Rank scores with multiple tie breaks

I'm about to organize a competition where the rules are weighted to make the scoring as even as possible - giving the lowest ranking player the most advantage in the subsequent round. The anticipated result of this will be very close scores (and much excitement) needing multiple tiebreaks to sort them out.

Name Points 1st 2nd 3rd ....... 8th
John 77 5 2 .... 1
Fred 65 3 6 .....0
SAm 77 5 1 .....2
Rich 99 4 8 .....5

Now I think I'm halfway to my solution. I'm thinking the solution (I'm happy to use a helper cell) would be to add the points + weighted 1sts + weighted 2nds + weighted 3rds ...... weighted 8ths. This way I can rank the order of the helper cell. What I want is that no matter how many 2nd places there are they won't equal a 1st. No matter how many 3rds they won't equal 1 2nd place.... etc. In my example 2nd place would be John because of the tiebreak in 2nd places. The first part of my formula is:

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this is where I come unstuck.

If anyone can help out to 3rd or 4th place I think I'll be able to extrapolate to 8th places.