France '40 - 8,8 Hard Attack Value

[Jeff Conner]

Gentlemen

You have to remember that the hard attack value takes into consideration both the armor penetration and the accuracy of the weapon.  So, when comparing it to the 75mm L24 gun of a PzIV, you have better accuracy due to the flatter trajectory and higher velocity of the 88mm round, in addition to the significantly better penetration.  This higher value becomes important when firing at ranges beyond one hex where there is a range modifier.  And probably even more important than this is you have to remember that there is an effectiveness modifier that compares the defensive value of the target to the hard attack value.  If the hard attack value is greater than the defense, the modifier is not linear.  So a hard attack value of 39 is not three times as lethal in the game than a unit with a hard attack value of 13.  Unless, of course the defense value is greater than 39, in which case it is three times as effective.  Clear as mud?  John Tiller is a mathematician by education and so things that we might struggle with are second nature to him.  

After reading through this before posting it, it seems like an example might help.  I am going to use arbitrary values to make the math a bit easier.  If we have a weapon with a hard attack value of 40 shooting at a target with a defense value of 4, then the armor effectiveness modifier is 1/squareroot of 10, which is about .31 and the modified attack value is about 12.5.  If a different unit with a hard attack value of 4 were to shoot at the same defender, the armor effectiveness modifier would be 1 since that hard attack value is equal to the defense value and the modified attack value is still 4.  Thus, all other things being equal, the unit with the higher attack value will cause slightly more than 3 times the losses, even though the hard attack value is ten times higher.  Clear as mud now?