You can't shut down the Pi completely with the stock hardware, but there are a number of things you can do on the 3B+ to bring down the idle power consumption.
Check out this thread which has command-line commands to turn off some of the hardware (credit goes to the user who did the testing):
https://www.raspberrypi.org/forums/view ... p?t=208110
Normal idle is ~380-440 mA. If you turn off USB/Ethernet you can save ~200 mA, if you turn off Wifi/BT you can save a further ~50 mA.
So you should end up around ~160 mA idle if you turn everything off, which will give >2x the battery life.
I've done some much less precise testing of my own with a cheap USB current meter and these numbers seem about right.
Power management/gating in the 4-core CPU is actually pretty good, it's the USB/ethernet chip that takes a ton of power.