Sunday, 29 July 2018

Power from Paint: Raider 'Rithmetic

Another weekend of gaming goodness is over and that means it's time for another post!  I've had a lot of fun playing 40K, various board games and also indulged an hour or two working on some terrain; this means there are plenty of topics to choose to blog about! However, this post will be a little bit different to my normal topics (warning: word heavy, picture light, includes maths).

My Dark Eldar took to the battlefield against the Dark Angels. The First Legion deployed an elite force and unfortunately suffered a defeat against the Kabal of the Sand Viper! The Dark Angels army included a Land Raider which died early in the game under sustained Dark Lance fire, and this event got me thinking; Land Raiders have a pretty poor reputation game-performance wise and are perceived as very expensive points wise, but is this really the case?

WIP Land Raider Crusader
Let's have some fun with a little thought experiment as I'm interested in this question from a couple of perspectives:
  • I love the aesthetics of Land Raiders, but I'm hesitant to field them in my Space Marine armies due to the perceived inefficiencies (and I have several Land Raiders in my collection!)
  • Having a more informed view about how many of my Dark Eldar anti-tank shots to put into a vehicle to kill it
There are a number of ways to look at this problem, but I've tried to keep it fairly simple. Let's think about the Land Raider's role:
  • It's a transport (it can carry 10 Marines)
  • It's got quite a lot of guns (4 Lascannons and 2 Heavy Bolters)
So it's something of a multi-role beast; let's compare it to the more specialized vehicles in the Space Marine Armoury:
  • The Rhino (a transport which carries 10 marines)
  • The Predator (a tank fitted in this example with 2 Lascannons and 2 Heavy Bolters)
Ignoring the cost of weapons a Land Raider is almost 150 points more expensive than a Predator and 170 more than a Rhino! Ouch! Remember, this is just for the hull, before we stick any Dakka on it, so what is driving this difference? There are variations in special rules (the Rhino has Self-Repair to potentially heal damage, whilst the Land Raider has Power of the Machine Spirit to allow it to fire at full effect when moving), but the key discriminator is on the Data Sheet Profiles:
  • Rhinos and Predators are Toughness 7, 3+ Save (the former with 10 Wounds and the latter 11 Wounds)
  • Land Raiders are Toughness 8, 2+ Save, 16 Wounds
Do those numbers really make enough of a difference to justify the jump in costs?

Dark Eldar Archons may now pay attention! We are going to delve into some Maths Hammer to explore these profile differences, and the examples involves shooting hypothetical tanks with hypothetical Dark Light weapons 😈.

Here's the little formula we are going to plug some numbers into:

Average Damage Per Hit (DPH) = 
Average Weapon Damage (DA) * Probability of Wounding (PW) * (1- Probability of Saving (PS))

And the weapons we are going to use are:
  • Dark Lances/Blasters: Strength 8, AP -4, Damage D6 (Average Weapon Damage 3.5)
  • Disintegrator Cannon: Strength 5, AP -3, Damage 2 (Average Weapon Damage 2)
Lances and Blasters can be considered the same as we are ignoring range and to hit modifiers (we are looking at Hits, rather than Shots). 

Probability of Wounding is derived from the Wound Roll chart in the rule book (p.181). Probability of Saving is based on the Save Roll modified by the Weapons AP (so a 3+ Save combined with AP -3, only saves on a 6, so 1/6 (16%) PS.

Moving onto the examples: 
  • Lance/Blaster vs  Rhino/Predator: DPH = 3.5 * 0.66 * 1 = 2.31
  • Dizzie Cannon vs Rhino/Predator: DPH = 2 *0.33 * 0.83 = 0.55
  • Lance/Blaster vs Land Raider: DPH = 3.5 * 0.5 * 0.84 = 1.47
  • Dizzie Cannon vs Land Raider: DPH = 2 * 0.33 * 0.66 = 0.44
Now we divide Model's Wounds vs Average Damage Per Hit to give the Average Number of Hits to Kill the Model:
  • Lance/Blaster vs Rhino: HTK = 10/2.31 = 4.33
  • Lance/Baster vs Predator: HTK = 11/2.31 = 4.76
  • Lance/Blaster vs Land Raider: HTK = 16/1.47 = 10.9
  • Dizzie Cannon vs Rhino: HTK = 10/0.55 = 18.18 
  • Dizzie Cannon vs Predator: HTK = 11/0.55 = 20
  • Dizzie Cannon vs Land Raider: HTK = 16/0.44 = 36.4
So we can see that the Land Raider is twice as robust (to average hits) as a Predator or Rhino.

We are getting on top of things!
 But of course things aren't that simple! Remember those point costs we talked about at the start of the post? We can buy 2 Predators armed with 2 Lascannons and 2 Heavy Bolters for less points than a fully armed Land Raider (with 4 Lascannons and only 2 Heavy Bolters). Now we have twice as many Predator Wounds to deal with.

One Predator needed 4.76 Lance HTK, so two Predators will need 9.52 Lances hits to destroy the pair; the Land Raider still edges it out!

It's looking pretty good for the Land Raider right? There's still a few more things to consider.

Almost at the end of the article
The number crunching has only dealt with averages (and calculating these has explained the often disappointing results I seem to get with my Lances and Blasters). What these calculations don't factor in are the swingy results we get with D6 damage dice. I won't re-run all the sums but it doesn't take a genius to work out a Land Raider can die to 3 lucky lance hits (18 Damage total vs 16 wounds). 

A pair of Predators has other advantages: 
  • it offers redundancy: 3 lucky lances can't kill both and an opponent risks under/over killing when allocating shots
  • you can cover multiple fire lanes by positioning the tanks in different locations
  • for a few tens of points more than the Land Raider you can add a Rhino to the pair of Predators to run transport duty, thus focusing on the vehicle's specializations 
So in summary I think running multiples of the specialized Marine vehicles is the more sensible choice, but it's not clear cut; there is a place for the Land Raider (provided your opponent doesn't roll hot!) 

Astute Archons will no doubt appreciate they'll have to factor in the Probability of Hitting to determine the number of Shots they will need to allocate; but given circumstantial modifiers (movement penalties, Archon re-roll buffs) complicate the maths I'll let you work those out in situ!

This is quite different to my usual post and feedback is appreciated. Useful? Too long? Too complicated? Want to see more like them? Leave a comment below.

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