Wednesday, July 13, 2011

From the Pit: Mathhammer Pt1

I saw another article a today on International House of Paincakes about the mathematical side of ballistics in 40K. A while back I had done the same for Mordheim. Only with less maths, and more of my offbeat commentary. So I figured I'd post my version up for your enjoyment!

From the Pit:

Hello again, it’s time to talk about everyone's favorite Fantasy Skirmish game, Mordheim. I've really been investigating it lately to bring more stuff to you. Fresh stuff, stuff not everyone has thought about over and over again. I've really hit onto something this time though.

Close combat is a mug's game.

Do I have your attention now? I thought so. I'm not saying that close combat is not an important part of Mordheim, because it is, but comparatively speaking, it’s just not as powerful. When dealing with close combat, the difference is made not in weapon skill, but with what skills, abilities, and other stats that make the difference. On the other hand, Ballistic skill is not as dependent on the skills.

Let me break it down for you, in the most extreme case that I can. The highest weapon skill that any model in Mordheim can get is 8 (Vampire and Possessed Respectively). This is pretty high, however, if that person with a WS of 8 is in combat with someone with a WS of 1, he only needs to roll a 3 to hit, while the person with the WS of 1 needs to roll a 5 to hit him back! See, now that is interesting. However, normally you need a five to hit WS 8, except that the table changes. Once you get WS 4 or better you only need to roll a 4 to hit any WS higher available in the game.

So what exactly does a higher WS do for you? Well, it makes any WS lower then your own able to be hit on a 3+ instead of a 4+. Sounds good, right? Not so much, especially after WS 4. The vast majority of models in Mordheim fall between 2 to 4 WS. Most of the time that extra point or so in WS just goes to waste. Once you have WS 4, you hit everything possible in the game on a 4+, and anything lower at a 3+.

Close combat is decided more by what abilities your particular weapons have, the initiative, the number of attacks, and the strength of the damage! So a lot more goes into close combat, then missile fire...

Ranged Combat in Mordheim is dominant, and for one reason, Ballistic Skill. Unlike Weapon Skill, Ballistic skill is not a comparison skill. The best possible BS you can have in Mordheim is 7 for the elves, but most everyone else tops out at 6. This is important.

The easy way to figure out what you need to hit in Mordheim in ranged combat, is to subtract your BS from 7. Whatever the result is that is how much you need to roll over to get. Before any modifiers for cover, distance, or anything else, the lowest possible to hit roll you need is zero. A brief aside that most people don't realize is that Mordheim shooting does not have an 'always miss on a roll of 1' rule! So if you have a maxed out BS, you can almost always hit!

So let's stop for a moment and compare. The BEST weapon skill you can have has a minimum to hit roll of 3, while the BEST ballistic skill you can have has a minimum to hit roll of zero. Let's break out the mathhammer here.

Under the best of circumstances, WS 8 vs. WS 1, you have a 66.5% chance of scoring a hit.
Under the best of circumstances a BS 7 that did not move, firing at a large target not in cover at half range, you have a 116.5% chance of hitting

Conversely under the worse circumstances WS 8 vs WS 8, you have 50% chance of scoring a hit.
Under the worst circumstances BS 7, having moved, firing at a normal sized target in cover at max range, you have a 66.5% chance of hitting.

Wow. So under best circumstances, you have almost 50% better chance of scoring a hit with a ranged weapon then in close combat. Under the worst circumstances, that edge drops to a mere 16%. What makes the difference is that WS is almost never modified, BS is almost always modified in one way or another. Now, granted at higher levels that is taken to extreme. At lower levels, it is possible to take your BS to a level where it is impossible to get a hit. For instance a BS 1 with any modifiers you would need to roll a 7 on a d6, which we all know is impossible. However, that WS 1 trying to hit a WS 8 still has a 33% chance of hitting!

So while just mathhammering it out it would seem silly to do anything but shoot, right? Wrong. At the end of the day, both types of combat have their strengths and weaknesses, it’s just the to hit rolls that make the difference! I think that next time I'll work a bit more with close combat, proving that it wins games.

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