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Whilst these guys are mostly experimenting (they do know what they are doing though, the spear guy learns that the spear gets knocked away too easy on overly long pool-cueing attacks and the swordsman knows to rush and manages to do so at points but they're both experienced fighters in other weapons), the traditional method for spear vs shield is stab low, stab high. either you get through due to speed or you wear down the guy with a shield as moving them about, even light ones and having the force in the block to successfully deflect to shot rather than have it push the shield out of the way, is very tiring.
Spears are essentially hobbled by safety rules in a lot of things, theres a hell of a lot more that can be done with them if say, stabbing to the foot is allowed. after all, kill shots are not always required, sometimes its better to wound and maim to allow for killing after that.
Actually thats worth repeating, one shot kills are not always required. And by the surprisingly low casualty counts for most battles involving such weapons (with most kills being in the rout) its safe to assume that one-hit-kill shots are somewhat rare. Battlefield grave finds such as the Visby and Towton graves also indicate a lot of limb wounds.