If you're curious about the odds of getting a certain unit from a beacon, you can check the drop rate in-game. To view the drop rates, go to the 'Recruitment' window, then press the 'i' icon in the top-left corner. This will give you detailed information on the drop rate of each unit available in the game. Here's a breakdown of the drop rates for each type of beacon:
Public beacon
Common: 38%
Uncommon: 60%
Rare: 2%
Specialist beacon
Rare: 89%
Epic: 10%
Legendary: 1%
Expert Beacon
Epic: 90%
Legendary: 10%
Elite Beacon
Legendary: 100%
When recruiting with a Specialist Beacon, you are guaranteed to obtain a Legendary unit on your 101st recruitment.
Starting from your 80th recruit, a pity counter will appear, allowing you to track how many more recruits are needed to reach the guaranteed Legendary.
Note: The counter will reset if a Legendary unit is obtained before the 101st pull through direct recruitment. Only direct recruitment using a Specialist Beacon counts toward the pity counter. The counter will not reset if a Legendary is acquired by any other means.