What are the catch rates?

General Discussion
1

Idk if my luck is just terrible or the odds are rigged, but I’ve been trying to catch a lvl 16 relicanth on 1 hp and used ~30 balls.

2

Just bad luck, nothing is rigged. You might need to prepare.

Counting

You may try this calculator (the game uses ORAS mechanics):

If you use a Poké Ball, the chance of catching 16 level Relicanth with 1 HP and no status is 17.398%, or 82.602% of failure.
The chances of not catching n times are (1-0.82602^n)×100

With 50% you can catch in 4 Poké Balls, with 95% you will catch in 16 balls.
(1-0.82602^30)×100 ≈ 99.68% of catching (and you say ~30 balls, that might be lower).
With 27 attempts that is ≈99.43%.

How rare is that?

  1. The fact is that you may never complain when you catch your creatures with a single try. And you may have a lot of series when you catch it quicker.
    Such odds (with the given data) are about 1 in 200 catches, that means that it will happen about three times if you decide to fill in all the Pokédex!

  2. The critical hits have 6.25% chances. Have you ever seen two crits in a row? That is 0.625^2 ≈ 0.39% rare, or ≈99.61% in will not happen! Which do appear.
    That is almost as rare as not catching 1 HP 16 level Relicanth with 30 Poké Balls.

Prepare

You need to increase your chances.

Steps to catch Legendaries

  • What: Send out Ralts with Syncronize ability and with desired Nature
    Why: The encounter is guaranteed to have the same nature in this game; most natures increase one and decrease another stats, very beneficial!
    Where: Ralts Route 3, catch 20 of each nature and Syncronize ability to have the encounters’ natures you need all the time.
  • Switch to Durant with Truant ability, use Entrainment
    Why: The Legendary will have to skip every other move and hit less often!
    Where: Doable if you have 6 badges. Durant at Friend Safari Slot 2 (Nicknames are here: Friend Safari - The Pokemon Insurgence Wiki) has a 1/5 chance to be Truant (hidden ability). Not needed if that is not a Legendary.
  • Switch to Shuckle with Sturdy ability (level 45) or Baltoy with Focus Sash (level 34), and use Power Split.
    Why: Now Legendary hit less hard. And in contrast to just stat debuff (that will not affect critical hits), that will lower the critical hit damage!
    Where: Shuckle Midna Mine or Cyan Cavern, Baltoy Telnor Cave.
  • Switch to Onix with Sturdy ability, use Dragonify.
    Why: That will likely make the Legendary have no STAB moves to hit less hard (a unique TM of the game): Dragonify (move) - The Pokemon Insurgence Wiki
    Where: TM 117 Dragonify Torren Game Corner, and Onix Telnor Cave or Cyan Cavern.
  • Switch back to Shuckle or Baltoy, repeat Power Split for the same reason.
  • Switch to Axew (or evolved), use False Swipe until 1 HP.
    Why: that gets to 1 HP with no risk of fainting, to increase the chance of catching
    Where: Axew Broadcast Tower Mission 1.
  • Switch to Paras (or evolved) without Effect Spore ability with Leftovers, use Spore.
    Why: Spore has 100% chance and is the best for catching
    Where: Paras Friend Safari Slot 1
  • Catch with the best capturing device you have!

You may just lower Attack and Special Attack instead of Power Split to get less hits, and may alter the other points of the plan and used teammates at your desire.