Find text in vertical colum and go across to find value

I am making a score sheet for high school gymnastics and I need it to find a gymnast's name and return their score on a specific event. The following explanation is going along with my attached table so it may be easier to look at the table to understand what needs to happen.

When a gymnast (Let's say B) competes in all four events (Vault, bars, beam, and floor), they are recorded in the table at the bottom of the score sheet. Their name goes in the AA column, and their corresponding scores for each event go in the rows (So B got a 8.5 on vault, 6.625 on bars, 7.6 on beam, and a 8.1 on floor. Each of these numbers go into the cells in the appropriate column).
I already have the AA column formula which looks at all of the events and determines if a gymnast has competed in all four. However I am having trouble creating the formula that subsequently finds the gymnast's row in the event and returning the value of their average for that particular event.

I already tried to create a formula that uses index and match but it only seems to work sometimes. I left the formula in in case it helps you out.

Lastly, I have named ranges. Here are the corresponding ranges:
vaulth: B5:B14
barh: B17:B21
beamh: B25:B29
floorh: B33:B37

Can anyone make me a formula that would do this? If you aren't sure of what I'm asking I will be more than happy to explain more. Thanks!