Tuesday, October 27, 2015

Toughness Bonuses: Offense Vs. Defense

With all things being equal, how does an increase in defensive power from a mark of Nurgle balance out with the offensive and defensive power of additional models?

When I started working on the numbers for this article I had the the thought, 'Is this going to invalidate my first article?'  It doesn't because of a few special situations.  Units that don't get to attack because of range aren't going to see any of the offensive benefits of additional models.  The two units that immediately come time mind are cultists and havocs.  Both of these units sit in the backfield and the only reason that you generally add more models is simply for increased survivability.

Pure Math:
Lets start with pure mathematics.  If unit A hits 10% harder and unit B has 10% better defenses these don't simply cancel each other out.  We would end up with (1+0.1)*(1-0.1) or 1.1*0.9 which equals 0.99.  This means that defense edges out, but just barely.  As both overall offense and defense increase this gap widens.  With a 50% increase in offense and a 50% increase in defense we have 1.5*0.5=0.75.

If a unit adds additional models this will give a flat increase to not only the overall survivability but also the overall damage output.  For example, unit A has its survivability and damage increased by 25% each because it has additional bodies  Unit B would need their defense increased by 45% in order to balance out unit A's increase in the number of models.

**Warning: Incoming math!**
If I want to balance things out and figure out what percent of increased attack will cancel out with a different amount of increased defense I can do the following.
1=(1+x)(1-y)      Where x is increased attack and y is increased defense.

If I solve for y I end up with:


and since adding additional models increases both attack and defense I am going to add an additional x to the left side:


Now I can plug my percent (as a decimal) increase in cost from a mark of Nurgle, and I will be able to find the minimum damage reduction needed to make things balance out.

**End of Math**

Math Applied to 40k:
If we use the information in the previous post then we can plug the percent increase in points of a mark of Nurgle to find the break even points between offense and defense.

For example the cost of a single cultist increases by 50% when purchasing a mark of nurgle, and I have discussed the merits of when this is beneficial in terms of defense, but now that I am taking offense into account things change.  The cost of a mark of Nurgle only increases defense, but purchasing additional models will also increase the offensive capabilities.  The exact calculations are detailed in the math section above.

Toughness 3: Cultists

In order to balance out the 50% increased cost from the mark of Nurgle cultists would need at least an 83% increase in their durability.  This means that the only time that a mark of Nurgle is truly worth it is when they are facing off against strength 2 weapons.

Toughness 4: Marines, Chosen, Terminators, Raptors, Possessed, Warp Talons

StrengthDurability Increase

Regular marines increase their cost by 23% which means that they are going to need to increase their durability by at least 46.7% in order to be cost effective.  As a result a mark of Nurgle is going to be helpful when the majority of the firepower is strength 3 or 4.

Chosen have a more expensive base cost so they actually only need a 29.8% increase in durability; meaning that they are effectively protected against strength 5 unlike their basic marine counterparts.

Terminators need a 35% durability increase, so they are only helped against strength 3 and 4.

Raptors' cost increases by 17.6%, so they need at least 32.6% damage reduction.  Looks like mark of Nurgle will help out with strength 3, 4 , and 5.

Possessed fall into the same category as chosen.  They need a 28% increase in their defense, so a mark is effective against strength 3, 4 and 5.

Warp Talons are the real winner here.  Their base cost is so expensive that they only need a 24.5% increase in defense in order to warrant buying the mark of Nurgle.  A mark of Nurgle is almost always going to be worth the points, unless they are being hit by attacks that are strength 7 or more.

Toughness 5: Spawn, Bikes

StrengthDurability Increase

Spawn have an increased cost of 20%, so they need at least a 36% increase in their durability, so they mainly benefit against strength 4 and 5.

Bikes pay a high price for their mark of Nurgle, so they need at least 53.1% damage reduction meaning that they are really only helped against strength 4 attacks.

These results here were particularly surprising.  The two units that people immediately put marks on (spawn and bikes) are actually some of the least efficient.  Bikes are arguably the worst unit for a mark.  Spawn are a bit more complicated because they have a small unit size and it isn't always possible to add additional models or additional units.  Either way, this just adds on to me being less and less impressed by both spawn and bikes.

In the toughness 4 bunch we see that the elite units gain quite a bit from purchasing a mark.  Possessed, warp talons, raptors, and chosen all have a high base cost, so they want to have smaller units.  In addition, raptors and chosen generally don't add additional models because they can get all of their special weapons at a minimum squad.  Adding additional models to a chosen or raptor squad does not provide the same increase to damage (as other units) since so much of their damage comes from the special weapons.

1 comment:

  1. Yeah, math again!
    I love when I don't understand an article and I have to read it again! :-)