Mysql - generating trends of rank
In MySQL 8.0, there is a "straightforward" way using the windowing functions of RANK or DENSE_RANK.

If 5.7, there is no practical SQL way.  It would be better to pull the data into your app to compute the ranks.

I have a quibble with 1-2-2-2-3-... -- The guy with rank 3 is really 5th in the list.  The 3-guy will be disappointed when he drops to 4 or 5 tomorrow when the 2-guys' scores change a little.