Taking the shot - part I

It's always circumstantial  when you're at the game table; making the call on what you should order your squads to do is equally affected by the strategies being played, remaining forces, objectives, et cetera ... But sometimes you'll still find yourself having to make though calls, judging where to direct your heavy weapons. These are the times when simple math will help increase your chances at making more intelligible decisions. 

Using excel I've made some spreadsheets with data regarding the possible outcomes from using Long Fangs (BS4, firing at T4 models), including various armor saves.

17% to deal 0 wounds           ie. Ork Cannon Fodder

47% to deal 1 wounds

27% to deal 2 wounds

 9% to deal 3 wounds

48% to deal 0 wounds (4+ Save) ie. Cover Save

41% to deal 1 wounds (4+ Save)

10% to deal 2 wounds (4+ Save)

 1% to deal 3 wounds (4+ Save)

52% to deal 0 wounds (3+ Save) ie. Space Marine

33% to deal 1 wounds (3+ Save)

15% to deal 2 wounds (3+ Save)

 0.33% to deal 3 w.  (3+ Save)

83% to deal 0 wounds (2+ Save) ie. Terminator

15% to deal 1 wounds (2+ Save)

 1% to deal 2 wounds (2+ Save)

 0.05% to deal 3 w.  (2+ Save)

It quickly becomes obvious that there's a tremendous difference between firing at peasant rabble and true space marines. Whereas each long fang is around 83% likely to inflict at least 1 casualty when firing at regular orks, their effectiveness with the heavy bolter drops to 17% likeliness when the target becomes something clad in terminator armour.

Whilst this kind of simple math might appear to hint that it's "always better" to fire at targets which are easier to damage, there will be situations when you'll arguably want to focus fire key enemy units, making it possible to overlook that the outcome might be less than the optimum amount of wounds inflicted. 

But there will also be situations when your opponent might leave a weak opening that you should seek to exploit if the gain is sufficient, compared to the risk of achieving nothing.

To account for this we have to factor in a fictional value that makes a comparison possible between different scenarios.To make things easy and to illustrate how this can be done, I'll use some of the unit costs from the Space Wolves codex.

Wolf Scouts Pack - 15 pts / un-upgraded model
Blood Claw Pack - 15 pts / un-upgraded model
Wolf Guard Pack - 63 pts / terminator, Thunder Hammer & Storm Shield

to wound and kill 1 Wolf scout (without any saves taken):
 47% * 15   = 7.06
to wound and kill 2 Wolf scouts (without any saves taken):
 27% * 30   = 8.23
to wound and kill 3 Wolf scouts (without any saves taken):
  9% * 45   = 3.95

Average: ( 7.06 + 8.23 + 3.95 ) / 3 = 6.41

These values when summed together and divided will then give us a fictional value that can be compared to other values derived from using the same type of calculation against other targets.

to wound and kill 1 Blood claw (with a 3+ save taken):
 33% * 15   = 4.88
to wound and kill 2 Blood claws(with a 3+ save taken):
 15% * 30   = 4.44
to wound and kill 3 Blood claws (with a 3+ save taken):
 0.3% * 45  = 0.15

Average: ( 4.88 + 4.44 + 0.15 ) / 3 = 3.16

to wound and kill 1 Wolf Guard (with a 2+ save taken):
 15% * 63    = 9.74
to wound and kill 2 Wolf Guards(with a 2+ save taken):
  1% * 126   = 1.42
to wound and kill 3 Wolf Guards (with a 2+ save taken):
 0.05% * 189 = 0.08

Average: ( 9.74 + 1.42 + 0.08 ) / 3 = 3.75

This leaves us with three fictional values which hopefully will make us pick the best target to fire at. In this scenario a higher value will indicate that on average the opponent will loose a more valuable unit. Firing against the Blood Claws will result in a "fictional loss of 3.16 points" each time a Long Fang fires its' heavy bolter at a squad of 3 or more Blood Claws - whereas it will on average inflict a "fictional loss of 6.41 points" if the target instead are Wolf Scouts. Adding unit costs into the mix allows us to make better guesses to help support our tactical decisions. Allowing us to possibly see opportunities that otherwise might have been overlooked.  What I really want to emphasize is the comparison that can be made against over-prized Wolf Guard Terminators whom normally isn't a prime target for Heavy Bolters, which on average will net a "fictional loss of 3.75 points", compared against regularly priced Blood Claws at 3.16 points. This suggests that even though there is a substantial risk of inflicting no damage at all, the potential gain is still greater if one chooses to fire at the terminators. Though we shouldn't forget that the likely best choice will still be to use the Heavy Bolter against Wolf Scouts in the open, whom are unable to take any saving throws.

But even more importantly: these fictive values will not help you at the game table if you try to apply them to every shooting phase in every possible scenario. Being able to kill the opponents last troop to stop them from holding one more objective will likely be much more worth than killing some few extra paladins. Statistics and probabilities shouldn't be considered anything more than a useful means to help you re-think and get new perspectives on how to progress with various strategies. 

There are likely other ways to estimate and make similar comparisons, feel free to share yours or point out weaknesses in mine.