Boss pets

Boss pets are pets that resemble miniature boss monsters. There are two broad types of boss pets – those unlocked by specific drop by the boss in question, and those unlocked by other means.

Mechanics
The mechanics for the drop chance of the unlock item of boss pets released on 5 January 2015 is as follows:


 * Each boss has a base drop chance of the item, represented as $$\frac{1}{x}$$. For example, General Graardor's decaying tooth has a base drop chance of 1/5000.
 * Bosses with a hard mode have a drop rate that is 5 times higher when killed in hard mode. For example, the decaying tooth is 1/1000 in hard mode.
 * Each boss has an associated threshold, which is a number $$y$$. For example, General Graardor's threshold is 1000. This number relates to the total kills of the boss recorded in the player's Beasts tab in the Adventures interface.
 * The thresholds are all 1/5 of the drop chance's denominator multiplied by the number of pets. For example, the Dagannoth Kings have a drop chance of X/2500. One-fifth of 2500 is 500, but there are 3 pets, so the threshold is 3×500, or 1500.
 * For every $$y$$ recorded kills the player has of the boss, the numerator of the drop chance increases by 1.
 * This is rounded down, so having 1999 recorded General Graardor kills is treated the same as 1000 recorded General Graardor kills.
 * For bosses with a hard mode, the two kill counts are added together when checking the number of times the threshold has been met. Normal mode and hard mode kills are weighted equally; i.e. 1 hard mode kill has the same effect on increasing the drop chance as 1 normal mode kill does.
 * The numerator is capped at 10, so the drop chance will no longer increase once the threshold has been passed 9 times.
 * For example, a player with 2464 General Graardor kills and 603 hard mode General Graardor kills has 3067 total kills, so their decaying tooth drop chance numerator is increased by 3, giving a drop chance of 4/5000 (1/1250) in normal mode and 4/1000 (1/250) in hard mode.

In a purely mathematical format your chance $$f$$ of receiving a pet on any particular kill is


 * $$f = \frac{1 + \min( \lfloor \frac{ K + K_H }{D \times P \div 5} \rfloor, 9)}{D}$$

Where:
 * $$K$$ is your normal mode kill count and $$K_H$$ is your hard mode kill count
 * $$D$$ is the denominator of the base drop rate
 * $$P$$ is the number of pets available from the boss

Pets unlocked by drops
The majority of these pets were added in the boss pets update on 5 January 2015. They are all unlocked by obtaining a specific item drop from the relevant boss. A server-wide broadcast occurs when a player receives a drop. When the player uses the item, the message "As you touch the artifact [sic], a familiar face appears... ", consuming the item and unlocking the pet. Boss pets in this section are listed as follower pets in the Pets tab, the only exception being Vitalis.

Pets can be obtained while LootShare is active; however, they are not distributed via LootShare. Boss pets are always given to the player who would have obtained the drop if LootShare was not active.

These pets can be examined by anyone to display the number of kills of the boss the owner has.


 * Notes

Trivia

 * The Queen Black Dragonling and Dagannoth hatchlings were originally not planned to be released with the other pets, due to the Queen Black Dragon being "too big" and the Dagannoth Kings having old animations. Due to player feedback, they were included with the other pets.
 * The original concept was to allow players to obtain the pets by either getting the item as a drop, or by gambling reaper points for a random pet. The latter was scrapped later on.
 * For a short while after the update, you would get a notification in your chatbox saying "Your favourite bosses can now be obtained as pets, so what are you waiting for? Get out and catch them all!" This is a reference to the Pokémon franchise.
 * All of the examine texts of the boss pets that are unlocked by drops are plays on their larger counterparts' examines.