Friday, August 28, 2009

Falcon versus Wave Serpent: The Math

Hey there folks.

So Fritz over at Saim-Hann put out a post wondering which is more survivable, a Falcon or a Serpent. Having done the math-hammer in the past... my answer is that the Falcon's more survivable in a stand-off role while the Serpent's a better assault boat.
Serpents are less likely to be killed by melta, Demolishers and when Moving Fast.
Falcons are equally or more likely to be damaged in other cases, but also more likely to survive the results.

5th edition has really become the heyday of mechanized armies. With this, there's been a subsequent rise in melta too. So my general rule is that Falcons sit in the back and play DAVU tactics while Serpents are used to Transport anything that wants to get close.

This is just a general rule as the math does not include BS to-hit, cover, Fortune, Tank Hunters or other exotic situations. I also don't factor for rear-armour shots; this is both implausible to fairly calculate and I figure you're getting your just desserts if that happens. So all shots are considered to have already hit, the target is in the open, it is against AV12, and the Serpent Field is on. Here's the maths:
Wave Serpent Shaken Stunned Weapon D. Immobilized Wrecked Explodes
S6 8.33% 2.78% 2.78% 2.78% 0.00% 0.00%
S7 11.11% 5.56% 5.56% 5.56% 2.78% 2.78%
S8 13.89% 8.33% 8.33% 8.33% 5.56% 5.56%
S9 13.89% 8.33% 8.33% 8.33% 5.56% 5.56%
S10 13.89% 8.33% 8.33% 8.33% 5.56% 5.56%
S8 Ordnance 13.89% 8.33% 8.33% 8.33% 5.56% 5.56%
S10 Ordnance 13.89% 8.33% 8.33% 8.33% 5.56% 5.56%
S10 AP1 5.56% 8.33% 8.33% 8.33% 8.33% 11.11%
S10 AP1 Ord. 5.56% 8.33% 8.33% 8.33% 8.33% 11.11%
S8 AP1 5.56% 8.33% 8.33% 8.33% 8.33% 11.11%
S8 AP1 Melta 13.89% 8.33% 8.33% 8.33% 5.56% 5.56%
This is the chance per shot for a Wave Serpent to take a certain type of damage.
Or in graphical form:

Wave Serpent Sum Damage Dead Norm Dead SMF
S6 16.67% 0.00% 1.39%
S7 33.33% 5.56% 5.56%
S8 50.00% 11.11% 9.72%
S9 50.00% 11.11% 9.72%
S10 50.00% 11.11% 9.72%
S8 Ordnance 50.00% 11.11% 9.72%
S10 Ordnance 50.00% 11.11% 9.72%
S10 AP1 50.00% 19.44% 13.89%
S10 AP1 Ord. 50.00% 19.44% 13.89%
S8 AP1 50.00% 19.44% 13.89%
S8 AP1 Melta 50.00% 11.11% 9.72%
This is a Serpent's total chance to take damage and risk of being destroyed.

Falcon Shaken Stunned Weapon D. Immobilized Wrecked Explodes
S6 12.50% 2.31% 1.39% 0.46% 0.00% 0.00%
S7 17.59% 6.48% 4.63% 2.78% 1.39% 0.46%
S8 22.69% 10.65% 7.87% 5.09% 2.78% 0.93%
S9 27.78% 14.81% 11.11% 7.41% 4.17% 1.39%
S10 32.87% 18.98% 14.35% 9.72% 5.56% 1.85%
S8 Ordnance 31.56% 16.59% 12.42% 8.26% 4.63% 1.54%
S10 Ordnance 33.41% 23.38% 17.98% 12.58% 7.41% 2.47%
S10 AP1 9.26% 23.61% 18.98% 14.35% 9.72% 7.41%
S10 AP1 Ord. 4.63% 28.78% 23.38% 17.98% 12.58% 9.88%
S8 AP1 9.26% 13.43% 10.65% 7.87% 5.09% 3.70%
S8 AP1 Melta 4.63% 27.08% 21.99% 16.90% 11.81% 9.26%
This is the chance for a Falcon to take a certain type of damage.
In graphical form:

Falcon Sum Damage Dead Norm Dead SMF
S6 16.67% 0.00% 0.23%
S7 33.33% 1.85% 2.32%
S8 50.00% 3.70% 4.40%
S9 66.67% 5.56% 6.48%
S10 83.33% 7.41% 8.57%
S8 Ordnance 75.00% 6.17% 7.22%
S10 Ordnance 97.22% 9.88% 11.23%
S10 AP1 83.33% 17.13% 15.74%
S10 AP1 Ord. 97.22% 22.45% 20.22%
S8 AP1 50.00% 8.80% 8.34%
S8 AP1 Melta 91.67% 21.06% 18.98%
This is the Falcon's total chance to take damage and risk of being destroyed.

Falcon vs Serpent Shaken Stunned Weapon D. Immobilized Wrecked Explodes
S6 1.5 0.83 0.5 0.17 N/A
N/A
S7 1.58 1.17 0.83 0.5 0.5 0.17
S8 1.63 1.28 0.94 0.61 0.5 0.17
S9 2 1.78 1.33 0.89 0.75 0.25
S10 2.37 2.28 1.72 1.17 1 0.33
S8 Ordnance 2.27 1.99 1.49 0.99 0.83 0.28
S10 Ordnance 2.41 2.81 2.16 1.51 1.33 0.44
S10 AP1 1.67 2.83 2.28 1.72 1.17 0.67
S10 AP1 Ord. 0.83 3.45 2.81 2.16 1.51 0.89
S8 AP1 1.67 1.61 1.28 0.94 0.61 0.33
S8 AP1 Melta 0.33 3.25 2.64 2.03 2.13 1.67
This is a risk assessment comparison of the Falcon versus the Serpent, broken down by type of damage.

Falcon vs Serpent Sum Damage Dead Norm Dead SMF
S6 1 N/A
0.17
S7 1 0.33 0.42
S8 1 0.33 0.45
S9 1.33 0.5 0.67
S10 1.67 0.67 0.88
S8 Ordnance 1.5 0.56 0.74
S10 Ordnance 1.94 0.89 1.15
S10 AP1 1.67 0.88 1.13
S10 AP1 Ord. 1.94 1.15 1.46
S8 AP1 1 0.45 0.60
S8 AP1 Melta 1.83 1.9 1.95
The numbers above are a risk assessment of the Falcon vs the Wave Serpent for total chance of damage and being destroyed.

For the risk assessments, the number given is roughly how many times more likely a HoloFalcon is to get a result compared to a Wave Serpent.
A value of 1 means the two tanks are equally likely to get this result.
A value greater than 1 favors the Wave Serpent.
A value less than 1 favors the Falcon.


And here's a side-by side of their survivability based upon movement.

*Image borrowed from the good Master DarkSol's Photobucket.

5 comments:

  1. Only one issue here, you didn't include Rending, either in the maths or in the "I'm not considering" section.

    Since Serpents are immune, that may swing things somewhat.

    :)

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  2. Serpents are immune to rending?

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  3. @TKE: Fair enough on Rending. I don't see it as a huge swaying point, but it is yet another for keeping the Falcon away from Assault Cannons. I'll update the list in the next few days when I have a bit more access time.

    @mchmr667: The Wave Serpent field disallows any additional dice for armour penetration. Thereby a unit with Rending will not get the extra +d3 if they roll a 6 to Pen. Of course, this is only against shooting from the front/side. The only unit it really tends to matter against is an Assault Cannon, as a S6 with a Rending 6 means an auto Glance vs Serpents but an auto-Penetrate vs Falcons.

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  4. Thanks for the numbers- this helps in making decisions.

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  5. Really?!! The guys at the shop are not going to be happy to hear this...

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