Rare titans schedule

I couldn’t find this piece of information on the forum so I’ll share it.
My alliance, Dead Titans Society, have been collecting information on fought titans for a long while. Some weeks ago I put that information in a spreadsheet to look for trends, like performance against different colors, average flasks used, and so on.
One thing that emerged is that rare titans so far appeared following a pretty regular schedule: there is one rare every 10-15 titans and their color rotate following the series Holy, Dark, Fire, Ice, Nature.
This theory is based on really few samples (11 rare titans so far) so it may not take into account all of the process variance, but we used this scheme to predict the 3 previous rare titans and it worked all the times.
I don’t know if knowing in advance the color may be of any use, but knowing when more or less the next rare titan will appear can help planning the titans attack strategy, e.g. when you enter a hot window (last rare was 9 titans ago) you can let close titans go instead of flasking, in order to be always pretty full of flags on the next few titans.
I know many consider rare titans a waste of resources rather than an opportunity to get rare mats, but I hope this will be of help to someone.

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I’ve had the same observations, also heard of couple of rares that appeared under 10 titan intervals.
Also it appears that a Rare can’t come after an escaped titan. Not sure whether all escapes slow down the Rare, or only push it when it would appear.

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Thanks for your contribution @EvilSmoothie

Also in our database rares appeared only after killed titans (which is only 11 samples more, but it’s still a step closer to statistical significance).

I tested the 2 hypothesis doing 3 different counts:
a) titans between 2 consecutive rares
b) titans between 2 consecutive rares, minus 1 if the second to last titan escaped (hypothesis that escaped push rares by 1)
c) titans killed between 2 consecutive rares (hypothesis that every escaped slows down the rare appearance)
In our sample a) and b) have the same range of values (10-15) and similar standard deviations: 1.58 for a) and 1.40 for b).
On the contrary c) has a smaller range (8-12) and a much smaller standard deviation: 1.16.
This means that on our sample the variable number of escaped titans explains pretty well a big slice of the variance of the intervals between rares. If this fact holds for a larger number of observations the most straightforward conclusion would be that every escaped titan slows down the appearance of the next rare. This would also explain why in some cases rares appeared before an interval of 10 titans: if you kill them all (or most of them) they appear earlier on average.
It would be interesting to know what’s the rares appearance rate for an alliance that kills all and every titan

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We would need @Kerridoc or @bluenoser or some other top of the list alliance member to contribute. Not sure how many alliences chaon 12* atm but I’ve heard there is some.

Interesting. Perhaps an escapes are counted a fraction of a titan? Maybe the fraction of the escaped titan HP damage you do? (I believe that fraction multiplied by stars is credited toward your titan score as well)

Tagging anchor, zero, or dante would probly be best bet

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We collected data such as remaining health of escaped titans, but in order to infer such a formula the number of variables grows (model and coefficients) and so a larger sample is needed, especially if a random factor is included.
I like this idea and I’ll try to add a few columns to our spreadsheet with more sophisticated predictors based on this assumption and let you know if I find something

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I heard back from @Rilf that they are seeing rates every 10mdays or so, +/-2.

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@Rilf you’ve been summoned above

I can check later for more details. I have made a new tracking sheet which 7DH, 7DD and 7DF are using for about 7-8 month. So all data since rare titans are out.

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Ok. So passing DOES affect rare spawns.
Departed and Fermented (missing some early data from june and july) kill 12star back to back while we do not yet at Hunting.

Image shows titans spawened (not days as it is 23h) from one rare to rare.

@Kerridoc @alcaselzer @Rigs

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Thanks for your contribution Rilf!
The intervals for 7dd and 7df would confirm the hypothesis that rares spawn once every 8-12 KILLED titans, except for that one 7 that may be an outlier in case the interval behaves as a normal-like distribution with some thin tails that includes sporadic 7s and maybe 13s.
Also the 17 in 7dh may make sense if in that case more titans than usual escaped.

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Maybe every killed titan gives a specific amount of chance to spawn the next rare.
Like every kill adds 7% and it is correlating.
But restriction is it can not spawn before 6? 7? Kills

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No. From rare to rare. So to know how many were between reduce the number by 1

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EDIT: I’m a douche, I didn’t realize that clicking on your image @Rilf, I could see more figures than in the embedded image, so I’m editing the whole message to include data missed from the image and data from sdh killed titans intervals (following message).

EDIT2: Added data from @GrandGousier, thanks for your contribution! I don’t know your alliance name, so I’m referring to your data with a short for your name “grg”

Premise: in what follows I’m considering a merged sample consisting of data from 7dh (16 samples), 7dd (21 samples), 7df (18 samples), dts (10 samples), and grg (18 samples) for a total 83 samples. Each sample corresponds to the number of killed common titans between 2 consecutive rare titans. (So the numbers are reduced by 1 wrt to Rilf’s table)

The merged sample has this face, which starts to look less and less a belled distribution after GrandGousier data, because of the high eccentric peak at 7; I superimposed a gaussian distribution fitted to the data (red line, mean 8.5, std 1.48):
image

Here’s also the sample split per alliance. There’s a bit of variance among alliances, even if the distribution shape doesn’t change much. This may just be due to actual variance that will even out with more samples or it may indicate the presence of some factor that we are not considering yet):
image

Notice that in the first image I used the interval occurrences, while in the second image I had to normalize the numbers to make them comparable between alliances, so you see the frequency instead (occurrences / total samples for that alliance)

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As 12 is the maximum so far, 7% would mean 12x7%=84%.
If we go by 8% we are at 96%.

#edit @alcaselzer
7dh kills:
10
10
11
8
13
10
8
11
9
7
11
11
8
8
8
12

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Edited my previous message to include updates

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raretitan
A little drop during holidays :sunglasses:

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Can you also recover how many titans were killed between any 2 consecutive rare titans?

Results of alliance Les Archanges (french)

raretitan

I realize that the days number has a gap as because of the rotation you can have 2 titans the same day
Thank you 7DD for your Alliance War Team Planner :
:smile:

(The 1rst Unicorn was killed. Yes is missing)

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