything theoryhammered, I gladly take requests.

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Re: The value of Murderous Prowess

Post by Calisson »

Thanks for the analysis and number crunch (the first one of many, for sure).
5+ KB is rumoured to be attained by nobody less than Tullaris (you'd bet).
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Re: The value of Murderous Prowess

Post by Scyloc »

Hi Daeron,

Please keep up the good work.

It is always interesting to read your input.

Numbers of course speak for themselves. However i feel you misrepresent the damage increase in your first table "Mundane Attacks" where you write that the damage increase of Murderous Prowess is anywhere from 13.9 to 2.8 %
The correct presentation would be either your values as increases in flat percent points.

Or quite simply stating that Murderous Prowess increases damage by 16.7% across the board compared to not having Murderous Prowess.

To expand on your example going from 16.7% chance to wound (on 6s) to 19.4% to wound with Murderous Prowess, is indeed an increase of 2.8 percent-points, but an increase of 16.7% of damage.


When looking at the way you present the numbers, one can easily be lead to believe the gain is minimal.
Last edited by Scyloc on Tue Oct 01, 2013 7:38 pm, edited 1 time in total.
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Re: The value of Murderous Prowess

Post by Kurze »

I always enjoy reading your reports mate, very interesting stuff. I'm more of an aesthetic gamer and I tend to forget the numbers side of our hobby. I'm also a shocking dice roller so any rerOll I can get suits me just fine :)
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Re: The value of Murderous Prowess

Post by MangoPunch »

@ Scyloc, looks like it always increases damage output by 16.7%, regardless of opponent:

............Base.........With MP......Damage % Increase
2+.........83.3%.......97.2%.......16.7%
3+.........66.7%.......77.8%.......16.7%
4+.........50.0%.......58.3%.......16.7%
5+.........33.3%.......38.9%.......16.7%
6+.........16.7%.......19.4%.......16.7%........<--Same for Killing Blow


Oh Math!

P(normal)=x+/6
P(MP)=P(normal)+(1/6)*P(normal)

Damage increase % = P(MP)/P(normal)-1 = 1/6
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Re: The value of Murderous Prowess

Post by Scyloc »

Yes Mangopunch. That my point when i write:

"it increases the damage by 16.7% across the board".
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Re: The value of Murderous Prowess

Post by Helle »

You're both right, Scyloc and MangoPunch. The damage is increased by 16.7%.

Nevertheless, Daeron presentation of data is appealing as it shows how much more wounds MP will cause. Maybe he should change his phrase to avoid confusion.
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Re: The value of Murderous Prowess

Post by Daeron »

Good remarks, thank you. The confusion can certainly arise, partly because I used the percent point notion on some parts, and not for others. The 16.7% increase is not across the board in case of special rules such as poison though. But I will try to improve the consistency of the numbers tomorrow and after tomorrow.
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Re: The value of Murderous Prowess

Post by Marchosias »

I think you calculate the KB chance wrongly. A normal KB has a chance of 1/6 (as you say). When rolling on 6+, all the remaining 5/6 can try for the KB once more and produce another 5/36 chance. On the other hand, when rolling on a 2+, all rolls between 2 and 5 are "wasted" on normal hits and do not receive the chance to be a killing blow. Only the ones can do so in a reroll, which means the chance of a rerolled KB is only 1/36.

To sum up: On 6+, you have a 11/36 chance of KB and a 25/36 chance of not doing a wound.
On 2+, you have a 7/36 chance of a KB, a 7/9 chance of a normal hit and a 1/36 chance of not wounding.

Other than that, good work!
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Re: The value of Murderous Prowess

Post by Daeron »

Well.. Murderous prowess would only permit to reroll 1's by the look of it. I think you worked out a reroll on all failed wound rolls.
I love me a bowl of numbers to crunch for breakfast. If you need anything theoryhammered, I gladly take requests.

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Re: The value of Murderous Prowess

Post by MangoPunch »

Scyloc and Daeron, wasn't trying to be critical of either of your posts. Daeron I love the statistics you bring and am looking forward to more of your analysis on the new book.

-JGB
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Re: The value of Murderous Prowess

Post by Shadoer »

MangoPunch wrote:Scyloc and Daeron, wasn't trying to be critical of either of your posts. Daeron I love the statistics you bring and am looking forward to more of your analysis on the new book.

-JGB


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Re: The value of Murderous Prowess

Post by Scyloc »

Hi Daeron, your statistics on KB and poison is very interesting.

I am sorry if i sounded snippy or anything.
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Re: The value of Murderous Prowess

Post by Bounce »

Some cool stats there.
I can see Murderous Prowess being nice for most of our units. Although it seems a bit silly if the cauldron of blood gives re rolls to wound and we have re rolls 1 to wound already. Particularly for a unit like executioners :(
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Re: The value of Murderous Prowess

Post by Omnichron »

Bounce wrote:Some cool stats there.
I can see Murderous Prowess being nice for most of our units. Although it seems a bit silly if the cauldron of blood gives re rolls to wound and we have re rolls 1 to wound already. Particularly for a unit like executioners :(

Yeah, the cauldron is probably not as useful with the executioners... except of that possible extra attack with frenzy. I feel a bit sceptical about CoB altogether, but I'll wait and see for the actual rules (and that is for another topic as well ;) )

Nice diagrams. I think we will notice that extra reroll to wound for all our high strength attacks.. as well as those troops which gives us plenty of attacks. It fits our army very well.
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Re: The value of Murderous Prowess

Post by Daemon of khaine »

comparing the rumours to the HE, I thought of something useful for Murderous Prowess: combat characters

HE characters get Martial Prowess, which is useless to them
but DE characters get to re-roll 1's to wound standard

there's nothing worse than a 100-300 points character rolling 1's to wound
now, DE characters are pretty much immune to that

and between high WS, I, ASF and usually a high S, this means DE characters will hit and wound better than most other races' characters
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Re: The value of Murderous Prowess

Post by Dalamar »

Yes, we are the epitome of glass cannon now. In fact the cannon is so powerful that it's possible for it to damage itself.
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