Hm....

I am just thinking, Agility is the stat for faster movements right? So, with Yui putting all her skill points in Strength, wouldn't her running be slower too? Or maybe it's her endurance that would be lower?
This is just my speculation from something I read.

[quote=Wikia]
 "Kirito speculates that Godfree had focused on improving his strength stat alone, neglecting [agility], which is why he rejected running all the way to the dungeon."
[/quote]

To me it sounds like agility either helps with running speed or endurance of running.