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My numbers come from Robert Hardy's excellent military history of the longbow. He (and many others) argue that each of the three French "Battles" or divisions contained between 14,000 and 26,000 men. The numbers for english archers and men at arms are much clearer - paymaster reports indicate no more than 7000 english combatants on the field altogether, of whom at least 6000 were archers. Where do your numbers come from?
It makes good sense, your English archer could shoot 15 accurate arrows in a minute. Assume the English archers at Agincourt averaged 12 a minute and there were 6,000 of them as you say, that means in a minute well over 60,000 arrows had hit the french ranks, a 1000 arrows a second. And after ten minutes the English Archers would of shot over 600,000 arrows, and of course thats not counting your English men-at-arms who were waiting.
If there were 20,000 *knights* on the field, then clearly their support personnel would have added significantly to the overall number of French Combatants. Unless you believe that somehow the French fielded an entire army consisting *only* of knights and they left all of their retainers and their entire fighting tail twiddling their thumbs at home? A nobleman's status was *defined* by his ability to bring as many armed men as possible to the field. Your numbers make no sense whatsoever.
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7000 archers and 2000 men-at-arms against 20,000 french knights