Range Math

Firepower is a unit factor in and of itself, however, it is also important to understand that true firepower is also a function of range.  This is because range modifies firepower by changing the amount of space in which it may be applied.  In other words, range affects the amount of firepower that can be applied within a given space on an ASL map.

Using this math can help us assess relative strengths of different type of units and help us determine where the unit is most useful.  It can also help us improve a priori knowledge of when to take a shot.

Let's examine some of the things we know about range:

  • For each point of range, we know that we add 6 additional hexes times the range, in addition to the one hex from which fire would originate.  ex:  for a unit with 4 hex range, 1+6+12+18+24=61 hexes covered.
  • For this, we apply the number of firepower, except that the original hex is tripled and the first ring of hexes is doubled.  ex:  1(3F)+6(2F)+12F+18F+24F=69F or 3F+12F+12F+18F+24F=69F
  • Fire can also be applied at long range, which is halved.  ex: .5F(30)+.5F(36)+.5F(42)+.5F(48)=.5F(156)=78F
  • The total range effect on firepower for a range 4 unit, then is 147F
This means that for each range:
2: 48F
3: 90F
4: 147F
5: 237F
6: 312F

So we can see that BPV are distorted drastically in favor of units with longer range.  A Red Army 628 squad costs 12 BPV, while an SS squad costs only 15 BPV, despite having around 6 times as much in terms of total firepower.  But, let's face it, no one uses BPV anyway.

Of course, this is not the whole story.  You are unlikely to get a clear shot for your entire range (except perhaps in the desert.)  This is especially true in a city fight, where LOS are generally very short.

However, it does inform us as to where we want to place our different units.  It's just common sense that we will place units with longer range where their range will be more useful.  For this reason, I left MG's out of this analysis.

So while this analysis is nothing more than a confirmation of that which is common sense, it can inform better ASL play if you consider the possibility of maximizing your infantry, for example by keeping in mind that in open territory your 467 has about 4 times as much real firepower than your 838.  This might tell you to lead with your 467's until you can break their front line units and get your 838's to move in for the down and dirty street fight work.

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