What is the optimal ratio of the preceding to maximize chess progression?
The ratio should be about 1:1. For progression it is esssential that you lose enough games, i.e. play against strong opponents. Playing weak opponents and winning does not lead to progress. It is very important to analyse your lost games thoroughly: spend as much time on analysis of a lost game as you spent on playing it. If you have little occasion to play stronger players, then you should study grandmaster games as a substitute for play.
According to my experience much more practise. Chess is not accumulating declarative knowledge it is rather a procedural skill. It's like cycling or skiing, reading books is a minor part. Best is playing, analyzing, playing...
It's different for different people.
What improves skill most:
Playing opponents at roughly your strength, to a little bit higher.
Analyzing your games.
Playing on longer time controls.
Watching GM lectures on youtube.
Practicing tactics trainer.
What has the least benefit for improving your skill:
Game after game after game... never stopping to analyze
Opponents that are too weak to be much of a challenge.
Opponent that are too strong for you to understand why you lost.
I disagree with
"Opponent that are too strong for you to understand why you lost."
The stronger your opponent, the more you learn. You have to spend time to fully understand why you lost. I have played against grandmasters who were kind enough to analyse after the game and point out their view on the game. If you want to have fun, then crush the weak, but if you want to make progress, then play as strong opponents as you can get. I am opposed to play in U1700 or U2000 tournaments. Open tournaments are great: you win against the weak and then you can play the strong and learn from them.
Playing too many games against a much higher rated opponent is disheartening to most. They lose morale, and a will to play.
Most players when playing against an extremely strong opponent relative to them self usually make a great many mistakes. They will have many points where they went wrong. When you have 10 screw ups in a game it's hard to isolate 1 or 2 key points to work on.
Think of it sort of like "That which doesn't kill you only makes you stronger." However there is a limit to this.
So a bit of a work out, getting slapped around, and knocked on your butt can have a way of making you tougher... That's vs someone around or a little above your skill level.
However if a 9 year old girl were punched in the face 10 times by Mike Tyson it would not greatly improve her fighting ability. She would never want to get in a ring again! You can argue "Well she just should have ducked the first punch", and "She should have thrown some punches of her own". The result however was already a forgone conclusion. She had no shot there.
However if that same 9 year old girl got beaten up by say a 13 year old girl a little bigger and stronger, and faster... it was not completely 1 way, the 9 year old got a punch or 2 in. You got something to work with as her boxing coach. There were points in that fight the 9 year old could have turned it around. There were things she could have done to defend herself better. She can learn from this.