## Thursday, July 19, 2012

### 6th Edition Hull Points By the Numbers

EDIT:  I had a slight error in my calculations for the wave serpent.  I updated the graph with the improved calculations.  The Wave Serpent turns out to be slightly more survivable in this edition than the last.  As a bonus I also added graphs for armor 12 and 13 vehicles.

I was thinking the other day about how bad the 6th edition vehicle damage changes hurt my poor Wave Serpents.  Unfortunately the addition of hull points to the probability calculations takes you from Stats 101 to Stats 102.  The application of Excel and a few binomial calculations later, I think I've got some equations to compare 5th and 6th edition vehicle survivability.

I wish I retained more knowledge from my college statistics course, but I'm pretty sure the numbers are close enough for Govt' work.

All the calculations here are based on the chances of getting a vehicle kill with 5 hits.  I had to state the probabilities this way to account for the cumulative effects of hull-point attrition.

First up is the Wave Serpent.  These number account for both the energy fields and jink save.

Probability to Kill a Wave Serpent in 5 Hits

As you can see the wave serpent maintains fairly close survivability between 5th and 6th.   Eldar's situation may be less dire than I assumed.

I then decided to take a look at the Rhino and Land Raider to see how they both fared in 6th.

Probability to Kill a Rhino in 5 Hits

Probability to kill Chimera From the Front in 5 Hits

Probability to kill a Vindicator From the Front in 5 Hits

Probability to Kill a Land Raider in 5 Hits

You'll notice that the rhino lost a significant amount of survivability in this edition while Land Raiders stayed about the same.

Overall, you may notice that the curve for damage potential for the major strength/ap combos in the game got a lot smother.  Melta doesn't present as significant a jump in combat effectiveness against armor as it used to.  In fact against lighter armor, a Lascannon becomes a good choice.  It looses only a little effectiveness for a major range advantage.  Melta still remains the go-to weapon for dealing with AV14.

You should also consider that glances don't effect your ability to move and shoot anymore.  Outright kills are usually less likely for most weapons, so most kills will be by hull points.  While vehicles may die faster, they will in general be more useful while they are alive.

I worked up one more chart for you guys to look at.
Probability of Kill as Number of Hits Increases(St 7 vs Armor 11)

We've gained a much steeper curve in terms of measuring the effect of weight of fire.  What this means is that that putting a few extra guns on a target will get you better results more quickly.  To get an 80% chance of a kill you need about half as many guns in 6th to do the job.

#### 6 comments:

1. Are you factoring in the damage results that cause a vehicle to lose additional hull points? There's something of a hold-over from 5th edition where Weapon Destroyed results convert to Immobilized results, but additional Immobilized results convert to the loss of an additional hull point. Three Lascannon shots can wreck a Land Raider if two obtain immobilized results upon penetrating, for example.

1. No I didn't factor that in. Those situations would be pretty rare, probably less than a 2% shift in probabilities. The probability getting an extra hull point this way would be less than blowing up a Land Raider with a Lascannon 2 times in a row. I don't think it would have a big effect on the trends.

2. THIS... This is excellent. A man after my own heart. Well done.

3. Greetings!

That's a nice article. However, when I do the same calculations, I get very different figures from what I can see on your diagrams, at least for Wave Serpents.

For example, consider firing at S8. I assume that by "5 hits" you mean 5 shots that have already hit and only roll for armour penetration. So, here are binomial probabilities of removing exactly X hp with 5 S8 hits that I get (rounded):

Exactly 0 HP : 0,03
Exactly 1 HP : 0,16
Exactly 2 HP : 0,31
Exactly 3 HP : 0,31
Exactly 4 HP : 0,16
Exactly 5 HP : 0,03

This gives me the probability of removing 3 or more HP P(hp) = 0,31+0,16+0,03 = 0,5

Then, binomial probabilities of scoring exactly X penetrates with "Explodes" result with 5 S8 hits that I get are (rounded):
Exactly 0 Explosions : 0,75
Exactly 1 Explosions : 0,22
Exactly 2 Explosions : 0,03
Exactly 3 Explosions : 0,00
Exactly 4 Explosions : 0,00
Exactly 5 Explosions : 0,00

This gives me the probability of scoring 1 or more 'explosion' P(explode) = 0,22+0,03 = 0,25

Next, I calculate the total probability of a kill: P(kill) = P(hp) + P(explode) - P(hp)*P(explode) = 0,63

If I factor in jink save (5+ cover), I get the following numbers.
For HP:
Exactly 0 HP: 0,13
Exactly 1 HP: 0,33
Exactly 2 HP: 0,33
Exactly 3 HP: 0,164
Exactly 4 HP: 0,041
Exactly 5 HP: 0,00
Probability of knocking off at least 3 HP is P(hp) = 0,164 + 0,041 = 0,21

For explosion:
Exactly 0 Wounds : 0,83
Exactly 1 Wounds : 0,16
Exactly 2 Wounds : 0,01
Exactly 3 Wounds : 0,00
Exactly 4 Wounds : 0,00
Exactly 5 Wounds : 0,00
Probability of scoring 1 or more 'explosion' P(explode) = 0,16+0,01 = 0,17

Effective probability of a kill: P(kill) = P(hp) + P(explode) - P(hp)*P(explode) = 0,34

So I get 63% chance of killing a Wave Serpent with 5 S8 hits if it has no cover and 34% if it is in 5+ cover. Both results seem quite different from 45.62% that I see on your diagram.
BTW when I use the exact same macros to calculate the chance of "5th edition kill" I get the same result of 44,5% as you do. This gives me additional reason to suggest that your calculation of chances for 6th edition kill might be a bit off.

Sorry for such a long comment.

1. I did some double checking on my math, and I do have an error for the wave serpent. I had 4/5 instead of 4/6 for getting past the cover save. Fixing the error gives the .34 result you where expecting for the cover save. I'll update the graph.

This actually makes wave serpents slightly more survivable in 6th than 5th.

2. >> This actually makes wave serpents slightly more survivable in 6th than 5th.<<

Please note that this is only true for small numbers of hits, and quickly becomes the opposite once the number of hits increases. Considering S8 hits against a Wave Serpent, 8 hits and over would already show a greater chance of killing a WS in 6th than it was in 5th despite 5+ cover. Specifically for 8 hits it's 0.654 kill chance for 6th vs 0.610 kill chance for 5th.

0,654
0,61