Calculating Rolling Average Ignoring 0 Values

What I have is a spreadsheet with a whole bunch of sporting data on it. see attachment for an idea of the layout, Stats.jpg

In these data each round a player is given a rating. What I want to do is calculate is the average rating for each player across the last 3 and 5 games they have played. When a player misses a game they get a rating of 0 for the round. I want 0 ratings to be ignored in the running averages. Additionally, games yet to be played have a 0 in the cell and should be ignored. To get overall averages ignoring 0's was simple I used the averageif function, but I couldn't figure out how to use that but only extract the last 3 non 0 values. I currently have data up to round 12, so if a player has played in 12, 11 and 10 then the 3 round average should just be the average of these 3, but if they missed for example round 11 then the 3 round average should return the average of 9, 10 and 12.

The data is set out in the following way.

In column B I have a list of player names from cells B3:B618.

Across row 1 from N1:AM1 are labels "round 1" "round 2" etc.

The ratings for each player in each round are in N-AM and from 3-618. i.e. N3:AM3 contains the weekly rating for player 1, 4 contains player 2 etc.

I would like the 3 round averages to be returned for each player in column L and 5 round averages in column M.