Nice work! What did you assume for how guild statue bonus affects the probability?
It is 26% exactly as it should be. 
With regard to souls and glory, I cannot get the numbers right but the ratios between gold/glory/souls is essentially identical in the simulation versus the actual data.
| Ratio | Actual | Simulated |
|---|---|---|
| Gold/Glory | 34.5 | 33.6 |
| Gold/Souls | 9.2 | 9.7 |
| Souls/Glory | 3.8 | 3.5 |
There is little point in comparing these things, they look well within possible error. For me, most important is the fact that there is no bias of selecting which kingdom gets to pay the tribute, it is all random and independent because simulation matches the actual data. Variability in these things is multiple times higher but total numbers are all consistent and this really matters IMHO.
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So long story short, assuming everything maxed as far as possible, what is the average # of tributes I should expect?
Count up your kingdoms. Give your self 1 point for each kingdom below 3 stars, 2 points for each kingdom at 3-8 stars, and 3 points for each kingdom at 9 stars. Divide your total points by 10, multiply by (1+Guild Bonus/100) (so 1.01 for a 1% bonus, up to 1.06 for the 6% bonus), and that is how many kingdoms you should expect to send tribute each time you collect.
Edited to include the guild bonus. Thanks for the correction.
Does that take into account guild bonus?
Akots
Thanks for powering through the Data - a quick question as I know I didnāt have great luck in this data set but say I had a couple tribute pulls like some of my guild mates. Like the 20 below my guild mate pulled a couple days ago. But for arguments sake what if I had gotten say 2 20ās and 3 x 19ās what impact if any would that have had to the data set?
Cheers
Calvin
We need to hide this thread from the devs and tattletailsā¦ I donāt think they realize how much tribute we get, and Iād rather not help them figure it out lol.
But with all these triple tribute chance avg tributes are increasing
For the record Iāve never seen a 19 or 20 in my life playing on my account that is from a guild mate that has much better luck than I do
Derp. It didnāt, but I have now corrected it. Thanks.
It roughly corresponds to maximum on the plot which equals 8 but strictly speaking, one should use median and not average and percentiles and not standard deviation to described the probability frequencies. Anything from 4 to 13 should be roughly within 5%-95% percentile. Getting 0,1,2,3, or 14 and higher numbers is extremely unlikely.
You are welcome.
I briefly checked and removed 5 of your numbers at 14 tributes while adding 3 at 19 and 2 at 20 instead leaving all the rest same as they were. The probability for two-tailed Mann-Whitney test went up from 0.904 to 0.968 which means that these scores of yours would result in even a better overall fit for a random model. Otherwise, no substantial impact here, makes little difference in the long run considering total number of samples.
Actually, 3.3 million in 45 days for an end-game player is quite on the low side. At rather relaxed schedule, an end-gamer makes something around 2 million/week only in gold which totals at about, lets say, 12 million and tribute is only about 25% of that and you need to check in at least every two hours or maybe even more frequently. And some active players that frequent PvP ladder can make about 5-6 millions/week easily. So, this percentage goes further down to 10-12%. Considering how much effort it took to build up all this power levels, this is not something completely unreasonable.
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Iām sitting at all except 4 or 5 kingdoms at double tribute and yet Iām lucky to get 6 kingdoms give tribute and id be winning the lottery if I got 5k gold ever.
Ok after 144 days of meticulous tracking and 2000 tributes later my findings are now posted here for the world to see
Of interest to me is that I only managed 17 collections of 16 kingdoms and 5 collections of 17 kingdoms. I never once received any collections greater than 17 and Iām virtually maxed out in almost every way in this game which could just be bad luck but perhaps itās something more - anyway hopefully the math savvy among us will dive in and let us all know!
Here is the grand total of resources and average by day for the tributes collected
Cheers
Calvin
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This is a ridiculous amount of effort on your part. Cheers for that! Are you willing to let us copy data from the spreadsheet so we can do our own analysis and histograms?
Sure I opened it up so others can download and do with the data as they will. Please share your findings here if anything of note is found.
My next labour of love is the Treasure Hunt which Iāve captured 416 matches so far. Once I get to 1,000 Iāll post that in the TH thread started awhile back with @Bolatsi
Cheers
Calvin
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For computing expectations, weād also need a list of how many kingdoms are at what tribute chance.
I can copy this over the shared sheet if that helps just let me know. I have Whitehelm in red as that was my āhomeā Kingdom for the entire 2000 tributes to keep the variables to a minimum. That said I did have a few kingdoms level up (maybe 5) in the 144 days as new content was released and I did not mark this when it occurred (which in hindsight I should have). However all the days / dates are listed in column H so it is feasible to go back and figure out what was released on what day etcā¦ if one wanted to
Edit - I believe all the 9 Star Kingdoms I should have listed at 30% tribute chance as they all go to triple Tribute chance so I updated the original jpg posted to reflect that change.
Cheers
Calvin
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Ok I added in a second tab to show the kingdom info as well so it should all be there for the folks that want to dive in
Cheers
Calvin
What was your average # of kingdoms per tribute?