I'm actually confused about this thing. You see in Y1 I thought Agility mainly affected your Movement speed and your intial vertical jump (This hardly ever came into play with anything but It's in the description so I included it) but recently I've been hearing people say it Agility has nothing to do with your sprint speed which leaves me with 2 questions.
What is agility supposed to do and if it doesn't have anything to do with your sprint speed why does it increase it the more you spec for it? I'm super confused right now lol.
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If you jump between 2 posts, for example, more agility will allow you to change your direction in mid air to a greater degree, turn sharper, etc. As far as running and walking speed goes, get someone else with you, have a foot race, then crank up your agility and re-race. Make sure no one is using the arc blade speed perk (or is it gunsinger?) or carrying a weapon that gives speed and agility boosts.