ECR-Minimum. How much you should play per day.

There is still a lot of uncertainty about how many games you should actually play per day to maximize your earnings.
When I started playing, there was often talk of 75% or 78% ECR as the minimum value per day.
In the meantime, I have read different values, from 50% to 70%, 80%, or even 95% to achieve certain results.
But I have also read that the ECR value does not matter at all.

To check this (and no, I am not a mathematician 😆), I tried to calculate the loss of ECR per game with different minimum ECR values per day.
For this purpose, I made 3 tests. In the first test, we see a player whose minimum ECR value is always 99% and who perfectly times it to play again at 100% ECR.
Test 2 is a player whose minimum ECR is ~75%, so he is back at 100% after 24h of waiting.
Test 3 is a player whose minimum ECR is ~50%, so he needs 48h waiting time to be back at 100%.

Specifications:

-The regeneration of ECR is 1.05%/hour, so 25.2%/day.
-You lose 1% of your current ECR per game. So with 75% ECR you only lose 0.75% per game.
-We assume 10 DEC at 100% ECR in my calculation, just to simplify the calculation. In the end, it doesn't change anything anyway.
-We expect to alternate between winning and losing. The exact distribution is relevant for the earnings, but hard to calculate or take into account (Win streaks, or if the number of wins happens in the first half [higher ECR] or second half [lower ECR] of the games).
-Following formula is used to calculate the new ECR after each game: 100×(1-1÷100)^x=ECRnew.

1. Test: constant between 100%-99%.
2. Test: from 100% to 75%
3. Test: from 100% to 50%
3.2. Test: from 75.2% to 50% (day 2 of test 3).

Test 1:

25 games
50% win rate
12.5 wins a 10 DEC = 125 DEC.
Also on consecutive days 125 DEC.

Test 2:

28 Games
50% win rate
14 Wins a ~9 DEC = ~126 DEC.
Also on consecutive days ~126 DEC.

Test 3.:

68 Games
50% win rate
34 Wins a ~7.3 DEC = ~250 DEC.
On subsequent days: see test 3.2.

Test 3.2:

40 Games
50% win rate
20 Wins a ~6.2 DEC = ~123 DEC

a) If we look at tests 2. and 3.2. we do not exactly end up with 125 DEC. But you can assume, had I not rounded, we would end up with exactly 125 DEC per day 😊

b) So overall you can see that it makes no difference how much percent we play down to. So if you want to play a lot on one day and don't have time on the other, then play down to 50%. But please remember to play your quests! 😅 It also means that we don't have to worry so much in the middle of the season for example 😄

c) But never leave the ECR at 100%. This way you lose earnings constantly!

d) For the start of the season this also means that we can easily play a lot of games to move up to a higher rank, because at the beginning of the season the DEC income is much higher and also you can get to your rank from the last season faster, by which you earn e.g. 2 Chests in Silver 3 directly at day one.
From my point of view we don't want to play 40 games per day the whole season, even though we would only have to play 25 games or 28 games with higher ECR because I am lazy and in order to be able to go full speed again at the beginning of the next season, we have to have the ECR refilled anyway at the latest at the end of the season. Otherwise, the number of games we need to play per day will increase from season to season.
This means that we have to skip one day during the season (instead of regenerating 25.2% ECR/day and playing again, we get 50.4% in two days and end up at 100% again). With that, the numbers are the same. We just get to a higher rank faster, which of course is instrumental in the DEC reward. So the imaginary ~125 DEC we get more on the first day, we lose again by waiting another day. This gives us some tactics options.

e) Also it means for some players (especially beginners) who rent for single days, that they can or should fully power through on these days to maximize the DEC income. This is especially important when making the jump out of Bronze 3.

Here you can see the individual ECR steps between 100%-50%:

edit: And i see a little mistake right here 😆 So i am german and the phrase "GESAMT bis Spiel 28" means "TOTAL until Game 28". Sorry for that 😅

For calculation and rounding errors please forgive me. I probably could have automated the calculation process with Excel or something similar, but I don't know how to do that and I also enjoy doing calculations manually 😆