From what I understand (this is mainly my own opinion as there's very little factual evidence) the archers didn't carry any arrows during war. Standard sheaves were created by guild fletchers and arrowsmiths, and became government issue.
At the start of a battle, shaves of arrows would be handed out to archers. The most likely situation is that all the arrows conformed to a type - a specific, military standard size and length. The fletchers would make up countless thousands of the same arrow.
If you take the English Warbow Society / British Longbow Society standard arrow as an example, it's 32" long, around 1/2" to 3/8" diameter, with 7" fletchings whipped with silk. It was armed with a Type 10 bodkin (simple and fast to make.)
You'd end up with thousands of bags of 24 of these arrows, regardless who was shooting, and what weight bow they were using. When the sheaf ran out, if there were any more a runner would collect some and the shooting would continue.
The idea of archers carrying their own arrows is, I believe, more a hunting situation as during warfare there would be carts of arrow bags and arrow boxes provided by the government.
I also don't think archers would have "run out to collect arrows" between attacks. Historical battles didn't really work that way, and the two sides wouldn't take a break (especially not during a conflict such as Azincourt) so that the enemy could replenish their stocks of ammunition! Even if they did all go running out together to "re-load" all the arrows would be the same, so it wouldn't make a difference to accuracy.
There are all sorts of random myths regarding different arrowheads being used by archers for different approaching targets, but when you factor in the fear, short time frame and chaos it's hard to imagine each archer going through their choice of arrows to find the one that best fits. It would more likely be a standard head on every single arrow.
Just my uninformed opinion of course - I know there are a couple of pieces of medieval artwork showing archers with arrows in their belts, but I do definitely think that arrows during warfare were provided by the government, not the archer.