How to automatize a scoring table for tennis table competition?

Good morning to the community.
I am working on the file "Scoing Table Tennis Table".
I would like to create a tournament for tennis table.
I would like to automatize the process to make the scoring table for a competition.
In the exemple, in the table A1:E5, the player 1 loses against the player 2 (9-11), wins against the player 3 (11-2), loses against the player 3 (10-12).
The table located in the table range J8:012 represents the cumulative score of game1 and game2.

I would like to add player (player 5, 6) and have a table ranking that change with this supplements of players. I would like for exemple to add player 5 in J6 and J13.
I would like to have an update of the score when I enter a new score. I would like for exemple that the table located can cumulate the score of many games (game 1, game 2, game3).

Thank you for your help.

Capture.JPG

Thank you for your answer @HansDouwe and the time you took.

It's almost working perfectly.

1. In cell P12 and Q12, the score of the player2 is 0 W and 0 L. It should be 0 W and 3 L.

2. I've forgotten to mention that I would like to add in column U and AD, the number of points with a filter. I would like in the example to have this ranking for the game 1:
The team has a best rank if she has more points. If two teams have the same amount of points, the team with the best difference has a better rank. (i put the results in the picture)

3. I would like to add a player 5, 6... and have an update of the leaderscoreboard.

Scoring Table Tennis Table 2.xlsx

Wonderful, it's working perfectly.
Thank you a lot @HansDouwe.

Mine not as elegant, but I think it gives the results you wanted. Please check as the results differ from Hans.

For Game 1:
W =SUM(IF(IFERROR(FILTER($B$4:$E$7,$A$4:$A$7=$G4)-TRANSPOSE(FILTER($B$4:$E$7,$B$3:$E$3=$G4)),0)>0,1,0))
L =SUM(IF(IFERROR(FILTER($B$4:$E$7,$A$4:$A$7=$G4)-TRANSPOSE(FILTER($B$4:$E$7,$B$3:$E$3=$G4)),0)<0,1,0))
Points + =SUM(FILTER($B$4:$E$7,$A$4:$A$7=$G4))
Points - =SUM(FILTER($B$4:$E$7,$B$3:$E$3=$G4))

Need to re-range for Game 2 and Game 3.

File attached with players increased to 5.

Thank you josephteh. I check your reply tomorrow.

I checked your proposal @josephteh.
+ Your proposal introduces the idea of total for the points difference.
- Your proposal doesn't update the number of player if I add one or I remove one.

But in summary, it is showing me an other solution. Thank you again.