Mathhammer Monday – Bolt Throwers

For this version of Mathhammer, I thought that I would delve further into the High Elf Bolt Throwers. Since the bolt throwers allow you to choose whether you use the multi-shot or a single shot, I was curious as to when it is advantageous to use each.

These calculations were a bit more involved that the previous ones, and had me using a formula which I roughly ‘understand’. That being said, maybe these numbers are completely off, but they seemed about right to me!

The best way that I came up to compare the efficiency of the bolt throwers was to determine what their chances were for causing at least [x] number of wounds at each armour save and Toughness level.

Also, I realize that some of these toughness/armour save combinations do not exist (and probably never will), but I included the full range for completeness.

For the calculations below, the following assumptions were made:

  • No modifiers are present (no BS modifiers, no bonus/penalty to wound, etc)
  • The target does not have a ward (or regeneration) save

Summary of the Results

For those of you who don’t want to wade through all of the tables below, Here are the generalizations (in bold) of what I came up with from the results below:

  • Use the single shot against monsters and knights (2+ AS or better or Toughness 5-7 models)
  • Use the multi-shot against everything else

After stating it like that, maybe this exercise was a waste of time, since I think that is how people generally handle it.

Single Rank of Models

The calculations in this section relate to if you are firing at a single model or a single rank of models. Some things worth noting for this:

  • The single shot can only cause 1-3 wounds on a single model (or rank of models), so it has been omitted from the 4-6 columns.
  • Since the single shot ignores armour saves, the values for it are static throughout the separate tables. It has been included for easy comparison with the multi-shot at the target armour save level.

Red text indicates that it is the higher percentage chance.

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Multiple Ranks of Models

The calculations in this section relate to if you are firing at a unit with multiple ranks. The assumptions used are:

  • Models only have one wound  (i.e. the single shot will continue to pierce ranks if it wounds)
  • There are sufficient ranks for the single shot to pierce (up to 6)
  • Since the single shot ignores armour saves, the values for it are static throughout the separate tables. It has been included for easy comparison with the multi-shot at the target armour save level.
  • The multi-shot values in this table are the same as for the single model, but are included for easy comparison with the modified single shot percentages

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