Boss hunting is one of the many things Tibia has to offer besides getting levels and doing Quests. Even though most creatures with a rare spawn are commonly called bosses by players, not all of them are actually bosses.
A boss creature is a unique creature that is some sort of leader of that race. Most boss creatures have one unique spawn, but that's not always the case (e.g Tyrn, Grorlam and some Killing in the Name of... Quest bosses). Nevertheless, there are many rare creatures which are not bosses but still of interest because they can be tamed and killed for rare items and their Bestiary entries. The easiest way to tell the difference between a boss and a regular creature is to look at their name on the Server Log: bosses have their names capitalized, whereas regular creatures do not (this can also be checked on the official Kill Statistics pages). Regular creatures' names are also preceded by indefinite articles (a/an), whereas boss creatures aren't (some of then have ‘The' embedded on their names instead).
For simplicity, we'll use "bosses" for both boss creatures and rare spawn creatures on this article.
Speaking of the Kill Statistics, this page is crucial for boss hunting. If it wasn't for these records, you would only be able to know when a boss spawned if you found it yourself or if a friend told you about it. However, by keeping an eye on the Kill Statistics we can know when each boss spawned for the last time and try to predict when it will appear again. For example, look at the spawn frequency of Gaz'haragoth:
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This plot clearly shows that after 14 days of being seeing for the last time, Gaz'haragoth can spawn again. It also shows us that after 27 days, the chance of it appearing drops significantly. With this information in hand, even though you can't predict exactly when Gaz'haragoth will appear next, you can tell if there's a chance of it spawning or not. Since this boss has the distinctive characteristic of spawning not long after the Server Save, it's easy to check whether it's there or not.
But how can the other points in the plot be explained? As you can see, there's a small increase again in 35 days until about 52 days, which corresponds to approximately twice the previous interval, meaning this data comes mostly from situations when Gaz'haragoth spawned but was not registered in the Kill Statistics (because it wasn't killed nor killed any character). This is the first important thing to know about the Kill Statistics: it will only register the boss if it was killed or killed at least one character.
The 1 day appearance is also very high, actually much higher than the other values. This can also be easily explained, and it's an example of the second most important thing to know about kill statistics. Even though we usually think about the Tibian day based on the daily server saves, that's not how Kill Statistics work. The statistics are updated once per day at around 3 a.m. CET/CEST, which is 7 hours before the Server Save. Because of this, and specially with Gaz'haragoth, there's often data of a given boss appearing two days in a row, when it was in fact the same boss that killed players before the statistics update but also after (or died after). As we know, Gaz'haragoth usually kills a significant amount of players, so this appearance before and after the statistics update for the same Gaz'haragoth is quite common.
Finally, the appearances between 2 and 14 days can be explained by the first ever Gaz'haragoth appearances in a given server, when the boss is present every day at the Roshamuul mountain until it's killed for the first time. Since the boss is always there, there's always a chance that someone decided to peek at it and died 3, 4 or n days after the last curious player that did the same thing.
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On the plots above we can easily see the minimum and maximum amount of days they can take to spawn and the points relative to 2x and 3x the spawn interval. Since these bosses don't have any special mechanisms of first appearance such as Gaz'haragoth, there's absolutely no record of them appearing within less than 12 days.
Something else you may have noticed is the fact that usually the first day and last day of appearances have a smaller frequency than the other ones. This is also caused by the Kill Statistics update time. Every time the boss is registered after the update time, the interval before and after that appearance will be offset by one day. When compared to the previous appearance, it will look like the boss took one more day to appear than it actually did. When compared to the next appearance, it will look like it took one day less. That is, of course, if these 2 appearances were not affected by the update hour as well. When predicting a boss appearance, this first day is what is usually called a "Low Chance" of spawning, because we don't know if the least appearance was affected by the Kill Statistics update hour or not.
Not every frequency plot looks that clear, however, due to the characteristics of each boss specifically. Let's check Undead Cavebears:
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It's not a secret that Undead Cavebears spawn every 3 days, in 3 different waves of 1, 2 and 3 cavebears each, 4 hours apart from each other. The thing is that this 8 hour span often leads to cavebears being killed before and after the Kill Statistics update on the same day, which generates intervals of 1 day and also 2 days until the next appearance. If they are only killed after the update hour (which happens often because they are frequently tamed), it may also generate 4 days interval data. Starting at 5 days, the data can be a result of any combination of these reasons.
The plot for Midnight Panthers is somewhat similar to Undead Cavebears:
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The major difference is the lack of occurrences in one day. This will mostly happen when the panther kills a character before the kill statistics and is killed afterwards, usually when players leave a low level character near its spawn place to check it. It can also be the result of the update hour effect and the rare, yet possible, appearance of a Panther within a 2 days interval. The somewhat small difference between the 3 days frequency and higher frequencies is due to the fact that only one midnight panther spawns per round and many players are looking to tame it. If it's tamed without killing any character, it will not be registered in the kill statistics.
This kill statistics driven approach is, however, not useful for all bosses. The main factor that makes it useless in some cases is the existence of multiple and independent spawn locations. For example, the White Pale:
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If anything, this plot only tells us that rarely any world goes over a month without killing at least one White Pale. Other than that, it tells us absolutely nothing about its spawn frequency because it can appear on 3 different locations. To understand the spawn frequency of a boss like this we would have to know where each appearance was and calculate the intervals for each spawns individually – which is not possible simply by looking at kill statistics. The same goes for the Crustacea Giganticas (multiple spawn places and variable respawn in the Seacrest Grounds), Tyrn and many other bosses of low interest such as Teleskor and Oodok Witchmaster.
This analysis can also be made for the long interval bosses, such as Ferumbras, though it's not as useful since many players will be alert for these bosses when they are about to spawn, even if they are unsure if the minimum interval has already passed or not.
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This plot does show us something we had already seen, but much more clearer: the chance of Ferumbras appearing seems to be the same for any given day once the minimum time has passed (1/15 ≈ 6.7%). Of course, once the interval is reached and the raid is imminent, every day without Ferumbras increases the chances of it spawning, up to the point when 175 days have passed and the data shows that Ferumbras will not take longer than that to spawn, so the chance should be 100%. It's important to note that even though this behaviour seems very consistent for many bosses (such as Gaz'haragoth and PoI bosses shown on the beginning of the article), we cannot say with absolute confidence that the same rule is valid for all bosses, and some of them may have different frequency distributions that are clouded by other factors.
One thing we cannot tell about boss spawning based on the kill statistics is the time of the day which they spawn. We know that some bosses have tight rules, such as Gaz'haragoth and Omrafir, but as for the other bosses it's up to the boss hunter's own experience, and maybe subject for another article.
Finally, even though the data to make this analysis originally comes from the official website Kill Statistics, the analysis wouldn't have been possible without GuildStats. GuildStats has been gathering the Kill Statistics of all worlds since 2015, and thanks to their detailed records we could calculate the intervals for each boss. If you don't know GuildStats.eu yet, make sure to pay them a visit, they have lots of interesting information!
Below you'll find a gallery with the plots for all the bosses we analysed, even those without predictable patterns. Make good use of them, and happy boss hunting!