you may try this:
Have hardcoded points in a seperate table for each rank. And created a temp table to find the rank first. Then inner join temp table with points table to map point based on rank.
declare @avgrank table(avg1 int ,rank1 int )
insert into @avgrank( avg1) values (95)
insert into @avgrank( avg1) values (90)
insert into @avgrank( avg1) values (85)
insert into @avgrank( avg1) values (83)
insert into @avgrank( avg1) values (76)
insert into @avgrank( avg1) values (75)
insert into @avgrank( avg1) values (75)
insert into @avgrank( avg1) values (73)
insert into @avgrank( avg1) values (72)
insert into @avgrank( avg1) values (71)
declare @points table(rank1 int ,point int )
insert into @points values (1,140)
insert into @points values (2,130)
insert into @points values (3,120)
insert into @points values (4,110)
insert into @points values (5,100)
insert into @points values (6,90)
insert into @points values (7,80)
insert into @points values (8,70)
insert into @points values (9,60)
IF OBJECT_ID('tempdb..#tempavg') IS NOT NULL
DROP TABLE #tempavg
SELECT avg1, RANK() OVER (ORDER BY avg1 DESC) AS Placing
INTO #tempavg FROM @avgrank a
SELECT avg1,Placing, p.point FROM #tempavg ta INNER JOIN @points p ON ta.Placing = p.rank1