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# Tribute statistics

For a while now, I have been wondering what the red guardian bonus to tribute means. It says +X% to tribute, where X is a number from one to six, depending on the guild. I see (at least) two possible meanings for this:

1. Multiply tribute chances by 1.0X, so if X is 6, so a level 10 3 star kingdom would have a 21.2% chance of occurring.

2. Add X to the tribute chance, so a level 10 3 star kingdom would have a 26% chance of occurring.

To test this, for the last few weeks I have been collecting statistics on all my tributes. With 29 three star and three nine star kingdoms, I had 405 kingdoms in 49 tributes 8.266 average; with four nine stars, I had 1519 in 186 = 8.16 average. Unfortunately, the last figure is between my two hypotheses. The first is almost ruled out (over five standard deviations too low), while the second is looking shaky (three standard deviations toohigh). To conclusively rule out both requires many thousands, not many hundreds of tributes. So it would be nice if people would post their tribute statistics, if they have them. Please include how many three and nine star kingdoms (and less than three stars), how many kingdoms gave tribute, and how many tribute attempts you did. Thank you.

Youâ€™re completely right about 49 tribute collections not being enough. I saw wild fluctuations over periods of hundreds of tribute collections, totaling thousands of kingdoms. I went from more than three standard deviations below expectation to almost exactly expectation. One of our forums archaeologists can no doubt come up with the thread where it was discussed.

Edit: and the red statue adds to the tribute chance. There may be some oddness surrounding early players whose kingdoms arenâ€™t at level 6 yet, but good luck getting good data when those players advance rapidly (changing their tribute chances).

My guild leader (@Calv1n) has been tracking his tributes for a few weeks now. Iâ€™ll flag him and see if his data might be compatible with your methods. Heâ€™s pretty end-game, so I donâ€™t think much will have changed with his kingdom status or guild bonus. Although we might have crossed red level 100 mid-way through his data collection.

Hereâ€™s the most recent thread IIRC, but it doesnâ€™t come to a definitive conclusion: it shouldnâ€™t be 21.2%, but it might not be 26% either.

49 tributes was my first set; my second was 186. Still not enough for statistical significance, but enough to at least show how the data is going.

@Courtenay thanks for posting this and discussing it with me on Discord the other day i appreciate it and hope we get a few more folks that post their data.

For myself I have:

Kingdoms 1 @ 6 stars, 9 @ 7 stars, 17 @ 8 stars and 5 @ 9 stars

Out of the last 360 Tributes collected the data is as follows:

2952 total Kingdoms (8.2 average)

Just for additional info for those wondering in those 360 tributes I collected:
1,631,049 gold, 2,593 gems, 183,734 souls, 147,570 glory and 5,346 gold keys
and this has all been in less than 26 days so far that I have begun tracking the data averaging about 14 tributes a day (thanks Vita!)

Cheers
Calvin

For a base tribute chance bonus at 20%, there are 3 options:

1. 20% + 6% = 26%
2. 20% + 6% of 20 = 21,2%
3. 20% and then 6% = 24,8% (two separate events)

I asked the devs about that but for strange reasons I never received an answer. Pretty sad as there is absolutely no reasons to keep that secret to the player. As it show precise numbers (10%, 20% or 30% and 2%, 4% or 6%), we have the right to know how is working the red statue.

Lets make one more tryâ€¦ @cyrup @Kafka @Ozball

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Could you explain how to get your option 3? I have tried your options 1 and 2; between Calvinâ€™s and my data, your two (my one) is ruled out, and your one (my two) is not looking healthy, so number 3 is better than the other two, but I do not understand how to get it from 20% and 6%.

In this reasoning, you have a 20% chance to get tribute the first time. If that fails, you then have a 6% chance. So the odds that both will fail are 0.8*0.94, or 0.752. This leaves a 24.8% chance that you got a tribute.

Ah, thank you. That possibility never occurred to me; there is a very good chance that is what is happening.

The Red Bonus should be additive:

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@Ozball is there a â€śceilingâ€ť for the tributes? I can remember getting 0 (yes zero) at least 4 times in the last several months but I have never gotten over 18 ever despite having 32 kingdoms at the ranks listed above. Is it possible to get 20 or higher and if so why is the % so much higher to get 0 than is it to get 32 (Based on what Iâ€™ve been able to piece together I donâ€™t believe anyone has gotten higher than 20 ever so Iâ€™m assuming that was the highest possible in the coding and it hasnâ€™t been changed as new kingdoms were added or the coding is such that after 20 it doesnâ€™t matter as itâ€™s not counted anyway?)
Cheers
Calvin

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If there are 32 kingdoms available then the maximum possible tribute is 32 but nobody will ever receive that because the probability is too low. Something like 1 chance in quadrillions or quintillions (if its how to say in English).I calculated months ago with 28 kingdoms but I dont remember the exact number.
With the actual 32 kingdoms and with maximum stars with available troops, I would say there is no chance to see a 23. Maybe even a 22. Of course with more kingdoms released in future and more kingdoms at nine stars, that wont be true.

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Nihmhain says that tribute bonuses are supposed to be additive. However, the numbers Calvin and I are too low for that interpretation. I have not run Calvinâ€™s numbers yet to get an exact figure, but eyeballing it bewteen the two of us we are at least four standard deviations low for just a straight addition, and probably more, while we are close to spot on for Grundulumâ€™s alternative.

I made a 1000 tributes study some months ago. There is no way possible that 20% base stat and 6% bonus from red statue are working to give 26%. My numbers were much closer to 24,8% (20% and then 6%). Thats the 3rd option I wrote 8 posts above.
The probability I had were for all kingdoms at 20% base chance and red statue at 6% but I had during my 1000 tributes test 1 and then 2 kingdoms at 30% base chance. And despite having these 2 kingdoms at 30% base chance, I still had a final result that was corresponding to 24,83% chance.

I would like to be educated here.

Based on a probability of 24.8%, how do I calculate the odds of getting a 0 kingdom tribute? How about 1, 2 etc?

I can then keep track when the number of kingdoms increase.

What you are seeking is a crash course in binomial probabilities. Hope that helps!

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If 24.8% is a chance of getting a tribute from a kingdom, then 75.2% is a chance of getting no tribute. For multiple kingdoms, you have to assume that chances for each kingdom are random and independent from each other, which is probably true but we donâ€™t know for sure.

For random and independent events, probability of multiple outcomes is multiplication of the probability for a single outcome by number of events. So, if you have 20 kingdoms, chance of getting no tribute at all will be approximately 0.752^20=0.00334, around 0.33%.

For 1, 2, etc you can use binomial calculator ( http://stattrek.com/online-calculator/binomial.aspx ) or make a spreadsheet as @Truxton posted.

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Cheers, Iâ€™m just lazy actually and hoped someone would just do it for me.

Calvin gives results for 360 tributes with five nine star kingdoms, and I have 282. He had 2952 tributes; I had 2407. Combing these figures gives 5359 kingdoms in 642 tributes, with an average of 8.35. Of the three hypotheses of what the 6% bonus means, that first, that it just a 6% increase, is completely ruled out; it is over 11 standard deviations too low. The second, that it simply adds to percent chance, so a 20% goes to 26%, is 4.7 standard deviations too high. This does not quite reach the five standard deviation threshold to rule it out completely, but it is looking pretty sick. Truxtonâ€™s third hypothesis is looking pretty good; it is .6 standard deviations higher than the result.

(I was considerably luckier than Calvin; my results were nine tenths of a standard deviation higher than those predicted by the third hypothesis; Calvinâ€™s were almost 1.6 standard deviations lower.)

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