are application submission timing & scholarship amount also correlated?

hey everyone -

according to what i know when you submit can affect your chances of being admitted to a certain school

so earlier submissions could lead to higher chances of being accepted in general

but i was wondering whether the timing of your application could affect your scholarship amount as well-

especially i was wondering if i should apply to a certain school asap if i have the median lsat for that school, or shld wait for a better lsat score if my goal is not only A but A + max scholarship