Kingdom Tribute - Is Guild Tribute Chance Bonus being accounted for? Bug?

TL;DR - Data I collected shows guild tribute bonus NOT being added to city tribute chances.

Results

I’ll start with result - I’ve documented below how I did the calculations as well as shared the spreadsheet with the data & calculations. To clarify - the below chart show odds of X number of cities sending tribute - NOT how much tribute you get.

For the chart below & for duration of my data collection -

• All 25 cities at lvl 10, all cities below 3 stars [every city has 10% tribute chance]
• Guild bonus = 2% [Red statue @ lvl 38]

Measured data was taken over the course of 7 days where I collected tribute ~70 times.

As is evident - Measured rates differ pretty substantially to what the statistical calculations says they should be.

BUT - if I set guild bonus = 0% & repeat the calculation - look how much closer measured is to calculated.

My question - is there a bug in the code not factoring guild bonus into tribute calculations?

Assumptions

When tribute is collected, each city independently checks to see if it should send tribute. i.e. 25 independent trials, each with their own chance of success.

The guild tribute bonus (Red & Yellow statues) applies to ALL cities. i.e. if guild tribute bonus is 5%, every city gets a 5% increase in tribute chance.

How to Calculate Tribute Chances

Two cases to consider here.

1. All cities are the same lvl - represented by “Bernoulli Trials” - every experiment has the same chances of success. The odds are trivial to calculate and follow the binomial distribution.

2. NOT all cities are the same lvl - represented by “Poisson Trials” - not every experiment has the same chances of success. Odds are much more complicated to calculate, typically solved by a mathematical technique referred to as convolution.

After a lot of research, trial & error, & dabbling in the R statistical tool, I made a google spreadsheet that will allow you to enter the tribute chance for each city and guild bonus. Found here.

It may be that the 5% is not additive but multiplicative. Meaning each kingdom would gain 5% on 10% so 10*(1.05) = 10.5% chance. Likewise a 20% chance kingdom (3 stars) would go to 21% and not 25%.

1 Like

A fair point - but to my knowledge, no other bonuses multiply like this elsewhere in the game.

one is a tribute CHANCE, the other is tribute AMOUNT,

aren’t you unnecessarily overcomplicating things? The best way to see that the guild bonus does in fact work, is checking the tribute amounts you get for a SINGLE kingdom (at some point it’s rare occurance that only 1 kingdom procs, but it happens) and I did check that - and I can assure you that the Statue % bonus does work.

Furthermore it seems to work in our favor. Because it doesn’t just increase your overall tribute from multiple kingdoms by the flat amount the guild guardian provides, but it also increases with the amount of tributes. (i.e. with 10% guardian bonus, 1 tribute will get increased by 10%, two by 0,1*1,1, then *1,1 for each next tribute.

e/ actually I might have entirely misunderstood you, I was talking about tribute amount, you were talking about the tribute chance. Pardon me, I will leave the reply in tact in case it’s of interest to anyone.

Excellent point - I completely missed that one is chance and one is AMOUNT.

I will recalculate & edit.

Actually it is three gold stars where your tribute chance gets doubled. So depending on your progress you might have multiple tribute chances of 20%…

Given that each kingdom has its own tribute values, and you can’t actually see which ones are contributing to the tribute, I’m not sure how you came up with those “expected” tribute amounts. At best you’ll sort of generally approximate the average over a large number of tribute collections, but expecting things to line up nicely with that amount of variables and that small of a data set is never going to work.

Unless you’re applying fancy statistical modeling like regressions and variable isolation, in which case carry on.

(Professional data analyst here… I could probably model some stuff but it’s way too much work. I trust that the devs have done their homework.)

My calculation above is simply HOW MANY cities are sending tribute - not how much is sent when tribute is sent.

1 Like

For the record - the amount bonus is working correctly as far as I can tell - it’s pretty easy to check on 1-kingom tribute, as someone mentioned.
The chance bonus on the other hand - well, I felt for a long time it’s not working. With all kingdoms at 3+ stars and Guild bonus 6% it’s 6.5 kingdoms on average and e.g a 12-kingom tribute is over twice as probable as a 1-kingdom, it definitely didn’t feel that way when I collected. I was too lazy do do any statistics and wrote it off as recall bias - of course it still can be that, but I’d like to hear an official word from a dev.

Good point - but it was simply a typo on my part - all cities are below 3 stars.

Your math is accurate. See charts below for all cities having 20% chance + 6% guild bonus.

I just joined the boards to make a very similar post. I’ve been collecting data for the past few weeks, after kvetching privately for a few months about how low tribute seemed. I kept my city levels constant during the test and stopped when Silverglade just launched (since I bought it and changed my parameters) Here is my data:

Cities: 26

=3-Star Cities (20% tribute): 13
<3-Star Cities (10% tribute): 13
Guild bonus: 3%

Total collections: 117

Average cities: 4.04 cities
Expected Average: 4.68 cities (13*.13 + 13*.23 = 4.68)

I built a tribute simulation in Python and ran it 10 million times in a few trials to confirm my expectations, and it did. For my setup, running 10 million times, here are the expected percentages:

Average Tributes: 4.68
Tribute Dist:
0 Cities, 54748 Times, 0.5475 Percent
1 Cities, 318420 Times, 3.1842 Percent
2 Cities, 887435 Times, 8.8743 Percent
3 Cities, 1580036 Times, 15.8004 Percent
4 Cities, 2008327 Times, 20.0833 Percent
5 Cities, 1942166 Times, 19.4217 Percent
6 Cities, 1488985 Times, 14.8898 Percent
7 Cities, 927709 Times, 9.2771 Percent
8 Cities, 478805 Times, 4.7881 Percent
9 Cities, 206196 Times, 2.0620 Percent
10 Cities, 75992 Times, 0.7599 Percent
11 Cities, 23315 Times, 0.2331 Percent
12 Cities, 6155 Times, 0.0616 Percent
13 Cities, 1387 Times, 0.0139 Percent
14 Cities, 267 Times, 0.0027 Percent
15 Cities, 49 Times, 0.0005 Percent
16 Cities, 5 Times, 0.0001 Percent
17 Cities, 3 Times, 0.0000 Percent

To get a sense of how far off an average 4.04 tribute is from the expected value, with a dataset of 117 gathers, I ran the simulator with 117 tribute gathers over a series of 1 million trials (this took a little while) to see how often I got an average 4.04 tributes or less.

I received 4.04 or less in just 139 of 1,000,000 trials, or 0.014%. Looked at another way, the odds of my actually-gathered data being simple bad luck is about 1 in 7,200.
Side note: This potential “bad luck” would have to come after I noticed that my tribute looked low, built a model to see how much tribute I should be getting, watched for several more weeks, and finally decided that it wasn’t my imagination and started gathering data.

Therefore, I am coming to the inescapable conclusion that tribute is not coming in at the expected rate if the guild bonus is additive, such that I have 13% and 23% chances.

If, however, GoW implemented tribute as a multiplier, so my 10% becomes 10.3% (as some have suggested) and my 20% becomes 20.6% then my gathered data would be nearly perfectly average: (13*.103+13*.206 = 4.02). Unfortunately, that would also make the guild bonuses pretty much near useless. Without guild bonus, I would expect 3.9 tribute. Thus, a 3% guild bonus makes a whopping 0.1 tribute difference in my circumstances.

P.S. I loved your charts and discussion. I appreciate someone digging in and doing the statistics! Data nerds of the world, unite!

3 Likes