SQL Server 2019

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create table students (studentid int, studentscore int,    rankc int)
insert into students values (1, 77, 1)
1 rows affected

insert into students values (2, 87, 3)
1 rows affected

insert into students values (3, 67, 2)
1 rows affected

select * from students


studentid
studentscore
rankc


1
77
1

2
87
3

3
67
2


update students
set rankc = T1.Ranking
from students T2
left join (select RANK() OVER (ORDER BY studentscore desc) as Ranking, studentid
             from students a ) T1
on T1.studentid   = T2.studentid         
3 rows affected

select * from students


studentid
studentscore
rankc


1
77
2

2
87
1

3
67
3