How to reduce the mean on a dataset without changing the order of the data

Question

I created a list of anime I have completed and for each anime that I have completed I give it a score based on how good I thought it was. Now over time there are like 200+ anime in that list. But I now feel like my scores are very inflated. I want to change my scores such that it reduces the mean score a bit. Also whatever I do to the score of a single anime must be done to all the scores on the list to keep it fair. So I was wondering if there is a mathematically correct way of changing each score in such a way that for any 2 anime A and B, if A had a higher score than B before the transformation, it must have a higher score than B after the transformation.

Some simple transformation like reducing every score by some amount 'x' would not work since the minimum score you can have is 0 and if there is an anime which had score < x before the transformation then after the transformation it will end up having a negative score which is not allowed. I just want some way to shift the whole bell curve to the left a bit properly.

There has to be a proper function that can do this right? I am not that good at math so please forgive me if my description of the problem is not technical enough.

Edit: Thanks to bobeyt6 for suggesting I should divide every value with a number to reduce the mean. But I still have a question. If I want my mean to go to a specific number. Lets say my mean right now is 7.6 and I want it to be exactly 5 after I do the transformation, how do I pick which number I should divide with?

Answer 1

Try dividing all the scores by a number. This way, it will be above zero and maintain the order between them.

For example, if your list was $2, 4, 6, 8$ then you could divide by, say, $2$ to get $1, 2, 3, 4$ which maintains the order without going below $0$. Of course, you do not have to limit yourself to integers.

Not sure if this is the best method, but it works.

Edit: If you want your mean to be a particular value $a$, and your mean is a value $\mu$, you need to divide your mean by $\fracμa$. This is because the mean is the sum over the number of elements, and dividing all the numbers by any number $n$ also divides the mean by $n$.

If you have any questions about my edit ask in the comments.