Thursday, June 23, 2011

40k-metrics: Unit by Unit Analysis

Today's guest article was written by Timmah, and he does a great job of taking my basic framework and using the data it gives you to make more in depth analysis.  He discusses how you compare units internally from a codex.  Hive Guard or Tyrannofex better at anti-mech?  He will give you the tools to decide.  But don't let me explain it...

In the initial article, Nike looked at an army’s ability to do a variety of tasks that were associated with winning.  With this, a framework was set to what a competitive army would look like in terms of numbers when you applied the formulae.  This however is just scratching the surface of what we can do with these numbers and formulae. 
These numbers give us a framework to start comparing units within a codex.  Starting with the Tyranid codex, we know that the army is perceived to be weak when it comes to anti-tank shooting.  Taking a look at the main long ranged anti-tank units we have:


DRPG
DLRPG
Tyrannofex

4.17
1.67
Hive Guard

3.33
0
Harpy

2.26
0.57

These all have a long range high strength gun and the ability to take on most armored vehicles.  So, judging just by the numbers, it seems obvious that the Tyrannofex is far and away the best choice.  It will kill the most rhinos during a game and has the best chance of taking on a land raider.  If we stop here, our list would play 3 Tyrannofexes and then maybe splash in a few hive guards. 
These numbers by themselves don’t tell the whole story.  Warhammer is still a game of limited resources, meaning that gross output alone doesn’t make our list composition decisions.  It’s the efficiency vs. points of the unit.  So we take the numbers and divide by the points cost of the unit, this will give us DRPG and DLRPG on a per point basis.  Meaning we can standardize all the numbers at 1 point.

Points Cost
DRPG
DLRPG

DRPG
DLRPG
Tyrannofex
265
4.17
1.67

0.0157
0.0063
Hive Guard
50
3.33
0

0.0666
0.0000
Harpy
170
2.26
0.57

0.0133
0.0034

This gives us much more reliable numbers when comparing dissimilar units within a codex.   The end result showing that Hive guard gives you over 4 times the rhino killing power of Tyrannofexes on a point by point basis.  The harpy is left in the dust when it comes to rhino killing, showing that it is truly an inferior choice.  The Tyrannofex does however prove to be the most efficient at killing land raiders at a distance.  A very different result occurs when we use these numbers to build our list.  Now, Hive guard will be maximized while Tyrannofexes will be splashed for more rhino killing and a way to deal with land raiders.
Okay, so now we know how to properly evaluate dissimilar units that do the same task.  What happens when we need to measure the same unit at different squad strengths?  Grey hunters are the perfect example for this.  Not only do a lot of people debate the size you should take, but they also have the option for an attached Wolf Guard with even more options.

Points Cost
DMS
DMCC
DRPG
DLRPG

DMS
DMCC
DRPG
DLRPG
5 Grey Hunters melta, combi-Melta Wolf Guard
103
1.67
2
3.67
2.33

0.0162
0.0194
0.0356
0.0226
5 Grey Hunters Melta, 2x combi-Melta Wolf Guard
108
1.67
2
4.28
2.72

0.0155
0.0185
0.0396
0.0252
5 Grey Hunters Melta, combi-Melta/PF Wolf Guard
123
1.67
3.33
3.67
2.33

0.0136
0.0271
0.0298
0.0189
7 Grey Hunters melta, combi-Melta Wolf Guard
133
2.12
2.67
3.67
2.33

0.0159
0.0201
0.0276
0.0175
7 Grey Hunters melta, combi-Melta/PF Wolf Guard
153
2.12
4.33
3.67
2.33

0.0139
0.0283
0.0240
0.0152
   
Given all the different options we can see which units are the most points efficient.  Based on how the numbers change, we can see how different things affect the numbers.  Some conclusions that can be drawn:
Wolf guard with power fists are very points efficient for killing marines on the charge.  We see this as the numbers spike up sharply when adding him into the unit. 
The second conclusion is that if a list is in need of units to kill rhinos or land raiders, the double combi-melta wolf guard is the way to go.
This list gives us a good idea of what we are getting when we purchase a grey hunters squad.  This lets us analyze our list, see what it needs and add supporting elements to match.  For instance, with a space wolf gun line, close combat units will be needed.  This list will show us the best options for supporting the gun line.  5 Grey hunters with attached wolf guard with a power fist/combi-melta may be our best option.  It is close to the most points efficient at DMCC and it fits nicely into a razorback.
Finally, when building a list, you may just be looking for all around point’s efficiency.  In this case, the 2nd set of scores will be added together to give us an overall idea how points efficient a unit truly is.


Overall
5 Grey Hunters melta, Melta Wolf Guard

0.0939
5 Grey Hunters melta, 2x combi-Melta Wolf Guard

0.0988
5 Grey Hunters melta, combi-Melta/PF Wolf Guard

0.0894
7 Grey Hunters melta, combi-Melta Wolf Guard

0.0811
7 Grey Hunters melta, combi-Melta/PF Wolf Guard

0.0814

For grey hunters, the double combi-melta wolf guard proves to be the most efficient thanks to its boosted scores in tank killing.  This number can also be toyed with.  If you are just looking for DMCC and DRPG abilities, you can very easily add those 2 scores to give you the most efficient option.
In the end, Warhammer is a game that favors those players that can maximize their scarce resources.  This analysis gives a player one more tool in doing that before they ever toss a dice.

Thanks again, Timmah.  Great contribution!

5 comments:

  1. How about defensive metrics? Below is really basic mathhammer, but it's the approach I use - heavily based on Sandwyrm's posts on thinking outside T6 here: http://theback40k.blogspot.com/2010/10/thinking-outside-of-t6-troops.html

    *Shooting defense*
    Assume 4+ cover for infantry, beasts and ICs; no cover for vehicles or MCs
    Heavy weapons (S8/AP2) number of shots to kill/wipe out
    Bolters (S4/AP5) number of shots to kill/wipe out

    Statline is #models/T[x]/W[unit total]/SV

    vs Tervigon @ 1/T6/W6/3+ MC
    S8 vs 1 model/T6/W6 = 7 hits
    S4 vs T6/W6 = 6+/3+ = 108 hits

    vs 6 tyranid warriors @ 6/T4/W18/4+ cover
    S8 vs. 6 models/T4/W18/4+ = 15 hits [(6.25 IDs = .5(shots*.833333)]
    S4 vs. 6 models/T4/W18/4+ = 72 hits [18 = .5(shots*.5)]

    vs. 5 terminators w/SS @ 5/T4/W5/2+,3++
    S8 vs. 5 models/T4/W5/3++ = 9 hits [5=.66666(shots*.833333)]
    S4 vs. 5 models/T4/W5/2+ = 60 shots [5=.166666(shots*.5)]


    *Assault Defense*
    Power fist S8/no save; number of hits to kill/wipe out
    Power weapon S4/no save; same...
    melee weapon S4

    vs. T6/W6/3+ MC
    S8p vs 1 model/T6/W6 = 7 hits
    S4p vs 1 model/T6/W6 = 36 hits
    S4 vs 1 model/T6/W6 = 60 hits [6 = .6(shots * .166666)]

    vs. 6 tyranid warriors @ 6/T4/W3/4+
    S8p vs. 6 models/T4/W18 = 7 hits
    S4p vs. 6 models/T4/W18 = 36 hits
    s4 vs. 6 models/T4/W18 = 54 hits

    vs. 6 MEQ @ 6/T4/W1/3+
    S8p vs. 6 models/T4/W6 = 7 hits
    S4p vs. 6 models/T4/W6 = 12 hits
    s4 vs. 6 models/T4/W6 = 18 hits

    vs. 5 terminators w/SS @ 5/T4/W5/2+,3++
    S8p vs. 5 models/T4/W5/3++ = 18 hits [5=.33333(shots*.833333)]
    S4p vs. 5 models/T4/W5/3++ = 30 hits
    S4 vs. 5 models/T4/W5/2+ = 60 hits

    Haven't tried this with vehicles, but I think you get the idea. Combine this with Timmah's points value ratio approach and it would give a binary weighting approach.

    I have some chicken scratches on metrics for maneuverability - but wanted to keep it extremely simple; basically 0 points for basic 6"/run movement capabilities; 1 point per unit with fleet, jump, beast, and/or outflank/deep strike; 2 points for fast and/or skimmer vehicles.

    Thoughts?

    ReplyDelete
  2. Damage per Point (DPP) is what I work out on units for seeing how effective upgrade are, and how effective they are against each other. Of course sometimes the raw numbers do not give you the whole story. Gargoyle need Adrenal Glands to glance APC's even though it drops there DPP.

    The one thing I learnt from this article is that a Wolf Guard can take two combi-weapons! The idea never occurred to me...

    ReplyDelete
  3. Thank you for this informative article- I hope you continue this series.

    Since I am still relatively green, would you mind explaining what each of the acronyms are located in the columns above?

    ReplyDelete
  4. @Gonewild, Do you mean the DMS, DMCC columns?
    If so look at the previous article -
    http://nike40k.blogspot.com/2011/06/40k-theory-its-all-about-numbers.html

    If you are meaning Ghostin's post?
    MEQ = Marine EQivilant
    T4 = Toughness 4, 3+ mean a Save of 3+, and so on

    ReplyDelete
  5. I really like this analysis. I have done some extensive unit by unit lists for vanilla marines.

    I find that because the damage to vehicles is determined on a per game basis - it can really skew the overall values. I am going to test it out at a per turn value to see which I prefer.

    It is definitely a very valuable tool. The one thing I'm really struggling with is selecting shooting/cc or both vs. vehicles. When I have it a little more together I will email you to get your thoughts.

    ReplyDelete