History XII: I Was a Sword in the Hand-grip

The scourge of perfect vs imperfect information continues.

Wins in blue, losses in red. Number of forces for A and D

From this we see that larger forces win battles, overwhelmingly. That's somewhat of an obvious conclusion. However, we should instead look at the battles which subverted mere numbers.

Ratio of force sizes to ratio of killing rate. Wins in blue, losses in red.

Very rare, and the ones that do have a significant power advantage, as shown by the $\alpha/\delta$ ratio. However, it's also interesting that the attacker can sometimes lose despite a numbers advantage. It's possible to determine a rough set of equations to determine if one has an advantage in both numbers and power, but I'll leave that for another day.

To improve the chance of victory, then, we'd like to do a little scouting before-hand, and only attack if we believe we have a numbers advantage. The quality of the estimation will depend on our hegemony's tech level.

Minor note: at tech level 11, attacking forces will have access to engineering capabilities, and so the effect of a defending castle is neutralized.