UPDATE 13:00 ET, 02/06/2021: Sony Santa Monica has confirmed that the next God of War game has been delayed into 2022, making it the winner of this particular race.
Two of the biggest PlayStation games are easily Horizon Forbidden West. They're both third-person action-adventure games, yet another unfortunate thing they share in common is a vague "2021" release date. It seems probable at some point that one or both of them will be delayed into 2022 - it's more a question of whether the new God of War or Horizon will be delayed first, and for how long.
Without touching on the second point, the reason delays are likely is that both titles are not only the latest in a high-budget action series, but flagships for PlayStation as a platform. Developers Santa Monica Studio and Guerilla Games are owned by Sony, which isn't (knowingly) about to risk tanking the PS5 because it rushed games out the door. As history has proven, it's better to annoy fans and investors in the short term than sour them permanently.
That makes it difficult to nominate one game over another for being the first to get a delay, but there are useful clues for making a guess. The first is the amount of publicity material released to date - on that accord God of War: Ragnarok "wins," since Sony has yet to show any in-game screenshots or footage for it, whereas Horizon Forbidden West has had both since summer 2020. The latter game was, however, notably missing from the most recent State of Play event, which signals that Guerilla also has plenty of work left to do.
What About The Latest God Of War & Horizon Rumors?
There have been recent rumors of a Horizon Forbidden West delay, which puts a point in that game's favor. This should be taken with a baseball-sized grain of salt, though, since the source of that information is uncertain, even if the leaker in question has made accurate predictions before. Even major publications sometimes get rumors wrong - the facts themselves can change, especially if a source turns out to be deceptive or otherwise faulty.
The safest bet would be God of War: Ragnarok. If Santa Monica Studio isn't ready to show gameplay at all, it seems implausible that it could have anything more than a beta version - unpolished, but feature-complete - ready by the end of 2021, particularly with hundreds of people still working remotely during the COVID-19 pandemic. Of course the Horizon Forbidden West team could still pull out a surprise, perhaps because if it's further ahead, it will have a better sense of what it can and can't accomplish.
