10th Mathhammer: The Basics and Termagants vs. Tac Marines
Aug 6, 2023 22:01:41 GMT
infornography, mattblowers, and 2 more like this

### Post by synapticinsight on Aug 6, 2023 22:01:41 GMT

Greetings Tyranid dice junkies, today I'm posting some numbers I've crunched for termagants and how their weapon options from the index stack up against the tactical space marine. You can skip to that below, but first I'd like to go over some of the basics of calculating probabilities and how I present the data. If there is interest, I'll post more numbers and stats for various units and matchups in 10th edition.

1: 1/6

2: 1/6

3: 1/6

4: 1/6

5: 1/6

6: 1/6

And that isn't very illuminating, because most of the time in 40k we don't care about the probability to find a single die-roll probability... Instead we want to know the probability of finding a particular value OR GREATER. This type of distribution is known as a cumulative distribution function (CDF). [For the big math nerds out there, we technically want the (1 - CDF), but the principle is effectively the same]. The CDF or probability of rolling a result or greater (X+) is shown below:

1+: 100%

2+: 83.3%

3+: 66.7%

4+: 50%

5+: 33.3%

6+: 16.7%

OK, cool, I think those numbers are pretty well known by most 40kers, but maybe the terminology is a little new. The other big CDF to know is for 2d6, because this is used for battleshock tests and charge rolls. The CDF numbers work out like this:

1+: 100%

2+: 100%

3+: 97.2%

4+: 91.7%

5+: 83.3%

6+: 72.2%

7+: 58.3%

8+: 41.7%

9+: 27.8%

10+ 16.7%

11+: 8.3%

12+: 2.8%

Alright, lets flesh those numbers out a bit: Typical battleshock test for a space marine (6+) passes 72% of the time. A charge roll out of deep-strike (9+) will only succeed 27.8% of the time. A typical not-in-synapse tyranid unit will only pass a battleshock (8+) test 41.7% of the time. Ok, enough of the basics...

Table 1: Termagants (10 models) vs Tac Marines expected wounds delivered in a single shooting round:

Hmmm... Ok, generally not great, but we can gleam a few interesting details. Spinefists have the least chance of failure and the best chance of inflicting 2 or more wounds at 56.5% (more often than not you will remove a tac marine model). The Devourers come in second and the Fleshborers are the clear worst option, damage-wise. We can also take a look at how the numbers change with swarming instincts and those "sustained hits 1":

Table 2: Termagants (10 models) with Swarming Instincts vs Tac Marines expected wounds delivered in a single shooting round:

Ok, better, slightly. Now the most likely outcome for Spinefists and Devourers will remove a tac marine model, and spinefists have a reasonable chance of pushing 3 or more wounds at 45.3%. For me, this makes spinefists an obvious pick against fleshborers. Even though fleshborers gain "assault", one round of spinefist fire can outpace 2 rounds of fleshborer shooting... so I might not mind giving up the shooting for an advance roll if I can get the shots off next round.

Finally, we can look at the best-case scenario where the termagants get Swarming Instincts and the benefit of Symbiotic Targeting from an Exocrine (reroll 1s to hit):

Table 3: Termagants (10 models) with Swarming Instincts and Symbiotic Targeting vs Tac Marines expected wounds delivered in a single shooting round:

As expected, best-case, but still not especially great. At 60pts per squad, no one is expecting killing machines. Termagants should do what they do best, take objectives, soak fire, and annoyingly respawn.

OK, that's it for today. Let me know if you want some more Tyranid mathhammer, and what stats/numbers you would be interested in seeing in future posts.

**--The Basics:**Ok, many of you probably already know what's in this section, but I'd like to make sure we start from the beginning so everyone is on the same page. First up are some basic statistics from dice rolls. Whenever we have multiple outcomes with different probabilities, we call that a probability distribution function (PDF). For a simple d6 roll, we have a flat probability distribution function where any outcome has a 1/6th probability. So the PDF for a d6 roll is:1: 1/6

2: 1/6

3: 1/6

4: 1/6

5: 1/6

6: 1/6

And that isn't very illuminating, because most of the time in 40k we don't care about the probability to find a single die-roll probability... Instead we want to know the probability of finding a particular value OR GREATER. This type of distribution is known as a cumulative distribution function (CDF). [For the big math nerds out there, we technically want the (1 - CDF), but the principle is effectively the same]. The CDF or probability of rolling a result or greater (X+) is shown below:

1+: 100%

2+: 83.3%

3+: 66.7%

4+: 50%

5+: 33.3%

6+: 16.7%

OK, cool, I think those numbers are pretty well known by most 40kers, but maybe the terminology is a little new. The other big CDF to know is for 2d6, because this is used for battleshock tests and charge rolls. The CDF numbers work out like this:

1+: 100%

2+: 100%

3+: 97.2%

4+: 91.7%

5+: 83.3%

6+: 72.2%

7+: 58.3%

8+: 41.7%

9+: 27.8%

10+ 16.7%

11+: 8.3%

12+: 2.8%

Alright, lets flesh those numbers out a bit: Typical battleshock test for a space marine (6+) passes 72% of the time. A charge roll out of deep-strike (9+) will only succeed 27.8% of the time. A typical not-in-synapse tyranid unit will only pass a battleshock (8+) test 41.7% of the time. Ok, enough of the basics...

**--Termagants vs Tac Marines:**Alrighty, here's how I break things down. For a minimum size unit of termagants (10), I will give the probabilities for A) most likely amount of wounds inflicted, B) The cumulative probability that LESS than the most-likely value will be inflicted, and C) the cumlative probability that MORE than the most-likely value will be inflicted. For example: If I say: "2 wounds (35%), < (25%), > (40%)", then this means the most likely outcome of the attack would be two wounds inflicted (which happens 35% of the time). There would then be a 25% that one or less wounds are inflicted, and a 40% chance that 3 or more wounds are inflicted. It is important to note that it is very possible that cumulative sum of probabilities for the "greater-than" or "less-than" number EXCEEDS the most-likely number. This might seem counter-intuitive, but it is very important to understand to best grasp the amount of damage you may be able to inflict, and which weapons or units outperform other ones. Ok, on to the numbers. Lets look a the three weapon choices for termagants: Fleshborers, Devourers, and Spinefists:Table 1: Termagants (10 models) vs Tac Marines expected wounds delivered in a single shooting round:

Most Likely | < | > | |

Fleshborers: | 1 wound (38.5%) | 30.9% | 30.6% |

Devourers: | 1 wound (32%) | 17.5% | 50.5% |

Spinefists: | 1 wound (29.1%) | 14.1% | 56.5% |

Hmmm... Ok, generally not great, but we can gleam a few interesting details. Spinefists have the least chance of failure and the best chance of inflicting 2 or more wounds at 56.5% (more often than not you will remove a tac marine model). The Devourers come in second and the Fleshborers are the clear worst option, damage-wise. We can also take a look at how the numbers change with swarming instincts and those "sustained hits 1":

Table 2: Termagants (10 models) with Swarming Instincts vs Tac Marines expected wounds delivered in a single shooting round:

Most Likely | < | > | |

Fleshborers: | 1 wound (33.9%) | 22.2% | 43.9% |

Devourers: | 2 wounds (27.1%) | 34.8% | 38.2% |

Spinefists: | 2 wounds (25.9%) | 28.8% | 45.3% |

Ok, better, slightly. Now the most likely outcome for Spinefists and Devourers will remove a tac marine model, and spinefists have a reasonable chance of pushing 3 or more wounds at 45.3%. For me, this makes spinefists an obvious pick against fleshborers. Even though fleshborers gain "assault", one round of spinefist fire can outpace 2 rounds of fleshborer shooting... so I might not mind giving up the shooting for an advance roll if I can get the shots off next round.

Finally, we can look at the best-case scenario where the termagants get Swarming Instincts and the benefit of Symbiotic Targeting from an Exocrine (reroll 1s to hit):

Table 3: Termagants (10 models) with Swarming Instincts and Symbiotic Targeting vs Tac Marines expected wounds delivered in a single shooting round:

Most Likely | < | > | |

Fleshborers: | 1 (30.7%) | 16.7% | 52.6% |

Devourers: | 2 (25.2%) | 26.1% | 48.7% |

Spinefists: | 2 (23.4%) | 20.9% | 55.8% |

As expected, best-case, but still not especially great. At 60pts per squad, no one is expecting killing machines. Termagants should do what they do best, take objectives, soak fire, and annoyingly respawn.

OK, that's it for today. Let me know if you want some more Tyranid mathhammer, and what stats/numbers you would be interested in seeing in future posts.