First and foremost, Apex needs a name change ASAP if it does indeed come back. It needs to be seen and presented as a new tournament series so APEX's dark past of inappropriate sexual harassment and whatnot is signified in the past, and hopefully doesn't expand from that past. We want that to die... ALL OF IT!
I'm not even going to mention all the terrible TO's and organizing, because quite frankly none of that compares to the awfulness of what Alex Strife did to all those people. It was despicable, and we need to bury the APEX tournament series name and ZENITH tournament series name (both his creations) forever.
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Second off, it needs to actually be organized. APEX was organized like straight booty. As Tafo said, Mango would joke that he could show up 3 hours late and be early. I know several people who had pools start 4+ hours late at various APEX events. Honestly, the entire leadership at the top probably needs to be dumped if I'm being really honest, because it's never been organized in the slightest at a top management was. They would say things and then reverse it A LOT, including tons of DQ's.
I've heard seemingly half of Cali Smash stated "I hate APEX, and I would never go to it again" from top players to people nobody even knows, from anywhere from Facebook public posts, announcements on commentary, or just random conversations. Why? The organization sucked EVERY YEAR (Apex 2009, 2010, [there was no 2011,] 2012, 2013, 2014, and 2015), and multiple people I know got DQ'd from random reasons, pools and bracket matches changed, and so all... all from poor communications! Why would you go to that unorganized mess of APEX halfway across the country or world when you can go to all these other huge events?
This lack of organization is made into even a bigger issue with what Tafokints said. Nintendude, arguably the best TO on the APEX staff, wasn't even aware of this announcement until it happened. That's how bad they are with communication.
So in order to fix all this, they gotta start with communication. The staff has to know who's in charge, then the public needs to know. Then the staff must select the chain of command and their powers and responsibilities, and then the public needs to know the. The staff needs to make sure it properly delegates that power, and STICKS TO THE GAME PLAN! The staff then needs to properly go after sponsors, acquire a big venue (last year's venue that Red Bull found APEX was good from what I hear), acquire the proper setups and amount of setups, and the staff must double and triple check everything and have everything ready A MONTH before the event, not day two after TO's that weren't APEX TO's take the reigns.
If they organize, plan, structure, and time things right, it should be easy enough. Every other tournament seemingly does it without much issue.
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Third off, the APEX crew and staff not just needs to communicate and organize better, they gotta treat lower level TO's better. I've heard some pretty bad stuff, similar to what Tafo said. Basically anyone who has ears in the competitive community has. If they treat their lower level staff right, give them power and don't interfere with it or take it away (sans them abusing it or not doing things right), then things will go smoother for the players. Then, the event will go smoother.
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Lastly, NEWPEX's staff should be humbled by half a decade of failures. They should want to start a new leaf, use what they learned by those failures, and show the world that without Alex Strife and his shade involved, that they can do great things. Hopefully they do their best to prepare early, get things in place early, tournament organize correctly early, and make all the necessary preparations. If they do that and actually run things on time for once (and not over 7 hours late like the last 2 years), then the NEWPEX staff and event will hopefully make a huge step forward.
Edit: This is an extra comment, but booking APEX later in the year sounds wise. Booking a tournament in the American Northeast in the middle of Winter sounds like a disaster waiting to happen. APEX has narrowly avoided having storm issues. CEO was booked properly this year, and still many people aren't able to go because of it or are going to arrive way later than they had hoped.