5++ Is The New Pink

Let's do some quick math to see how much difference a 5++ really makes for a raider's durability. I'm going to look at what I feel are the most important (and common) anti-armour weapons versus the different possible armour values for transports.

As previously, HIT is chance to hit, GNC is chance to glance, PEN is to penetrate, and XXX is chance to do something useful. (immob, wreck, explode are all what I consider "useful")

S7 (Autocannon)
	AV10 OT	AV10 OT 5++	AV11	AV12	AV14
HIT:	0.666	0.666	0.666	0.666	0.666
GNC:	0.111	0.074	0.111	0.111	0.000
PEN:	0.333	0.222	0.222	0.111	0.000
XXX:	0.259	0.172	0.129	0.074	0.000
S8 (Krak Missile)
	AV10 OT	AV10 OT 5++	AV11	AV12	AV14
HIT:	0.666	0.666	0.666	0.666	0.666
GNC:	0.111	0.074	0.111	0.111	0.111
PEN:	0.444	0.296	0.333	0.222	0.000
XXX:	0.333	0.222	0.185	0.129	0.018
S8 AP1 Melta (Meltagun)
	AV10 OT	AV10 OT 5++	AV11	AV12	AV14
HIT:	0.666	0.666	0.666	0.666	0.666
GNC:	0.018	0.012	0.037	0.055	0.092
PEN:	0.648	0.432	0.611	0.555	0.388
XXX:	0.549	0.366	0.419	0.388	0.290
S9 (Lascannon)
	AV10 OT	AV10 OT 5++	AV11	AV12	AV14
HIT:	0.666	0.666	0.666	0.666	0.666
GNC:	0.111	0.074	0.111	0.111	0.111
PEN:	0.555	0.370	0.444	0.333	0.111
XXX:	0.407	0.271	0.240	0.185	0.074
S4 (Boltgun)
	AV10 OT	AV10 OT 5++	AV11	AV12	AV14
HIT:	0.666	0.666	0.666	0.666	0.666
GNC:	0.222	0.148	0.000	0.000	0.000
PEN:	0.000	0.000	0.000	0.000	0.000
XXX:	0.074	0.049	0.000	0.000	0.000

Well there's like a thousand lines of HTML that I hope translates well into blogger...

Here we have statistics for a number of weapon types against a number of different armour values. Each set only represents a single "bullet" from whichever weapon is being fired. I do this for all my statistics because it is more useful for me to know what chance a S7 shot has against XYZ, than specifically an autocannon. That way if you have mixed units with different numbers of shots but similar strengths, it is easier to calculate. (mostly, regular vs cyclone missile launchers are why I started doing this) So if you want to figure out how likely something specific is to damage a transport, just take the XXX value and multiply it by however many number of shots you have.*

Anyways, as we can see, that little 5++ really adds quite a bit of durability. As we can also see, being open topped really really hurts. In every case, it is harder to penetrate an AV10 5++ than it is an AV11, and it's almost as hard as AV12. So the chance to get to the damage table is a lot lower, but once you get there it is so much easier to do useful damage that it still ends up behind everything else. Also interesting is that the 5++ blows everything else out of the water when it comes to meltaguns. Land Raiders are still better, but otherwise nothing here beats it against the melta rule. Even with OT and AP1 stacking. Crazy.

We can also see that survivability against S4 increases by a factor of about 1.5. Instead of 1 in 13, there is about a 1 in 20 chance of something bad happening to you from a boltgun. Considering that's one full squad's worth of rapid firing, this still isn't very good, but it's much better than without the save.

So there we have it. With these results in mind, and the fact that the 5++ upgrade is reportedly pretty cheap, it's absolutely an auto-include on every raider you bring. If you need to shave some points, you might get away with taking them from your CC delivery raiders since with sails they're practically guaranteed to get there intact anyways. I plan to take them on everything I can though.

============================================

* - This is actually only mostly correct. I'd consider it close enough, but technically it isn't statistically accurate. Allow me to demonstrate:

S8 vs AV11
HIT: 0.666
GNC: 0.111
PEN: 0.333
XXX: 0.185

So if you have 2 it would be:

0.185 x 2 = 0.370 => 37% chance for a CML to do something useful.

But, actually, it should be:

1-((1-0.185)^2) = 0.335 => 33.5% chance for a CML to do something useful.

Multiplying the chance for 1 shot by 2 gets us pretty close, but it doesn't really work that way. If we have 2 shots, there are 4 possible outcomes: both do something, one does something, the other does something, neither do anything. By doing 1-0.185 we find the chance that one will do nothing, raising it to the power of 2 (which, btw, represents the number of shots, so if you had something that was S8 Heavy25 you'd raise it to the 25th power**) gives us the chance that 0 missiles out of 2 will do anything useful, and subtracting this value from 1 gives us the chance that something will happen. (if there is a 10% chance for nothing to happen, then there is obviously a 100-10=90% chance for something to happen, you see?) That chance for something to happen could be that both missiles do something, that one does, or that the other does. I don't really care about the specifics though, as long as something happens, I'm happy.

** - Note that this will never yield an answer greater than 1. That is because this statistic doesn't represent the number of expected useful effects but rather the chance to get a useful effect against a single target. If you're looking for the expected number of transports your entire army will pop in a turn, then multiplying 0.185 by the total number of missiles will give you that answer. For multiple shot units though, you still need to do the above or else your results will be skewed. Sure a CML can shoot 2 missiles, but they can only hit a single target!

12 long fang MLs and 5 WG CMLs will yield:
(0.185 x 12) + [5 x (1-(1-0.185)^2)] = 3.898 expected effected AV11 transports per turn

Compare this to:
0.185 x 22 = 4.07 expected effected AV11 transports per turn

See the difference? Either way it's about 4, but we can see that it is actually just under 4 instead of just over it. The reason it is lower is because it takes into account the times you "waste" a missile from your CML when the first one destroys the tank and the second one becomes redundant.