Since MySQL 8.0, rank() window function is available.
Table
CREATE TABLE scores (score INT)
select * from scores;
+-------+
| score |
+-------+
| 1 |
| 2 |
| 100 |
| 5 |
| 3 |
| 100 |
+-------+
rank()
Rank of current row within its partition, with gaps
select score, rank() over (order by score desc)
from scores
order by score desc;
+-------+-----------------------------------+
| score | rank() over (order by score desc) |
+-------+-----------------------------------+
| 100 | 1 |
| 100 | 1 |
| 5 | 3 |
| 3 | 4 |
| 2 | 5 |
| 1 | 6 |
+-------+-----------------------------------+
dense_rank()
Rank of current row within its partition, without gaps
select score, dense_rank() over (order by score desc)
from scores
order by score desc;
+-------+-----------------------------------------+
| score | dense_rank() over (order by score desc) |
+-------+-----------------------------------------+
| 100 | 1 |
| 100 | 1 |
| 5 | 2 |
| 3 | 3 |
| 2 | 4 |
| 1 | 5 |
+-------+-----------------------------------------+