However, in practice, lamellar worn by infantry is still laced the same way, with the same kind of overlap (lower lamellae on the outside of the upper lamellae). Scale armour, whether worn by cavalry or infantry, overlaps the other way. Which suggests that the direction of overlap isn't a big factor in the protection.
That there is overlap matters. An arrow coming in will have to get through, typically, 2 to 4 layers of iron/steel to get through the armour.
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