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"Pink isn't a color. It's a lifestyle." - Chumbalaya
"...generalship should be informing list building." - Sir Biscuit
"I buy models with my excess money" - Valkyrie whilst a waitress leans over him

Wednesday, July 25, 2012

40k Metrics: 6th Edition Vehicle Mathhammer

Hey gang, Nikephoros here.  It’s rather obvious to everyone that I enjoy mathhammer.  I feel that there is an edge to be gained by being aware of the average potential of your units, and the ability to know which of the units in your book are most points efficient. 

6th Edition threw the old mathhammer for a loop in regards to killing vehicles.  It used to be rather straight forward to calculate the amount of shots it would take to shoot down a Rhino, but in 6th Edition it is very, very difficult.  I doubt most players have bothered trying to do it, so they may not be aware how tough it is to hammer out.  What makes it so hard?

It's still all about the numbers
In short, it’s because we have two parallel systems for killing vehicles operating at the same time.  One system is the hull point system, and the other is the penetration chart.  It is rudimentary to calculate how many hull points a unit can shoot away per turn, but what you cannot account for within that is the fact that at least 1/6ths of penetrating shots will explode a vehicle.  If you explode a vehicle with the first shot, it doesn’t matter how many hull points you can peel off with the rest of the shooting for the unit.  Additionally, some weapons are better at exploding vehicles than others, and that has to be taken into account.  Simply put, you have to take into account the overall likelihood that either one of these systems will kill a vehicle in a given turn, which is a really rather complex set of maths.

To solve this dilemma I created a script within Excel that calculates the odds of a particular unit to kill vehicles and I’m rather proud of it.  It uses the following logic to calculate the vehicle kills:

1.       At the very start of a simulation, create a unit of AV___
2.      Start Round 1
3.      For weapon #1, do a hit/miss roll.
1.       If the weapon hits, do a strength roll
1.       If strong enough, do a point of damage.
1.       If the damage kills the unit, skip remaining weapons and move to Round 2.
2.      Otherwise, if damage is high enough for penetrate check, then do it.
1.       If penetrate succeeds for instakill, then skip remaining weapons and move to Round 2.
2.      If the weapon misses, go to the next weapon for the round.
4.      If the unit still lives, repeat Step #3 for Weapon 2, 3, ....
5.      Start Round 2
1.       If the unit never died, it starts Round 2 at its current hull level.  Otherwise, start Round 2 with a fresh unit.
2.      Round repeats as Round 1 above.
6.      Repeat through Round 5.

A few comments.  As you can see, it presumes a 5 turn game, but you can tweak the settings for longer games if you like.  It runs 10,000 simulated games to get an average that should eliminate the outliers.  Also, it doesn’t allow for split firing, so units that can do that are shit outta luck.  This is much more refined than the 5th Edition mathhammer, since it allows for vehicle damage to carry over to the next turn.  You’ll also notice that logically the most vehicles any unit can destroy per 5 turn game is 5, which makes complete sense.  A unit with 200 meltaguns will still only be able to kill a max of 5 vehicles per game.

After I finished it, I went back and made it user friendly so you can literally put any shooting weapon in the game into it and custom make your unit with whatever loadout you want and run the analysis.  Download the .zip file hereOn the bottom right is your weapon pool.  Feel free to add every weapon in your codex in there.  It has slots for Weapon Strength, roll needed to hit, how many dice to add to strength for armor penetration, and what bonus you get rolling on the Penetration Chart.  Once you have the weapon pool filled, you go to the unit load out section on the left and add the weapons for the unit.  If you put Krak missiles as #1 in your pool and your Long Fangs have 5 of them, put “1” in the first 5 entries.

Once you’re done with the unit load out, hit “run analysis” and it will give you the results.  You’ll note that it changes slightly every time you run it.  This is because instead of just running the straight average of rolls, it simulates 10,000 actual games.  This is a large enough sample size, I think, that the results can be accepted.  But you can change that variable at the top too, if you feel like the results of 50,000 games is more reliable.

All in all, I’m very stoked about this and I hope you guys enjoy it.  Since 6th Edition vehicle damage is so much more difficult than previous editions, I would assume most people are going to get some value from it.

Last note, I couldn’t figure out a simple way to do twin linked weapons, so for my personal assumption I just raised the BS of the unit firing by 1.  Not perfectly accurate but good enough for me to draw conclusions from.

I’ll do a follow up article next week detailing some of the interesting results this program uncovers, and hopefully various people around the web will find some unconventional conclusions as well to add to the discussion.

Thoughts?  Comments?  Questions?

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