There are 4 matchups with 12 series each, for a total of 2^(12*4) = 281474976710656 possible outcomes. That's a lot of options to simulate, but no problem for my Distributed FizzBuzz Server on the Quantum Blockchain!
With every individual match assumed to be 50/50, these are the probabilities that each team will get into playoffs:
Latias 88.1% Hoopa 84.7% Palkia 84.7% Yveltal 60.1% Zarude 45.7% Koraidon 36.6% Mewtwo 0.0266% Chien-Pao 0%
These calculations exceed my ability to predict, so therefore I am sending good karma vibes to these matches so a miracle might happen
Mewtwo (12) - (0) Zarude
Gen 9 Random Battle: peap vs LoSconosciuto
Gen 8 Random Battle: FatFighter2 vs Sylveon used calm mind
Gen 7 Random Battle: ajhockeystar vs Betathunder
Gen 6 Random Battle: Elgino vs Micaiah
Gen 4 Random Battle: PrinceOfAllTacos vs SMB
Gen 3 Random Battle: HeadsILoseTailsYouWin vs freezai
Gen 1 Random Battle: Rage vs Mikon
Gen 9 Hackmons Cup: Petros vs MultiAmmiratore
Gen 8 Battle Factory: Regnite vs Wigglytuff
Gen 8 BSS Factory: Fragments vs Mishimono
Gen 8 Random Doubles Battle: snorlax142857 vs teresbahji
Gen 2 Random Battle: Thiago Nunes vs livid washed
Rip chien-pao's btw :(