Tuesday, April 29, 2014

Mathammer - Smash Attacks

As someone who doesn't get to the table nearly as often as I'd like, I get some enjoyment from theory crafting around the hobby. In particular, I find mathhammer for certain scenarios to be interesting. After discussing a Flyrant's odds in combat with a Riptide, I thought about looking at when a Monstrous Creature should or should not smash.


In particular, I wanted to look at two of the more common MCs from other armies - Riptides and Wraithknights, and how the math worked out for each Tyranid MC.
First up, figuring out when to smash against a Riptide. The table lists wounds caused (not taking into account invulnerable saves, which will reduce the number of wounds by 1/3 for all MCs.

Charge
Smash Charge
Regular
Smash
Tyrant
1.67
1.67
1.33
1.11
Swarmlord
2.00
2.22
1.67
1.67
Old One Eye
3.33
2.22
2.78
1.67
Tervigon
1.33
1.67
1.00
1.11
Haruspex
2.96
2.59
1.33
1.11
Harpy
0.89
1.67
0.67
1.11
Crone
0.89
1.67
0.67
1.11
Carnifex
2.78
2.22
2.22
1.67
Exocrine
1.33
1.67
1.00
1.11
Mawloc
1.33
1.67
1.00
1.11
Trygon
2.33
2.78
2.00
2.22
Tyrannofex
1.33
1.67
1.00
1.11

With a hive tyrant (without 2 CCWs), the odds are actually best to not smash. Even on the charge, where the odds are equal, rolling more dice for the attack means you are reducing the impact of bad luck. In fact, the only other time it is better to not smash is when the attacking MC will be wounding on 3s or better. 

Interestingly, the new Trygon profile means it is better to Smash. Because it has an odd number of attacks, it's still smashing with 3 attacks, but now it gets a bonus attack for additional sets of scything talons. The other MC I thought was interesting was the Haruspex, which does better than I expected, particularly on the charge. Granted, getting there is a whole other issue, but despite being decried, it actually should do well in most circumstances.

Next, I took a look at the same group against a Wraithknight:

Charge
Smash Charge
Regular
Smash
Tyrant
0.56
1.67
0.44
1.11
Swarmlord
0.67
2.22
0.56
1.67
Old One Eye
2.50
1.67
2.08
1.25
Tervigon
0.33
1.25
0.25
0.83
Haruspex
0.89
1.77
0.50
0.83
Harpy
0.33
1.25
0.25
0.83
Crone
0.33
1.25
0.25
0.83
Carnifex
1.67
1.67
1.33
1.25
Exocrine
0.33
1.25
0.25
0.83
Mawloc
0.33
1.25
0.25
0.83
Trygon
0.78
2.78
0.67
2.22
Tyrannofex
0.33
1.25
0.25
0.83

Obviously, the Wraithknight is a lot tougher in combat.This time, the Carnifex and Old One Eye are the only MCs that should not be smashing 100% of the time. 

So from all these numbers, the more important idea is what factors determine whether I should smash or not. Obviously, these are Attacking Strength vs. Target Toughness and number of attacks. 

First, let's look at attacks, particularly the Attack characteristic. An MC with an even number of attacks loses more by smashing than a MC with an odd number of attacks. The Hive Tyrant is an example of this; against a Riptide, volume of dice outweighs the bonus to strength. Looking at the old version of the Trygon is the same - when the Trygon had an even Attack characteristic (6), smashing was mathmatically worse against Riptides (2.33 vs. 2.22 on the charge and 2.00 vs 1.67)*. However, the effect of even attacks is secondary to Strength vs. Toughness.

For this comparison, the Haruspex shows the difference between wounding on 4s and wounding on 3s without a smash. Namely, that smashing provides a diminished return on investment when you're already wounding on 3s. As can be seen by the Trygon, it is worth giving up 2 attacks to go from a 4+ to a 2+ to wound. However, it is not worth giving up a single attack to go from 3+ to 2+. 

With these principles, we can look at how Tyranid MCs (or any MC really) will shape up against other MCs. The only caveat is that on multiwound targets that can be instant killed by S10. For example, while number of wounds inflicted on a T5 Daemon prince would be higher for all Tyranid MCs (except Harpies and Crones) if they didn't smash, the result of each wound caused by a smash attack will remove all remaining wounds on the target. 

However, against a T5 target with Eternal Warrior, only harpies and crones should smash; all other MCs should use their normal attacks wounding on 3s or better. 

So, in conclusion, a quick couple questions to ask to decide whether or not to smash:
  • Will I be wounding on a 5+ or worse? Smash
  • Will I be wounding on a 3+ or better? Do not smash
  • Will I be wounding on a 4+ and have an even number of attacks? Do not smash
There are obviously some exceptions, but these are general rules to quickly think through when you should smash and when you shouldn't.

*Edit: I failed to account for old Scything Talons. Re-rolls to hit reduce the impact of taking fewer attacks, making the wounds caused on a riptide 3.52 vs. 3.11 on the charge in favor of smashing, and  2.97 vs. 2.78 in later rounds, also in favor of smashing. So the exception to the rules above is if the model rerolls to hit, it will be better to smash unless you already are wounding on 3s.