Ever since I started hunting bosses after the Bosstiary update of Summer 2022, I have been wondering about exactly how the boss respawn window works. It took me several years of collecting data and investigating to finally reach a conclusion, which I will present here. My curiosity was first piqued when I read TibiaWiki's Bosses Spawn Frequency article. The author has done a fantastic analysis, including many interesting plots that showed the respawn windows quite clearly. There were, however, two features of the plots in particular that didn't seem to have satisfying explanations to me.
The first feature is that the first and last days of the plots seem to always have a slightly lower probability than the other days. The author claimed that this is caused by the Kill Statistics update time being 7 hours earlier than Server Save, which causes some killed bosses to appear to have an additional day in their respawn interval. The second feature, which was not addressed in the article, is the very small (usually less than 1%) probability before the first day and after the last day.
First we need to understand an important fact about bosses. Every boss has a duration which determines how long the boss or creatures are alive for before they despawn. For most weak bosses it is 1 hour, while for rare reward bag bosses it is higher, often 8 hours. Importantly, a boss can only spawn if there is enough time before Server Save for its full duration to pass. For example, Zarabustor is a 1 hour boss, so he can occur all the way up to SS-1. Furyosa is a 4 hour boss, so she can appear up to SS-4 but not after. Ocyakao is an 8 hour boss, so he can never appear after SS-8.
To get to the bottom of what was going on, I decided to write a simulator. It models bosses respawning and getting killed, along with correct times for Server Save and Kill Statistics. The output of the simulator is a plot, just like the ones from above. Then, I would play around with the simulator's rules that govern when to decide to respawn a boss, and keep tweaking the logic until the output plot looks the same as the real-life plots, including both of the unusual features I have mentioned. With the boss duration logic accounted for in the simulator, I eventually found a set of rules that matched the real-life plots.
Every boss has a min and max window that is a whole number of days. When a boss spawns, the game chooses a random time interval between the min and max window as a decimal number. It then adds that number of days, including the decimal part, to the current time. Then it finds which Server Save day that timestamp falls in. This is the next day that the boss will spawn on. When the server opens on that day, it will then select a random time to spawn the boss, making sure to not spawn it later than its duration would allow.
For example, Dharalion has a duration of 8 hours and a window of 6 to 8 days. Let's say he spawns on the 10th at 16:00 CEST (SS+6). The game will then choose a random time interval from between 6d0h0m and 8d0h0m. Let's imagine it chooses 7d12h30m. This gets added to the spawn time, resulting in 18th at 02:30 CEST. The game will then normalise this to be the Server Save of the 17th. Then, 7 days later, when the server opens on the 17th, the game will pick a random point in time between 10:00 (SS+0) and 02:00 (SS+16) to spawn him next.
The following properties emerge from these rules:
- The probabilities of the first and last day add up to be equal to the probability of each of the high chance days. This is evident in the graphs.
- A boss spawning early after SS means that for its next window, its first day is more likely than its last day. Conversely, a boss spawning late means that for its next window, its last day is more likely than its first day.
- A boss with a long duration cannot spawn as late as a boss with a short duration, which results in short duration bosses having similar probabilities for first and last days, while long duration bosses have much higher probabilities for their first day.
- When a boss spawns, you can look at the fraction into the current day, after SS, that it spawned, and then use that to calculate the probabilities of it spawning on the first or last day, the next time its window is open. In the above example, Dharalion spawned 25% into the day. This means that the next time it spawns a 6-day window is 3 times as likely as a 8-day window, because day 6 will be 0.75x as likely as a high chance day, and day 8 will be 0.25x as likely as a high chance day.
- The very low (usually less than 1%) probabilities for the days before and after the main window (days 5 and 9 for Dharalion) are an artefact of the Kill Statistics update happening at SS-7. For Dharalion to have a 5-day duration according to Kill Statistics, he needs to have a 6-day window, and the first kill needs to happen after the Kill Statistics update. To have a 9-day duration according to Kill Statistics, he needs to have an 8-day window, and the second kill needs to happen after the Kill Statistics update.
There are three other factors that can affect boss respawns that are worth mentioning.
Mid-day server downtimes
If a raid is scheduled to happen such that a warning for it appears in the Cyclopedia map and on the Observer app, and then the server goes offline, the raid won't happen when the server comes back up. The same might be true of bosses, but it is hard to know for sure, since there are no warnings for boss raids.
Server resets
If a complete server reset happens then raids and bosses can spawn again, even if they already spawned on the same day before the reset.
Maintenance
Sometimes bosses and raids get "lost" for no apparent reason, where their window passes by and they never occur. CM Liamas has commented about it in the forum, here and here:
In very rare cases, Ferumbras may not spawn if there is additional downtime on the day it is scheduled to appear.
It doesn't have to be a long, normal downtime; it can also happen when we install a fix that doesn't require downtime. It's extremely rare and the probability is very low.
