How important was individual skill in formation fighting?

[Dan Howard]

I wonder if there is any evidence for how those gladiator/soldiers performed in battle.

The Spartacus rebellion is a good place to start. The short answer to your question is "not well". Skill is important but discipline and experience are more important when fighting in formation.

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Can anyone explain why Mongol light cavalry would be taught how to hold a spear properly for a single jousting style duel even though his role is to be a hit-run archer? 

Because the premise is false. Some light cavalry acted as hit and run archers, others were skirmishers with javelins, others charged in with lances. The Mongol success was due to masterful employment of mixed-unit tactics.