This makes sense - I looked into it and was amazed at the number of things that want to keep track of where you are!
I am cautiously optimistic...I didn't turn the entire "Location Services" off (that would also turn off "Find My iPhone", but I did go into Privacy-->Location Services-->System Services to turn off things like "Location-Based iAds". Also, since I had gotten a recent message from AT&T saying my cell data was almost used-up (MOST unusual), I turned off "Wi-Fi Networking" (also under "System Services"). There are little arrows next to the items that have recently used your location, so that may be an indication which ones are draining the battery. I think the key is to turn off as many items as you can until you notice a marked improvement.
This is very similar to a battery drain problem I had with updating the OS on my old 3GS... The new OS default had something turned on all the time that was active - I think it was Bluetooth. It was constantly "fetching"....
Something else to look at. "Settings-->Battery" will show the proportion of battery used by each app in the last 24 hours or 7 days. So Mail and Safari have been draining my battery big time! I am hoping that Location Services is the culprit.
Ditto with my laptop, since I recently upgraded to OS 10.11.6 - huge battery drain. So I went to: System Prefs-->Security & Privacy-->Location Services-->turned off "Safari App" and also under System Services-->"Details" turned off "Safari & Spotlight Suggestions". Crossing my fingers that this will work. Especially since I am down to 9% and must now sign off....