DeletedUser10554
Disappointing ...... not worth the time, should I go on? These contest and i have played for two years now... stink drummer boys, color guards..... good to have when the game ask you to delete units, not worth a crap in battle.
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DeletedUser18851
Statistical analysis of 773 gold chests compiled from 21 players reveals ~59% chance that listed probabilities were false; mostly due to observatory prints, color guard camps and daily prize numbers
Introduction
Many players feel they get robbed by the events where Inno imposes probability on the rewards offered. Anecdotal evidence is easy to dismiss due to small sample size, so just about everyone who comes to the forums to complain gets shrugged off. It's too bad nobody has taken the time to compile a respectable amount of data and give these people a real voice. Until now.
Methods
Data pertaining to the opening of 773 gold chests was accumulated from 21 different players from different guilds across all 20 servers. Some was extracted from this thread, but the majority was collected by me on a 1-on-1 basis with individual players via in-game message, chat, or Skype.
The real occurrence (percentage) of each prize was determined. Due to suspicious results, a chi-square test was done on the numbers. The chi-squared test is used to determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories. Does the number of individuals or objects that fall in each category differ significantly from the number you would expect? Is this difference between the expected and observed due to sampling variation, or is it a real difference? This is what a chi-square test can answer. I won't go into detail on the calculations here as most probably are not interested, but you can look it up for yourself if you are.
Data & Results
Reward..........Total Observed.......Total Expected......Listed %......Observed %..........Chi-value
Daily Prize...........177.....................193..................25................23..................1.366
200 Eggs..............101.....................100..................13................13.................. 0.003
Color G. Camp.......97......................108..................14................13..................1.163
Foeberge Shop.....114......................108..................14................15..................0.309
Reno Kit..............82.......................77...................10................11..................0.286
10-FP pack...........48.......................46....................6.................6...................0.057
2 Obs Prints.........103......................85....................11................13..................3.798
120 Eggs..............51.......................54....................7..................7...................0.179
Apologies for the table -- spaces don't format correctly on this forum.
See raw data here (image too large to abide by strict forum rules).
From this data, you can determine the likelihood that the deviation from the expected values was due to random chance alone. To do this, you add the Chi-value for each category and look that number up in a chi-square table - reading with 7 degrees of freedom (df = # categories -1). Interpreting these tables is not easy at first, and I'm not going to explain it here.
Due to the deviation from the expected values seen (most notably) in the daily prize and the observatory blueprint numbers, the chi-square value of 7.160 is quite a bit higher than one would expect if only random chance were involved in the outcome. The chi-square test tells us that there is a 59% probability that something OTHER than chance is involved.
Discussion
Scientists only require a 5% chance that something OTHER than chance is involved to investigate their questions further to determine what is causing the results they are seeing. We are mere FoE players. A 59% chance that something else caused the deviation should be enough to make everyone question Inno, especially considering where the highest variance was seen. One must look for possible explanations. There are three possible explanations to account for this that I can see:
1) Sampling error
2) A bug affecting the actual probabilities
3) Purposeful manipulation of the actual probabilities
With the number of samples I have and the care with which I collected them, sampling error is very unlikely. With the incidence of bugs in the game, it would not surprise me at all if there was one here. However, the way in which the percentages were skewed and the undeniable fact that Inno is a for-profit business supports the third possibility -- that of purposeful manipulation. By decreasing the actual probability by 2% below the listed for the grand prize... well, I think everybody can figure that out for themselves. It would be very hard to detect on an anecdotal basis, and I believe this is what they would count on. Only through massive data collection and analysis would it be revealed; and even then, the presence of other prizes in the box that aren't rigged each help to disguise it.
Conclusion
You can draw your own conclusions. I have presented the data. My personal conclusion is that the daily prize, while listed at 25%, was actually coded to 23%. And that extra 2% was given to the observatory blueprints, making them 13% instead of the listed 11%. I view this as extremely likely. In this case, I would petition Inno to grant every single player who finished the Easter quest line a free SoK, Wishing Well, and Rogue hideout to their inventory as compensation for being lied to -- the three most sought-after daily prizes from the event. In the case that my second possibility -- that of a bug affecting the probabilities -- is true, I would petition Inno do the same as an apology for the bug. I'm sure Inno (if they even acknowledge this) will blame it on sampling error.
Introduction
Many players feel they get robbed by the events where Inno imposes probability on the rewards offered. Anecdotal evidence is easy to dismiss due to small sample size, so just about everyone who comes to the forums to complain gets shrugged off. It's too bad nobody has taken the time to compile a respectable amount of data and give these people a real voice. Until now.
Methods
Data pertaining to the opening of 773 gold chests was accumulated from 21 different players from different guilds across all 20 servers. Some was extracted from this thread, but the majority was collected by me on a 1-on-1 basis with individual players via in-game message, chat, or Skype.
The real occurrence (percentage) of each prize was determined. Due to suspicious results, a chi-square test was done on the numbers. The chi-squared test is used to determine whether there is a significant difference between the expected frequencies and the observed frequencies in one or more categories. Does the number of individuals or objects that fall in each category differ significantly from the number you would expect? Is this difference between the expected and observed due to sampling variation, or is it a real difference? This is what a chi-square test can answer. I won't go into detail on the calculations here as most probably are not interested, but you can look it up for yourself if you are.
Data & Results
Reward..........Total Observed.......Total Expected......Listed %......Observed %..........Chi-value
Daily Prize...........177.....................193..................25................23..................1.366
200 Eggs..............101.....................100..................13................13.................. 0.003
Color G. Camp.......97......................108..................14................13..................1.163
Foeberge Shop.....114......................108..................14................15..................0.309
Reno Kit..............82.......................77...................10................11..................0.286
10-FP pack...........48.......................46....................6.................6...................0.057
2 Obs Prints.........103......................85....................11................13..................3.798
120 Eggs..............51.......................54....................7..................7...................0.179
Apologies for the table -- spaces don't format correctly on this forum.
See raw data here (image too large to abide by strict forum rules).
From this data, you can determine the likelihood that the deviation from the expected values was due to random chance alone. To do this, you add the Chi-value for each category and look that number up in a chi-square table - reading with 7 degrees of freedom (df = # categories -1). Interpreting these tables is not easy at first, and I'm not going to explain it here.
Due to the deviation from the expected values seen (most notably) in the daily prize and the observatory blueprint numbers, the chi-square value of 7.160 is quite a bit higher than one would expect if only random chance were involved in the outcome. The chi-square test tells us that there is a 59% probability that something OTHER than chance is involved.
Discussion
Scientists only require a 5% chance that something OTHER than chance is involved to investigate their questions further to determine what is causing the results they are seeing. We are mere FoE players. A 59% chance that something else caused the deviation should be enough to make everyone question Inno, especially considering where the highest variance was seen. One must look for possible explanations. There are three possible explanations to account for this that I can see:
1) Sampling error
2) A bug affecting the actual probabilities
3) Purposeful manipulation of the actual probabilities
With the number of samples I have and the care with which I collected them, sampling error is very unlikely. With the incidence of bugs in the game, it would not surprise me at all if there was one here. However, the way in which the percentages were skewed and the undeniable fact that Inno is a for-profit business supports the third possibility -- that of purposeful manipulation. By decreasing the actual probability by 2% below the listed for the grand prize... well, I think everybody can figure that out for themselves. It would be very hard to detect on an anecdotal basis, and I believe this is what they would count on. Only through massive data collection and analysis would it be revealed; and even then, the presence of other prizes in the box that aren't rigged each help to disguise it.
Conclusion
You can draw your own conclusions. I have presented the data. My personal conclusion is that the daily prize, while listed at 25%, was actually coded to 23%. And that extra 2% was given to the observatory blueprints, making them 13% instead of the listed 11%. I view this as extremely likely. In this case, I would petition Inno to grant every single player who finished the Easter quest line a free SoK, Wishing Well, and Rogue hideout to their inventory as compensation for being lied to -- the three most sought-after daily prizes from the event. In the case that my second possibility -- that of a bug affecting the probabilities -- is true, I would petition Inno do the same as an apology for the bug. I'm sure Inno (if they even acknowledge this) will blame it on sampling error.
Last edited by a moderator:
DeletedUser6163
During events there are typically negative complaints and some responses to those complaints are "Don't like free stuff? Don't play the event!" While this may have been possible in prior events, more recently there have been moves on the developers parts to force us to play these events we do not like.
No one could have avoided the annoyances of the Easter event.. There was a popup that appears on every log in letting you know all about it and how many days you have left. There was a blue arrow that flashed until you bought something. There was an annoying popup to have to click when you collect your town hall daily, and not to mention those stupid eggs around your city that give 5 or fewer eggs per collection - they weren't worth the clicks necessary to collect. THEN there was a message in our inbox reminding us the event was almost over that further pushes back important guild mail and a little trumpet in our buff bar.
Inno, if you're gonna make events so unenjoyable these days, at least make it easier to ignore them.
No one could have avoided the annoyances of the Easter event.. There was a popup that appears on every log in letting you know all about it and how many days you have left. There was a blue arrow that flashed until you bought something. There was an annoying popup to have to click when you collect your town hall daily, and not to mention those stupid eggs around your city that give 5 or fewer eggs per collection - they weren't worth the clicks necessary to collect. THEN there was a message in our inbox reminding us the event was almost over that further pushes back important guild mail and a little trumpet in our buff bar.
Inno, if you're gonna make events so unenjoyable these days, at least make it easier to ignore them.
DeletedUser25571
I myself being a beginner and having 0 observatory prints didn't mind winning more of them as this saved me alot of fp donations. The only thing that i did find annoying is that i have 3-4 colorguard camps on at least a few of my 12 worlds and do not have the ability to gift them.
DeletedUser25351
I noticed the only time eggs were hidden outside the city was directly after redeeming a chest. Otherwise, no eggs were hidden.
qaccy
Well-Known Member
Roll a traditional 6-sided die 120 times. Do you think you're going to have each number come up exactly 20 times? Now roll it 1200 times. Do you think you'll see each number exactly 200 times? And if you don't, does that mean that the die is rigged? You may be free to form your own conclusions, but yours is still flawed in that nobody can definitively claim what any of the %s are. You see a couple points of deviation and use that to claim that the system is unfavorably rigged (you did also ignore that your 'study' gave more renovation kits and FP packs, and fewer color guards than expected), but any level-headed person would look at it and see 'yup, that looks like normal deviation to me'. But I'm guessing that being level-headed doesn't fit your anti-Inno world view, huh?
DeletedUser10528
Nice Work Death! It's good to see such a large sample size. I certainly agree with these results. I noticed more Obs BP's than I expected, and this makes perfect sense as to why I didn't see the Daily Prize awarded as often as I expected...
Inno bans players for cheating... I wonder how Inno plans to ban themselves for being the ones who cheated all the players out of Daily Prizes in the Easter Event?
I demand compensation!
DeletedUser18851
Do you understand what a chi-square test does? Obviously not. It is a commonly used and widely accepted test used by scientists and mathematicians all over the world to determine IF the amount of deviation you see is ACTUALLY due to random chance. Your entire argument is debunked by my use of this particular test. You might have known this had you read my whole report. Go educate yourself before you speak on such matters.
DeletedUser8152
@Deathjmp:
It's not statistically valid to cherry-pick two particular examples (obs BPs and the daily prizes) that have the most extreme deviations from the expected values. You have to actually use all the data from all the categories. If you do that the total chi2 is 7.16 (fixed!). The number of degrees of freedom is actually 7 (since there are 8 categories but the probabilities have to sum to one). Using a chi2 calculator that gives a total probability of 41% (fixed!) to have chi2 that size or or larger. So that is quite reasonable.
When you pick out the largest deviations as you did, then naturally they will be larger than the expected average deviation. To explain the issue better, imagine if there were 100 different prizes. Then it would not be surprising if among all those prizes, at least one was awarded a lot more or less often than you'd have expected, simply because there were 100 different chances for it to go wrong.
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Actually, here is a good example of the extreme case for what you're doing. Consider a lottery with a one in one million chance of winning. Say a million people enter and one of them wins. Then the expected number of wins per person is 0.000001. The person who won therefore beat his odds by a factor of a million... The chi2 for that one person is enormous. But you can't conclude that the contest was rigged, you have to look at the overall distribution including everyone who entered.
It's not statistically valid to cherry-pick two particular examples (obs BPs and the daily prizes) that have the most extreme deviations from the expected values. You have to actually use all the data from all the categories. If you do that the total chi2 is 7.16 (fixed!). The number of degrees of freedom is actually 7 (since there are 8 categories but the probabilities have to sum to one). Using a chi2 calculator that gives a total probability of 41% (fixed!) to have chi2 that size or or larger. So that is quite reasonable.
When you pick out the largest deviations as you did, then naturally they will be larger than the expected average deviation. To explain the issue better, imagine if there were 100 different prizes. Then it would not be surprising if among all those prizes, at least one was awarded a lot more or less often than you'd have expected, simply because there were 100 different chances for it to go wrong.
-----
Actually, here is a good example of the extreme case for what you're doing. Consider a lottery with a one in one million chance of winning. Say a million people enter and one of them wins. Then the expected number of wins per person is 0.000001. The person who won therefore beat his odds by a factor of a million... The chi2 for that one person is enormous. But you can't conclude that the contest was rigged, you have to look at the overall distribution including everyone who entered.
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ToastMonkey
New Member
If this is all true, and given the date and from knowing Deathmjp I have no reason to suspect otherwise, this is disheartening at the very least. There needs to be a satisfactory response from Inno on this, although I can't imagine them giving any compensation
DeletedUser18851
You may be right that you have to look at it that way. It's actually 7.160 and with df=7 that still comes out to a 59% chance of being rigged. Not high enough to stand in a scientific journal but I would encourage the players to make up their own mind.
DeletedUser8152
Sorry, you are right about the chi2 value, I miscopied a number. I will fix it and note.
Not sure I would characterize it as "a 59% chance of being rigged." More like, "if the stated percentages are right, then if you collected different samples of 773 results over and over again, you'd expect 59% of them would have chi2's smaller than this." So there's a better chance of seeing what you got then there would be to roll a 5 or a 6 on a fair die.
DeletedUser18851
I have amended the initial report to reflect a proper chi-square value.
DeletedUser10528
We as players don't need a scientific journal to come to the conclusion that Inno swayed the results to favor the house on daily prizes. I would bet if you ran the test over many more times you would NEVER find the daily prize greater than expected at 25%.
Fact is: Inno is a business, a business to make money. The house always wins, and they are not motivated to give away anymore than necessary. Possibly even less than necessary to appear "Fair" in the eyes of the players. The results are pretty clear to me, and if the daily prize was awarded more than expected, then we could believe everything was due to "chance". But I guarantee you, no matter how many times you run the event; you will find the observed percentage LESS THAN the expected percentage for daily prizes awarded.
No need to bring Rocket Science into this.. IT's INNO!
DeletedUser18851
In theory you are right. But in practice nobody really looks at it this way, because it's really not useful.
DeletedUser25273
My understanding was you typically want a better than 95% chance that this result couldn't be by chance before you considered it statistically significant. (More conservatively 99%, less 90%). 60% is just a bad day.
DeletedUser13838
Who is nobody? If you want to claim the stated probabilities are not correct you need a lot more evidence than this.
DeletedUser18851
Care to explain how what I've stated is incorrect?
DeletedUser14197
In all 6 of my cities, there was one egg hidden each day worth 3 eggs. I got it every day and not for trading for chests. When I traded for a bronze chest I got an egg worth 1 egg. When I traded for a silver chest, I got an egg worth 3 eggs and when I traded for a gold chest, I got an egg worth 5 eggs.
DeletedUser14197
I kind of doubt anyone would want them. Would be nice if we could sell them back to the game and get something for them.