with a as
(
select 22 as old_rank, 4 base from dual union all
select 44 as old_rank, 3 base from dual union all
select 66 as old_rank, 2 base from dual union all
select 88 as old_rank, 1 base from dual
),
old_order as
(select a.*, row_number () over (order by old_rank) rn
 from a
),
new_order as
(select a.*, row_number () over (order by base) rn
 from a
)
select t1.old_rank, t1.base, t2.old_rank as new_rank
from       old_order t1
inner join new_order t2 on t1.rn = t2.rn;

  OLD_RANK       BASE   NEW_RANK
---------- ---------- ----------
        22          4         88
        44          3         66
        66          2         44
        88          1         22

with a as
(
select 22 as old_rank, 4 base from dual union all
select 44 as old_rank, 3 base from dual union all
select 66 as old_rank, 2 base from dual union all
select 88 as old_rank, 1 base from dual
)
select a.*, nth_value(old_rank, base) over (order by base rows between unbounded preceding and unbounded following) new_rank
from a;

  OLD_RANK       BASE   NEW_RANK
---------- ---------- ----------
        88          1         88
        66          2         66
        44          3         44
        22          4         22