Calculating a percentage from a table that will grow

I have a table of results, 1st, 2nd and 3rd place - awarding each place a respective point.

I'm creating player profiles to see how many points, average placing etc. I've done those two stats. I now want to create a percentage finished in top 3. Because the table will have more data input into it afterwards.. i'm not sure on how to proceed creating this formula.

I have managed to count how many 1st, 2nd and 3rd places each player has gained and create a percentage over the games played so far, but not sure how to proceed to ensure the percentage keeps calculating when more data is added into the table.

I was thinking perhaps creating a new cell, counting the number of games, and then using that for the percentage?