Why?

I love wargames and I am fascinated by the mathematics underpinning different  systems.


The best games have very strong mathematical foundations that prevent them boiling down into a simple game of rock, paper, scissors.


I play Warmachine and Hordes a lot, and have recently become a Press Ganger (Volunteer) for Privateer Press. My current factions are Cygnar, Cryx, Mercs and Legion and so you may well see my perspective is biased by my play style.


My project for 2012 will be Trolls, but my painting plate is pretty full at the moment, and so it will be late in the year before anything happens with those big tough blue monsters.



Warmachine and Hordes have an incredibly tight set of tournament rules, a clear rulebook, simultaneous faction release schedule and utterly fantastic models. Then you have the fantastic 2d6 system of action success with the ability to gain extra dice and make the action a "sure thing".


Now I am not claiming to be any kind of maths professor, I studied triple maths at A level and have a BA Hons in Economics (so call me an enthusiastic amateur), but I like to explore stuff that I find interesting and thought I would share some of them with you. That is how I ended up with math-machine.

Heavy Warjack survivability

 "This guy is a wrecking machine!" Mickey Goldmill 1982

I love heavy Warjacks but they cost a fair chunk of points and in MK1 had a problem in the fact that the same points of infantry would almost certainly do a better job (and without need focus to boot). In addition, playing versus Cygnar would generally make you wish you left your Warjacks at home.


MK2 made things better. Free Warjack points, infantry toned down and Jacks (without Arc Nodes) made considerably cheaper. I still don't use "Heavies" as much as I would l like to and recently have given some thought to why that is.


Most heavies can dish it out, it is after all their #1 job. Get to a fully loaded Heavy to an enemy Warnoun and it should be time to shake hands. The problem lies in the fact that I feel some Jacks have a bit of a glass jaw, especially when you could be sinking as much as 12 or 13pts into a single model.


This has led to my using cheap Jacks where possible and staying well away from models like Thunderhead and DeathJack (although I own both).


So after playing around for a few day I came up with the following experiment.




Test:


How many hits would it take to destroy different Jacks per cost point of the model?
To explain further, if a model costs 6pts and needed 6 hits to be destroyed, then the survivability rating would be 1.00.

Assumptions:

1. Attacking model has Mat 6, P&S 17, and can perform as many melee attacks as needed to complete the job.
2. All defensive buffs the Jacks possess are up.
3. Damage is not tracked individually and so systems stay fully operational until the end.
4. Retribution "Field Generator" simply adds additional damage boxes to the Warjacks grid.

Example: 


I do not want to get into hot water with PP for publishing a list of Def, Arm, Pt cost and Damage boxes for its models and so will give as an example the Cygnar Ironclad, whose rules are freely available as part of the Quick Start Rulebook.
The Ironclad has Def 12, Arm 18, has 30 boxes and costs 7 points.
He will be hit 72.2% of the time by MAT 6 and will take 6 damage on average when hit by P&S 17.
This runs to 4.33 damage taken per attack and so the Ironclad will be destroyed after 6.93 attacks.
The Ironclad costs 7 points and so dividing 6.93 by 7 gives you the value 0.99, it's survivability rating.




Results: 


 The table 1.0 below shows the outcomes for each Warjack up to Wrath releases.

• The two ARM 25 Khador Jacks break the model and are top dogs in respect of survivability (no real surprise).
• A big surprise however, was how far up the list Erebus came. It boiled down to his Def and Arm both being 1pt better than the Slayer and him only being 8pts.
• Some big cost models like Avatar and Behemoth did quite well, 18th and 24th respectively.
• Thunderhead has terrible survivability at 60th place (I hardly ever used him and now it is a bit clearer why)
• Cheap models do well, but it is not that straight forward.
 

Conclusions:


All factions have access to models with good survivability but Khador rule the roost.
The next time a Cryx player moans about how easy to kill his "Heavies" are, tell him about the Slayer and Erebus.






Table 1.0:

Rank	Faction	Model	Survivability
1	Khador	Devastaor	N/A
1	Khador	Demolisher	N/A
3	Menoth	Templar	1.45
4	Cryx	Erebus	1.40
5	Cygnar	Centurion	1.33
6	Khador	Juggernaut	1.32
6	Khador	Marauder	1.32
8	Khador	Spriggan	1.24
9	Mercenary	Avalancher	1.22
10	Retribution	Sphinx	1.19
11	Khador	Black Ivan	1.18
12	Menoth	Crusader	1.16
12	Khador	Kodiak	1.16
14	Cygnar	Rowdy	1.15
15	Cryx	Slayer	1.14
15	Cygnar	Gallant	1.14
16	Mercenary	Driller	1.10
17	Mercenary	Nomad	1.09
18	Menoth	Avatar	1.06
19	Khador	Beserker	1.03
19	Khador	Decimator	1.03
19	Khador	Destroyer	1.03
19	Mercenary	Rockram	1.03
23	Mercenary	Rover	1.02
24	Khador	Behemoth	1.01
25	Cygnar	Ironclad	0.99
25	Mercenary	Freebooter	0.99
27	Retribution	Hypnos	0.98
27	Cryx	Reaper	0.98
29	Cygnar	Triumph	0.94
30	Khador	Torch	0.93
31	Retribution	Manticore	0.92
31	Retribution	Daemon	0.92
33	Cryx	Deathjack	0.91
34	Cygnar	Hammersmith	0.90
34	Mercenary	Mangler	0.90
36	Mercenary	Basher	0.87
36	Menoth	Castigator	0.87
36	Menoth	Reckoner	0.87
36	Menoth	Vanquisher	0.87
40	Cryx	Corruptor	0.86
41	Khador	Beast 09	0.84
42	Cygnar	Stromclad	0.83
42	Retribution	Banshee	0.83
44	Menoth	Guardian	0.82
44	Retribution	Hydra	0.82
46	Cryx	Nightmare	0.80
46	Khador	Drago	0.80
46	Cygnar	Avenger	0.80
49	Retribution	Pheonix	0.78
49	Menoth	Fire of Salvation	0.78
49	Menoth	Scourge of Heresy	0.78
49	Menoth	Blood of Martyrs	0.78
49	Menoth	Sanctifier	0.78
54	Cryx	Leviathan	0.77
54	Cryx	Desecrator	0.77
54	Cygnar	Cyclone	0.77
54	Cygnar	Defender	0.77
58	Cryx	Seether	0.76
58	Cryx	Malice	0.76
60	Mercenary	Mariner	0.74
60	Retribution	Discordia	0.74
60	Cygnar	Thunderhead	0.74
63	Cryx	Harrower	0.69
64	Mercenary	Mule	0.68
65	Mercenary	Rocinante	0.61