In all cases, the league_update_timestamp should correspond to when we do our overnight updates for your league, which effectively is just when the league standings are updated ('cause we try to take care of a lot of the other stats in realtime, at least as far as display goes). It'll happen once per day (unless things go horribly wrong on our side :D), usually somewhere around midnight to 2am. The distinction on our end is that for most of the realtime stuff that you see on the site, we're doing calculations on the fly; our overnight update is when we make sure we have final stats and actually store all the new information for the day.