ORIGINAL: herwin
I'm just learning the game, but I know something historical about the effect of odds--as of Friday, btw, when I completed the Bayesian analysis. Rather than calculating the odds in the traditional way, define a 1-1 attack as one the attacker has a 50-50 chance of a breakthrough with the defence being forced out of its position. So the combat power ratio corresponding to a 1-1 attack would be about 100% for an encounter battle, 200% for a hasty attack on a hasty defence, 300% for a deliberate attack on a positional defence, and 400% for a set-piece assault on a fortified line. The casualty percentage in a 1-1 attack averages about 15%, with the winner averaging about 10% and the loser averaging about 20%. The standard deviation of the casualty percentage is about a factor of 2. Now you say you want a 95% chance of a breakthrough? You have to increase your combat power by a factor of four. That doubles the casualty percentage on both sides. As a defender, you want to reduce the chance of a breakthrough to 5%? Again, you have to quadruple your combat power. National differences, tactical expertise, morale, and asymmetric warfare act as multipliers on the combat power needed for 1-1. And there ain't no such thing as auto-win. Well, there is, but it requires an 8-1 battle--a 3200% combat power ratio for an attack on a fortified line.
I'm always interested in improving my ability to apply statistics to problems. It's all very new to me (statistics), and some of your units of measure confuse me, so if I may ask a couple questions and make some comments:
1) Are these outcomes based on observed data or theorized?
2) 100% isn't a ratio! (I know, I can't help it - it's a comment not a question).
3) Explain your standard deviation unit of measure relative to the measures of your data. I don't understand your standard deviation of 2. I'm assuming you mean 2 percent standard deviation with casualties (so attacker 8 to 12, defender 18 to 22). Is that correct?
4) I don't understand your initial hypothesis that a 1:1 attack is a 50-50 chance of obtaining a "defender retreats' (or better) result. Is that correct?