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I'm seeing a lot of variance in the ratios. Some flails have longer handles, some have short. Some have chains as long or longer than the handle, some have almost non-existent chains. What are the advantages and disadvantages of various handle and chain lengths, and is there an "optimal" ratio?
Not an expert, but logically the shorter chain makes it easier to handle and relatively more precise.
A longer chain however, allows for a greater swing, resulting in a much heavier impact.
That however can also be achieved using a heavier ball on the flail. But that makes it heavier to lift and carry.
Using multiple balls however seem counterproductive, as it will make the flail harder to use compared to the impact you can achieve.
I suppose the idea is to make it harder to defend against, but if the defender has a shield, I think multiple balls are utterly inefficient.
So as far as I can tell there is no single optimal balance. It depends on the persons strength and agility, and I suppose it also depends on what type of enemy it should be used against. For a heavily armored opponent, a longer chain will be better to smash hard against the heavy armor, and the armor will make the opponent relatively slower to avoid attacks.
In short I think the bottom left or the one above seems best all round, if you want something more precise, other weapons will probably be preferable.
The best would probably be the bottom right, but with one of the balls and chains from the top left.
An advantage with the chain is to avoid a hard hit straining your hand and wrist. And that part can also be achieved with a short chain. But the chain also has the function that it can pass a defense that would block a cane. If you block the chain, the chain will bend and allow the ball to continue a short distance further. With a shorter chain the flail is easier to defend against.
I’m not thoroughly convinced by your mere claim of not being an expert.
I'd definitely say bottom left if you're going up against someone like a Roman hoplite, or similarly shielded but not so armored opponent. It doesn't take too much force to fuck up an unarmored arm, which a flail vs shield would be perfect for.
If they're shielded and armored, though, I don't think a flail is going to be so great.
Though as with all fighting, if one person is far more skilled than the other, they're winning most of the time, regardless of (competent) armaments.