I will probably most definitely buy a new battery(ies) then, what I do not understand though, is why it is so much worse now, after having been rooted.
It's due to the fact that what's happening gets worse over time. You're just noticing it more since the phone was rooted. (It's like buying a new car of a make you never had before - suddenly you notice how many of that make you see on the road. They were always there, you just weren't taking particular notice.)
The only issue I had before, was that it lost charge ridiculously quickly after it reached 30%. Now it goes from 100% and quickly goes down, freezes at about "half" battery, then shuts itself off, turns itself on, and is then in the teens of percentages.
These are all indications of the same thing. It's a bit technical, but lithium batteries grow little crystals when they're being used. (The industry is working on ways to make batteries that don't do this, but it's going to be at least a few years before they even figure out what to try.) Sometimes the crystal will short the battery. That's enough to shut the phone off. It's also enough to fracture the crystal so it's not there any more. When you turn the phone back on, the charge will be anywhere from the same (for a tiny crystal) to almost dead (for a very large crystal). The more it happens, in some batteries, the larger the crystals get.
I have taken the battery out a few times when it shuts itself off, and then turned it back on myself with the same result. Once it went down to 3%, stayed there for about half an hour, suddenly turned off and on, to then be at 17%.
It was partially shorted at 3%. Eventually the short burned out, but the battery was down to 17%. (The percentage you see is an estimate - it measures the voltage of the battery, which is a VERY inaccurate way of measuring the state of charge. But anything more accurate would cost about as much as a few expensive cellphones.)
I just let it die again, and now I am letting it charge while off to see if that makes a difference.
I am terribly un-tech savvy, but even with my minimal knowledge in anything electronics, I don't think it would have been able to change overnight without something else going on.
Lithium batteries discharge by themselves even if they're not in the phone. It's about 5% in the first 24 hours, then about 1%-2% a month. So yes, it can change a bit overnight, especially if it's totally fully charged (which it isn't if you unplug the charger the minute the phone says the battery is charged). The closer to 100% charge, the faster the self-discharge in the first day.
Almost everyone is un-savvy when it comes to batteries, I just happen to have been an engineer in the field for a few years. I see most people wanting to get the most time they can out of each charge, meaning using it until the battery is down to 1 or 2 percent. That's like sprinkling a little lead in your food. It doesn't kill the battery right away, but instead of at least a few years of almost full performance, it means that the battery will be dead in 6 months or so.