Leadership 2

 People talk a lot about math hammer(MH).  Most of the time they're crunching the outcome of a fictitious combats or determining the insane amount of firepower required to shoot down xyz monsters.  In 7th edition we used the math to tell us how many dice to throw at spells, the advantage of taking multiple bolt thrower shots over a single bolt, and the odds that our Treeman Ancient would hold on Stubborn 9 and not fail us.  While provocative and situationally handy, most of the MH'ing done in 7th edition was academic.  The real flavor of the game rested in the movement; judging distances accurately, lining up redirects, march blocking, etc.

The introduction of 8th edition presents us with an entirely different landscape altogether in the form of two major changes:

1. Everything is measurable at all times, there are no secrets or finesse of movement.
2. The charge distance is totally random. 

These two facets of the new system present the math-hammerist with a more powerful data set to flex.  8th Edition WFB has put the MH back in the movement phase.  It's never been said that competitive tournament warhammer is about the numbers, but it is about using an intuitive grasp of the odds to skew the game in your favor.  With the movement phase now firmly planted in the realm of probability, the chance for MH'ist to tilt the odds in his/her favor is significantly rendered.

Section 1.1: Average Charge Distance

For models using the standard +2d6" of charge the average is the familiar 7".  This is a familiar number from spellcasting theory, where the expectation value for each die thrown is 3.5; thus throwing 2d6 will net you 7" ~58% of the time.

For models with the Swiftstride special rule the average is 3d6" - the lowest die rolled.  The math here is a bit more complicated but the average is 8.5". This will include all flyers and models with movement values of 7 or higher.

Section 1.2: At Minimum Charge Distance

Perhaps an even better way to think about the extra charge distance rolled on the dice is to consider the odds of obtaining "at least [x] extra inches".  To visualize this, consider this graph:

The slope in blue represents the decreasing percentage chance of rolling at least [x] inches on 2d6 (indicated on the x axis).  Likewise the slope in red represents the same using 3d6 minus the lowest die roll.  I have stacked the percentage values on top of the respective distance for each graph.

Section 1.3: Using the percentages to your advantage (know thy foe)

Now that you can see first hand how the probability distribution relates to the random distance charged, you can combine these numbers with premeasured distance between units to force your opponent into making risky charge manoeuvres.

For the most part the basic movement values for the majority of infantry troops are either 4 or 5.  It is a more important distinction in 8th edition warhammer that in 7th edition.  If you have an extra inch of movement on your opponent you can use it to a much greater effect.

In general, if you are prepared to set up your army to take a charge, you should premeasure exactly the base movement value of the opposing unit + at least 7.5".  Why is this?  

Observe the change in the percentage on the blue slope as it progresses from 6 to 7, 7 to 8, and 8 to 9.  This is an indication of the increasing difficulty.  You will notice that the steepest change is from 7 to 8, where the % difference is on the order of 16%.  Not only does holding off 1" more than normal increase the odds of his charge failure by 1 in 6, but it also maximizes the potential for a successful counter charge in the event that his charge fails.

What if you have an extra inch of movement on your opponent (Say he has base 4 and you have 5)?  Then you can maximize your advantage furthur by placing your unit at his base value + 8.5".  You retain the same percent success rate on the counter charge while increasing the odds of his charge failing to 1 in 3 (33%).

Section 1.4: Swiftstriders

The new edition biases heavily against cavalry and other high movement troops.  I expect that, for the most part, their representation in the game will dwindle, to be replaced by more big blocks of RnF.  This makes sense for many reasons.  The primary reason is the new mechanics of combat.  With step up and initiative based attacking, hard hitting cavalry can no longer wipe the first rank on the charge and expect not to take armour saves from returning attacks.  The second reason is that the higher movement value no longer translates into "sure-thing" long distance charges. Hit hardest amongst this group are the old movement 9, 18" chargers, who can now only accomplish the feat 50% of the time.  So what is the use of cavalry on the new battlefield?  In this section I will briefly detail what I see as the new role for heavy cavalry and how to play against it.

Section 1.4.1: Playing by the Numbers - Cavalry as an Ace in the Hole

The new role for cavalry is in consistency.  In addition to their base movement, cavalry can complete a charge of an additional 7" with 80% efficiency.  In the new tournament world you will sleep easy on this consistency.  Cavalry don't fight anymore, they clean up.  Since fleeing units no longer flee from additional chargers, but are instead wiped out entirely, small units of cavalry offer the most surefire means of cleaning up after your RnF do the dirty work.  They will also find uses on the flanks as warmachine hunters.

...tbc