If you are interested in the range your ECR should be in if you play a certain amount of battles per day and don't want to read all the boring stuff, skip to the headings 'The logic' and 'The script'.
I'm sure that many people people play this game not only because it's fun, but also because DEC are worth actual money. While the amounts a casual player earns aren't much to write home about in high-income countries, they can make a tangible difference in lower income countries. Thus, people might be interested in how to make as much as possible in a day, taking ECR and the average amount of battles they play into account.
The Splinterlands Beginner's Guide recommends not playing more than 25 or so games per day (more like 28 or 29 actually), so that ECR doesn't drop too low. But this is a fun game. Sticking to only 25 games per day is simply an undesirable constraint. But we also like money, right?
So I have decided to create a simple mathematical model for this. The model is based on the following assumptions:
Please keep in mind that I have played the game for less than a week, my assumptions may be erroneous and the script below is the result of 20 minutes of late night keyboard bashing. If I am in error somewhere, do not hesitate to correct me in the comments.
What we are trying to calculate here is what number of battles creates a drop of exactly (or almost exactly) 25% percentage points for a given ECR. With this number, we will know which is our highest desirable ECR. The ECR at which you should stop is ECR - 25.
I will bore you with the math in the next paragraph. Those interested can simply look at the script at the end of the article.
Our daily decrease of ECR is 100 x e^(-0.01t), where t is the number of battles we play in a day and y is the starting ECR value. Our daily increase is simply 25. So basically, if you want to know at which ECR value to begin playing your 50/75/however many battles on a given day, what you need is to solve the equation y = 100e^(-0.01t) + 25* on, say, symbolab.com. Or do like I do and use this fancy Powershell script:
$Battles = Read-Host -Prompt "How many battles a day do you wish to play?"
$Result = [Math]::Round((100*([Math]::Pow([Math]::e, -0.01*$Battles))+25),2)
if($Result -lt 100) {
$Start = $Result
}
else {
$Start = 100
}
$End=[Math]::Round(($Start-25),2)
Write-Host "You should begin playing at $Start% Energy Capture Rate and stop at approximately $End% Energy Capture Rate."
function FullECREqv {
$a=0
for($i=1;$i -le $Battles;$i++) {
$a+=100*([Math]::Pow([Math]::e, -0.01*$i))
}
return [Math]::Round($a/100,2)
}
Write-Host "This is equivalent to $(FullECREqv) battles at full Energy Capture rate"
Read-Host “Press ENTER to continue...”
This script can be copy-pasted into a text file with a .ps1 file ending on any reasonably modern Windows machine and run from there.
Please note that this script is written in about 20 minutes, so it will return weird values for a number of battles lower than 30 or so. Nevertheless, it should give you a fair approximation on what ECR range you want to be in if you want play a certain amount of battles per day.