Count Matches, Not Games

I have a spreadsheet that is used to track stats during a tournament. In the past we have always used a number of games as the minimum before a team's rating can change. We would like to change it so it's a minimum number of matches instead. A match can be as few as 2 games and (currently) as many as 7 games. If you look at the sample spreadsheet I've attached, the match data starts in column J. I've marked the top of the sheet to delineate matches but I'm not sure how the count the number of unique matches. The formula should be (for the first team) in E5. I've filled in that cell for the three examples. Any help would be greatly appreciated.

Hi

Try this one.
E5

Formula:

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copy down each teams.

Regard

It seems to work, but is only counting games (for the first team as an example) in row 6. It needs to check both row 5 and 6 as not all teams will have stats in each match for both types of games. Is that possible?

Hi

Formula I gave you work for matches only, not game?
Countif every 5 columns as count 1, once you put the score in 1 or more up to 5 each matches. Sorry this only count 1 row 6, not both row 5 and 6. I try nothing work? Unless someone out there can crack it or not?

To countif a games instead as matches is this

Formula:

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This can count both row 5 and 6.

Regard

Neither of these solutions will work for me as I need to count matches (not games) and a match can consist of both types of games or just one (or the other) so it needs to look at both row 5 and 6 (in the case of the first team). I need to have this working by the 12th so I guess I will start looking for another approach.

Thanks for trying!