Quote Originally Posted by Puzz3D View Post
It doesn't assume that. The larger unit will always have more men engaged than the smaller unit. The smaller unit will loose men at a faster rate than the larger unit. The 60 man unit will not loose 2/3 of it's strength in beating the 40 man unit.
That's all true, but it's just quantifying the advantage of the larger unit that is tricky. I think all of what you have said above could be true and the 40 man unit be say, 70% as strong as the 60 man unit rather than less than 2/3 as strong as you stated. I don't see how it overturns my point that the larger unit typically cannot bring all its numbers to bear meaning that the combat strength of the smaller unit may be more rather than its numerical size.

To take the issue further, I think we need a mathematical measure of a units' combat strength. But I confess I don't know how to construct that. I can see how you could quantify a unit's offensive strength (e.g. expected casualities inflicted) and even its defensive strength (expected casualities suffered versus a benchmark attacker). But how do you put them together to measure overall combat strength? If it was just casualities inflicted minus casualities suffered, it would not be very useful for solving this argument as it might average around zero, so it would be hard to say if a unit is more or less than 2/3 as strong as another.

Strikes at a flank or rear of a man get a substantial combat bonus which further increases the advantage of the larger unit.
That's a good point - I am not sure if outweighs my point about inability to bring numbers to bear, but it certainly needs to be weighed against it.