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.
Statistical analysis of 773 gold chests compiled from 21 players reveals ~98% chance that listed probabilities for daily prize and observatory blueprints are skewed in favor of observatory blueprints
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 daily prize and observatory blueprint 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 compare any two or more categories using a chi-square test and determine the likelihood that the deviation from the expected values was due to random chance alone. To compare two categories, you add the Chi-value and look that number up in a chi-square table. Interpreting these tables is not easy at first, and I'm not going to explain it here.
Due to the high deviation from the expected values seen in the daily prize and the observatory blueprints numbers, I chose to do a chi-square test on those two categories. The chi-square value of 5.164 (with 1 degree of freedom) falls between the 0.05 and 0.01 range, and falls much closer to the 0.01 side, at approximately 0.02. What this means is that there is only a 2% probability that random chance is responsible for the amount of deviation we observed from what we expected to see. In other words, there is a 98% chance that something real is responsible for this deviation -- not just random chance.
Discussion
With a 98% chance that something else caused the deviation, 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. None of the other categories showed enough variance to be statistically significant. 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.
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%. 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.
Statistical analysis of 773 gold chests compiled from 21 players reveals ~98% chance that listed probabilities for daily prize and observatory blueprints are skewed in favor of observatory blueprints
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 daily prize and observatory blueprint 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 compare any two or more categories using a chi-square test and determine the likelihood that the deviation from the expected values was due to random chance alone. To compare two categories, you add the Chi-value and look that number up in a chi-square table. Interpreting these tables is not easy at first, and I'm not going to explain it here.
Due to the high deviation from the expected values seen in the daily prize and the observatory blueprints numbers, I chose to do a chi-square test on those two categories. The chi-square value of 5.164 (with 1 degree of freedom) falls between the 0.05 and 0.01 range, and falls much closer to the 0.01 side, at approximately 0.02. What this means is that there is only a 2% probability that random chance is responsible for the amount of deviation we observed from what we expected to see. In other words, there is a 98% chance that something real is responsible for this deviation -- not just random chance.
Discussion
With a 98% chance that something else caused the deviation, 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. None of the other categories showed enough variance to be statistically significant. 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.
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%. 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.
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?
Statistical analysis of 773 gold chests compiled from 21 players reveals ~98% chance that listed probabilities for daily prize and observatory blueprints are skewed in favor of observatory blueprints
Introduction
Many players feel they get robbed by the events where Inno imposes probability on the rewards offered.
If you do that the total chi2 is 6.94.
Sorry, you are right about the chi2 value, I miscopied a number. I will fix it and note.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.
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.
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.
In theory you are right. But in practice nobody really looks at it this way, because it's really not useful.
you need a lot more evidence than this.
I noticed the only time eggs were hidden outside the city was directly after redeeming a chest. Otherwise, no eggs were hidden.
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.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.