What was Odin's level? If it was around 50 or 51 then 6 to 7 min is not surprising. 60 should still be decimating 110 groups.
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I have a spreadsheet that lists what i80 fish are open given the current time, which is calculable without parsing game data (it's just current time *3600/175). Since weather is random as far as I know, there's no way to calculate what the next weather will be without parsing the game data to get the info from the Skywatchers, which is not something I'd do (against the ToS and all). However, I'm trying to figure out an easy way to manually input the forecasts.
Also, does anyone know if the weather is the same on every server? If so, maybe there's a pattern to it?
http://na.ff14angler.com/timetable.php
http://na.ff14angler.com/skywatcher
You'll need to do some basic cross-referencing yourself, and it doesn't include sightseeing, but here you go. Also for the timetable it has the time set about 3.5 hours back, presumably just to give a more aesthetically appealing grid, but the skywatcher is accurate to current Eorzea time. (not logged in, checked via http://www.ffxivclock.com/)
In any case, while not as convenient and one-stop shop as you requested, there's plenty of online resources to get exactly that information.
everytime the fate is a success Odin gets stronger, i dont know for behemoth though