20w idle is insane. Probably save more in the long run if you just get a more efficient router so it's not using so much juice during the times you have it on too.
I turn off my wifi off at night. This saves some energy and still allows me me to connect physically if I need to for work or whatever.
It may sound insane, but for folks that are operating gigabit or multi-gigabit fiber connections (certainly not the standard, but definitely becoming more available), the amount of CPU needed to route at gigabit+ speed, the switch chips that need juice, the WiFi radios that have 4+ antennae all needing amplification having a baseline power requirement, there's a surprising amount of juice required. If you're running one of those combo cable "modem" + router + WiFi access point jobbies, that's even more radios that need juice.
I didn't start getting a reasonable understanding until I started watching ServeTheHome videos, where they usually toss each device on some sort of Kill-a-Watt style meter, and then start putting the device under load to see how it changes.
The beast my ISP sends out says 5w power save (when does that activate when something is always connected?), 18w typical and 36w max (probably with usb devices plugged in).
Interesting. I own my modem. I guess that's not an option everywhere. Plus, options for modems are more limited than options for routers (or so it seemed a few years ago).
I turn off my wifi off at night. This saves some energy and still allows me me to connect physically if I need to for work or whatever.