Tribute rates as of 3.1

#1

On a whim, I decided to start tracking tribute rates. All my kingdoms are at level 10, with 5+ stars, my guild’s red statue is at level >100. Here’s a table with the totals as of this evening:

Kingdoms # Times Expected # Difference
0 0 0.03 0
1 0 0.26 0
2 1 1.29 0
3 5 4.07 1
4 11 9.28 2
5 19 16.3 3
6 25 22.9 2
7 37 26.5 11
8 21 25.6 -5
9 16 21 -5
10 11 14.7 -4
11 3 8.94 -6
12 7 4.71 2
13 2 2.16 0
14 1 0.87 0
15 0 0.31 0

That right hand column is the difference between what I expect based on probability (26% for each kingdom, times 29 kingdoms each time I collect tribute) and what I actually got. Ignore the loony number of 7-kingdom tributes; that’s at least close to the 7.5 average I expect. Instead, pay attention to how skewed the distribution is. 4-7 kingdoms (i.e. below average) are all coming up more frequently than they ought, and 8-11 (i.e. above average) are all coming up less frequently.

In fact, the average success rate, treating each kingdom as an independent Bernoulli trial, is 24.8% over 4611 trials. This is lower than the 26% I expect. It is, somehow, actually an improvement over the first 28 tribute collections (812 trials), which paid out at a dismal 23.2% rate.

Now, pay attention as I (probably mis)apply statistics. If the kingdom tributes aren’t being awarded with a 26% chance, what probability is consistent with my results? I use the Agresti-Coull interval, which I discovered on Wikipedia, to estimate the true probability associated with my results.

4611 trials, 1144 successes
alpha = 0.05 (corresponding to 95% confidence interval)

p_low = 23.6%
p_hi = 26.1%

So, based on these results, I am just barely within the 95% confidence interval that the tribute distributions are actually being awarded with a 26% chance.

More data is better. What have you all observed recently, or in the future? For ease of compiling data, I’d prefer to hear from late-game players like me who have a uniform 26% across the board. If someone who knows more stats wants to deal with combining Bernoulli trials at different probabilities of success, more power to you.

1000 tributes collected. Here are the results. Worrying
A.I. RNG hates me
#2

That’s about what I’ve seen. Mayhaps adobe worked a little different and inheriently rewarded more, or I was “very lucky”. Overall I’ve seen a substantial decrease in the number of kingdoms returned since 3.1 when I brought it up I felt a little rediculed.

#3

Tribute calculations are done server-side. The client is not responsible here (Air vs. Unity). They might have made a server-side change, of course.

#4

I’ve had a few 14 kingdom tributes on my ps4. Is 15 the maximum?

#5

This distribution is clearly skewed, so there might be a need to run a test to see if it is actually binomial. It can be approximated as normal distribution. Hence, it should be possible to run Kolmogorov-Smirnov test between actual and expected value. I’ve done it at http://www.physics.csbsju.edu/cgi-bin/stats/KS-test.n.plot

And here are the results. It means that even though both distributions are normal, your expected results are either calculated incorrectly (wrong percentage?) or the actual results are not following binomial distribution model. It can result from rounding to integers, it is possible because it is the only non-random data perturbation that was not tested as you don’t know the actual random number, only the bracket range where it goes. Since it is skewed to the left, it is likely that pRNG throws are rounded down.

KS Test: Results
Kolmogorov-Smirnov Comparison of Two Data Sets
The results of a Kolmogorov-Smirnov test performed at 12:55 on 21-SEP-2017
The maximum difference between the cumulative distributions, D, is: 0.1875 with a corresponding P of: 0.912

Data Set 1:
16 data points were entered
Mean = 9.938
95% confidence interval for actual Mean: 4.095 thru 15.78
Standard Deviation = 11.0
High = 37.0 Low = 0.00
Third Quartile = 18.2 First Quartile = 1.00
Median = 6.000
Average Absolute Deviation from Median = 8.44
KS finds the data is consistent with a normal distribution: P= 0.32 where the normal distribution has mean= 12.36 and sdev= 12.42
Items in Data Set 1:
0.00 0.00 0.00 1.00 1.00 2.00 3.00 5.00 7.00 11.0 11.0 16.0 19.0 21.0 25.0 37.0

Data Set 2:
16 data points were entered
Mean = 9.932
95% confidence interval for actual Mean: 4.714 thru 15.15
Standard Deviation = 9.79
High = 26.5 Low = 3.000E-02
Third Quartile = 19.8 First Quartile = 0.975
Median = 6.825
Average Absolute Deviation from Median = 8.22
KS finds the data is consistent with a normal distribution: P= 0.30 where the normal distribution has mean= 11.15 and sdev= 10.25
KS finds the data is consistent with a log normal distribution: P= 0.55 where the log normal distribution has geometric mean= 2.889 and multiplicative sdev= 12.70
Items in Data Set 2:
3.000E-02 0.260 0.310 0.870 1.29 2.16 4.07 4.71 8.94 9.28 14.7 16.3 21.0 22.9 25.6 26.5

#6

I had been tracking as well and saw a 36.15% decrease in overall - after the Unity port on the PC.

I continued to track deltas between staying on my mobile all day to collect tribute or my PC before and after Unity port to Mobile and saw 29.72% and more so I saw the number of kingdoms SERIOUSLY decrease from 4.6 average to 3.9 average number of kingdoms. The crazy part is the number of 1 kingdoms seemed to increase.

I have all my kingdoms 10th level and 6star+ except for the new one who is at 5 stars

#7

In before a dev response saying “the player was receiving tribute too often before due to an error in the formula; it has now been fixed to be more fair according to the economy.”

Note: This was intended to be a humorous comment, but I really am tiring of things being tweaked to the players’ detriment.

#8

I have had two single kingdom tributes in the last month.

#9

Odd, I feel like I always get 8 tribute rewards, which feels a little high for me. I guess it’s possible they somehow squeezed people toward the middle.

#10

I’ve noticed it too. All of my kingdoms are double/triple tribute chances and before 3.1 update i never had only one kingdom gives tribute. Now,it happened several times. With reduced gems from tasks,LT,etc…i’d say take x4 speed along with Dungeon,Soulforge and Unity back and give us back GoW before 3.1 update.

#11

Thanks for the contributions, everyone, but I am looking for tribute data collected over long stretches. Outliers stand out in our memory (like the 1-kingdom and 14-kingdom events mentioned above). These are rare events, so in theory they should show up only rarely in any set of tribute records.

Which brings me to another point: don’t start tracking data after a rare event. Or, if you do feel the urge to start tracking after an outlier, don’t include it in the totals you post here.

#12

Definitely need a much larger sample I would think. At about 10-12 tributes/day this sample represents about 2 weeks?

I have whole weeks where it feels the majority of tributes is under 7 and then others where the majority feel over 7. I’ve definitely seen more 15s than 1s in the last couple weeks.

Wish I could add to your data but I tend to pop on at all kinds of times when I have 30 seconds to collect and rarely will remember or have something available to record them reliably.

I know it wasn’t your intention, but nice job sucking in the conspiracy theorists who are now convinced we’re being shortchanged on tributes. Can’t wait to see even more posts from people all of a sudden “validating” their tributes seemed suspiciously low recently.

#13

In the last two weeks I’ve had numerous 12-14 kingdom tributes and nothing less than 4. Maybe it’s just me

#14

Idiots gonna idiot. As long as they are using their turn signals and vaccinating their kids, I am mostly okay with them. 4,600 independent tests of an event that ought to occur 26% of the time is far beyond the level where small-number statistics should matter. If the trials aren’t independent, or if there is some periodic forcing one way or the other, then the basic assumption I am making is invalid and my conclusions don’t hold water. Of course, if either of those things is true then the conspiracy theorists are right and the developers have put their thumbs on the scale somehow. That said, there is absolutely no evidence of this at present.

I have posted data that indicate my tributes are – not just feel – lower than I should expect them to be. Anyone who wants to may feel free to start collecting data of their own. Maybe I am unlucky, and I just happened to start collecting data in the middle of an extended dry spell. I am still tracking my own results longitudinally and cumulatively, so we’ll see what the time sequence works out to look like over the next days to weeks.

#15

As much as I hate conspiracy theorists (RNG favors AI!!!11!) and I have little knowledge of statistics I have to say that taking into account the decisions about the game a “tweaking” of tribute chance would not surprise me in the slightest.

#16

We haven’t made any changes to the tribute calculations on our end. I’ll keep an eye on this thread however.

#17

Durn it @grundulum! I just got done saying I wasn’t going to bother with trying to collect data on this and yet what did I start doing…

I’ll get back to you with my distribution as long as I don’t get lazy in there somewhere. And for the record none of my first 6 data points were under 7 so far. I’m intrigued and you sucked me into this madness!

#18

Thanks for the info

#19

@Grundulum

So just a quick update on 3 days of tribute collecting data so far:

For 39 tributes, I’m seeing the same distribution to your original list in that 80% of the values are falling between 5 - 9 kingdoms collecting & 20% outside of that range.

However thus far my 20% outside is skewed more positively than yours. Where 40% of your tributes outside of 5-9 are below 5 & 60% above 9, mine are 25% below 5 & 75% above 9.

Obviously I’m not confident 3 days of data is completely representative and that I didn’t just happen to start collecting in a luck streak. But at least initially this looks like there’s no foul play with tribute collection balance. Perchance you’ve just hit an unlucky streak or is it at all possible that your kingdom tribute chance isn’t maxed at 26% like you think it is?

Will continue to collect for a while to see if it changes drastically over time to match yours more

#20

Makes me wonder if there’s an off-by-one bug in the code (comparing a random integer to the probability with less instead of less-or-equal for example), so that it actually rolls a 25% chance instead of 26. Would be good if other people who are at different percentages could gather equally detailed data. I might start recording mine, as our guild only has the statue at a 4% bonus.