Forget that most people would consider it Friday until they go to bed when it's been Friday, even after midnight. The official clock date changes at 00:00. If you go to a party Friday night (say at 22:00, 10:00pm) and make it home and get to bed at 00:40 (12:40am) our heads usually make us think it's still Friday, when in fact it's actually Saturday - very early morning.

Look at the date by the departure time on your ticket. If that day says 00:40 or 12:40am March 15, then your plane leaves very early Saturday morning (what many people would consider Friday night), and assuming you come to the airport 1 hour prior to flight time, you'd want to arrive Friday night. If it says March 16 then that is what many people think of as Saturday night - but actually leaves very early Sunday morning March 16.

On that note, I'm very used to this distinction living in BOM right now where that is a distinction you need to know as many international departures straddle that late night/early morning boundary.

Being an eastbound redeye departing after 00:00, you're arrival date will be the same as your departure date assuming it's a non stop.