I also have this problem on a MacBook Pro that is about a month old (with the fancy touch bar). I will shut the lid with 30% or more in power, and a few hours later open it with 0% power.
At first I thought it was bluetooth devices, then I checked and in bluetooth settings/advanced I DO NOT have "Allow bluetooth devices to wake this computer." Nevertheless I made sure my magic mouse was turned off. This did not fix the problem.
I next checked to be sure that power nap was NOT enabled in energy settings. It was NOT enabled for battery, but was enabled when plugged in. I turned it off in both places just to be sure. I have not tested to see if turning off the power nap while plugged in will fix the problem I am having when not plugged in (it _should_ have no effect... but then my Mac should not be draining its battery either).
Then I went into activity monitor and looked at the energy dashboard. NONE of my apps say "yes" in the "Preventing sleep" column. However, I do see that the highest "average energy impact" is Amazon Drive with significantly higher "impact" than anything else:
Amazon Drive 19.95
Box Sync 3.95
Google Chrome 3.57
Mail 2.10
everything else is below 2, the vast majority below 0.25
So for lack of a better idea (since the Apple options do not behave as advertised, apparently) I'll try to uninstall Amazon Drive...