Average by category

The title isn't very good I know; I don't know the right terminology to explain the problem properly, but i'll give it a go:

In column A I have a list of names, all of them appear multiple times. In column B there is a corresponding percentage. I would like to create a formula that takes the average of all the percentages that have the same corresponding name, or 'category'. I don't want to just go through and do it manually since there are roughly 32,000 different values.

I did have one idea; in column C I pasted in a list of all the possible names in column A and then in column D I used countif to find out how many times each name recurred. If both columns A and C are in alphabetical order, I thought I could use the normal average function, by doing, for example AVERAGE(B1:BD1), but this didn't work. Is there some special way in which you can use a cell name (i.e. D1) instead of a number in a cell range? I tried brackets, speech marks etc. but nothing worked.

I have searched around a bit on this forum to see if my question had already been answered, and did some extensive googling, but I couldn't find a solution.

Thanks for your help! I'm sorry my first post is asking for help; i'll stick around afterwards and try and help out where I can.