363 réponses à ce sujet

[chcknwng]

Also, for the record, I bought 7 PSPs the other day and got 1 UR. Can't remember how many I got from the Earth DLC spending spree.

[ShadowHound]

Bought one this morning and got The Black Widow III

[UnknownMercenary]

18 PSPs, 4 URs. Going to go back to regular Spectre Packs for a while and track those.

[HNNNNNNG]

Well, in one day I bought like maybe 5 or 7 and I got the n7 shadow

edit: However I also got the javlin. 

I don't keep track of how many packs I buy :/

Modifié par HNNNNNNG, 22 juillet 2012 - 01:26 .

[ShadowHound]

Bought 2 more premiums and only got ammo mods and Berserker Package III

[CHAw]

For this past weekend, I got:

8 Ultra-Rares in 40 Premium Spectre Packs

xxHarbinger wrote...

Ok, I will begin to keep track from now on. But, can someone tell me what a Resurgence pack is?

Resurgence Packs are a discontinued pack that was available during the week after the release of the Resurgence expansion (the one that added geth and batarians). As I recall, they were similar to Premium Spectre Packs, but were guarunteed to include at least one of the Resurgence characters or weapons. Given that it is highly unlikely to be released again, and that it would have little value to most players even if it were, the statistics are listed more for historical reasons than because they have any use.

wngmv wrote...

Interesting. The drop rate does not follow a Poisson distribution. Actually the drop rate could be a constant, if Bioware does not use random drop rates (they could let the rate vary I just don't see a reason). What is random is how many URs you got from a fixed number of PSPs you buy. This is a binomial distribution. To be more technical, binomial and Poisson are related. But I do think it would be better to model it as binomial. If you model it as Poisson, you mean that no matter how many PSPs you guys buy, the average is likely a fixed number, which is clearly not the case here.  (The more you buy, the more UR you will get. Else why we bother with buying?)

Instead of agrregating, you could estimate drop rate for each individual/ buy. I have to take a closer look at the data but I assume we have enough to do a normal approximation than using the binomial.

 
I don't know very much statistics, so could you clarify further what the differences between binomial and Poisson distributions are, and why you believe that the data is better approximated with the former?

I was going to do another summary of results, but if I should be using a different method of error analysis, I'd like to know what it is first.

Modifié par CHAw, 29 juillet 2012 - 08:40 .

[CHAw]

Here's another summary* of results. This tally includes all of the data that acturater has up in the original post.

Per Orca_'s suggestion, I've included statistics dividing up pre- and post- Rebellion data. In keeping with Shampoohorn's analysis, I have also included average cost per ultra-rare. As wngmv has suggested that the data follows a binomial distribution rather than a Poisson distribution, I will not be including an error analysis until this question is resolved (which, incidentally, means less work for me ).


TOTAL

Spectre Packs: 2152
Ultra-Rares: 122
Chance of Ultra-Rare per Pack: 5.6691% 
Cost per Ultra-Rare: 1,058,360 Credits 

Premium Spectre Packs: 5172
Ultra-Rares: 653
Chance of Ultra-Rare per Pack: 12.6063% 
Cost per Ultra-Rare: 785,319 Credits 

Resurgence Packs: 71
Ultra-Rares: 4
Chance of Ultra-Rare per Pack: 5.6338% 
Cost per Ultra-Rare: 1,757,250 Credits 

PRE-REBELLION

Spectre Packs: 1660
Ultra-Rares: 78
Chance of Ultra-Rare per Pack: 4.6988% 
Cost per Ultra-Rare: 1,276,923 Credits 

Premium Spectre Packs: 2490
Ultra-Rares: 244
Chance of Ultra-Rare per Pack: 9.7992% 
Cost per Ultra-Rare: 1,010,287 Credits

Resurgence Packs: 71
Ultra-Rares: 4
Chance of Ultra-Rare per Pack: 5.6338% 
Cost per Ultra-Rare: 1,757,250 Credits 

PRE-REINFORCEMENT

Spectre Packs: 307
Ultra-Rares: 22
Chance of Ultra-Rare per Pack: 7.1661% 
Cost per Ultra-Rare: 837,272 Credits 

Premium Spectre Packs: 1399
Ultra-Rares: 198
Chance of Ultra-Rare per Pack: 14.1530% 
Cost per Ultra-Rare: 699,500 Credits 

POST-REINFORCEMENT (EARTH)

Spectre Packs: 185
Ultra-Rares: 22
Chance of Ultra-Rare per Pack: 11.8919% 
Cost per Ultra-Rare: 504,545 Credits 

Premium Spectre Packs: 1283
Ultra-Rares: 211
Chance of Ultra-Rare per Pack: 16.3679%
Cost per Ultra-Rare: 604,843 Credits 




* I did not include the following data in these updated numbers, as they were described as estimates and I am uncertain as to how acturater was handling estimates as opposed to hard numbers. I also did not include data from Sacramentum's videos, because I do not currently have time to watch the entirety of those clips; if somebody could summarize them for me, it would be appreciated.

PRE-REBELLION
Bayushi Pochi: 7 URs/200-220 PSPs; 3 URs/400-450 SPs
Hunter of Deathclaws and Tanks: 3URs/~40 PSPs
Dark Absolution: 6 URs/~100 SPs; 0 URs/~50 PSPs and RPs
UKillMeLongTime: 2 URs/? PSPs
PRE-REINFORCEMENT
Dantexr3: 1 URs/? VPs
Sovereign24: 1 URs/?
RhythmlessNinja: 2 URs/?
a load of stanton: 2 URs/? PSPs
AldarionnEB: 7 URs/~30 PSPs
Sharteel: 15 URs/?
The Krauser: 7 URs/? SPs; 2 URs/? PSPs
POST-REINFORCEMENT (EARTH)
Sacramentum: video
Poulpor: 50 URs/600 SPs and PSPs
HNNNNNNG: 1 URs/5-7 PSPs

Modifié par CHAw, 29 juillet 2012 - 08:40 .

[chcknwng]

CHAw wrote...

Here's another summary* of results. This tally includes all of the data that acturater has up in the original post.

Per Orca_'s suggestion, I've included statistics dividing up pre- and post- Rebellion data. In keeping with Shampoohorn's analysis, I have also included average cost per ultra-rare. As wngmv has suggested that the data follows a binomial distribution rather than a Poisson distribution, I will not be including an error analysis until this question is resolved (which, incidentally, means less work for me ).


TOTAL

Spectre Packs: 2152
Ultra-Rares: 122
Chance of Ultra-Rare per Pack: 5.6691% 
Cost per Ultra-Rare: 1,058,360 Credits 

Premium Spectre Packs: 5172
Ultra-Rares: 652
Chance of Ultra-Rare per Pack: 12.6063% 
Cost per Ultra-Rare: 785,319 Credits 

Resurgence Packs: 71
Ultra-Rares: 4
Chance of Ultra-Rare per Pack: 5.6338% 
Cost per Ultra-Rare: 1,757,250 Credits 

PRE-REBELLION

Spectre Packs: 1660
Ultra-Rares: 78
Chance of Ultra-Rare per Pack: 4.6988% 
Cost per Ultra-Rare: 1,276,923 Credits 

Premium Spectre Packs: 2490
Ultra-Rares: 244
Chance of Ultra-Rare per Pack: 9.7992% 
Cost per Ultra-Rare: 1,010,287 Credits

Resurgence Packs: 71
Ultra-Rares: 4
Chance of Ultra-Rare per Pack: 5.6338% 
Cost per Ultra-Rare: 1,757,250 Credits 

PRE-REINFORCEMENT

Spectre Packs: 307
Ultra-Rares: 22
Chance of Ultra-Rare per Pack: 7.1661% 
Cost per Ultra-Rare: 837,272 Credits 

Premium Spectre Packs: 1399
Ultra-Rares: 198
Chance of Ultra-Rare per Pack: 14.1530% 
Cost per Ultra-Rare: 699,500 Credits 

POST-REINFORCEMENT (EARTH)

Spectre Packs: 185
Ultra-Rares: 22
Chance of Ultra-Rare per Pack: 11.8919% 
Cost per Ultra-Rare: 504,545 Credits 

Premium Spectre Packs: 1283
Ultra-Rares: 210
Chance of Ultra-Rare per Pack: 16.3679%
Cost per Ultra-Rare: 604,843 Credits 




* I did not include the following data in these updated numbers, as they were described as estimates and I am uncertain as to how acturater was handling estimates as opposed to hard numbers. I also did not include data from Sacramentum's videos, because I do not currently have time to watch the entirety of those clips; if somebody could summarize them for me, it would be appreciated.

PRE-REBELLION
Bayushi Pochi: 7 URs/200-220 PSPs; 3 URs/400-450 SPs
Hunter of Deathclaws and Tanks: 3URs/~40 PSPs
Dark Absolution: 6 URs/~100 SPs; 0 URs/~50 PSPs and RPs
UKillMeLongTime: 2 URs/? PSPs
PRE-REINFORCEMENT
Dantexr3: 1 URs/? VPs
Sovereign24: 1 URs/?
RhythmlessNinja: 2 URs/?
a load of stanton: 2 URs/? PSPs
AldarionnEB: 7 URs/~30 PSPs
Sharteel: 15 URs/?
The Krauser: 7 URs/? SPs; 2 URs/? PSPs
POST-REINFORCEMENT (EARTH)
Sacramentum: video
Poulpor: 50 URs/600 SPs and PSPs
HNNNNNNG: 1 URs/5-7 PSPs

Sorry went to see Dark Knight Rises today and spent the whole night reading the bickering to death on IMDB. It made me realize how nice a place BSN is. I gave it some more thought and will post something tomorrow. Its already extremely late.

[Grotaiche]

Ah, I'm a bit late but here are last week's stats for me (all post Earth DLC) : 10 PSPs opened, got 3 URs.

[chcknwng]

 Alright, here's the promised post about Poisson and binomial distributions.
Buying N packs (where N varies from people to people) and getting X URs does not really follow a Poisson distribution. Poisson dist actually models count, not rate. An example of Poisson distribution: the number of cars passed throught an intersection during 10 minutes of time follows a Poisson distribution. Here's reason why I don't like the idea of modeling it as Poisson.

1. for X to be Poisson, the average (mean) has to be a constant.

Here the "10 minutes" is fixed. If you change it to 5 mins, it would be a totally different Poisson distribution (with a different mean). We don't have the number of packs each individual bought fixed. Each person would buy different numbers of packs. Therefore each mean would different for each person. Why do I care about the mean?

2. In Poisson distribution, the parameter of interests is the mean.

i.e.
the average number of cars passing throught the intersection (a count). We are not interested in how many UR each person gets from their spending spree, rather we are interested in the rate of getting UR. You can still calculate that, but it's not natural.

3. the range of X goes from 0 to infinity.

The number of cars passing an intersection could be a very large number (no upper limit theoretically). However, the range of URs you can get from N PSP is limited at 2N. If N is small, say N=3, this becomes a serious problem.


Introducing the binomial distribution. It's a repetition of same "experiments". The experiment can only have 2 outcomes. The simplest example is flipping a coin for 20 times and the number of times you get heads/tails, or buying 20 lottery tickets and win X of them (see the similarity?). The parameters we are interested in, are the probability of getting head, or probability of winning a lottery, which is exactly we want. 

Nothing is ever so easy: You could win 0,1,2, or even more (I've never heard of that so I supposed Bioware made it impossible to get more than 3 URs from a PSP). It is not a binary outcome anymore. Extending the idea of binomial distribution we get a multinomial distribution. Now there are 3 outcomes, getting 0,1,2 URs from one pack. We are interested in the probability of each of them. Ideally I would want the data containng how many double UR you pulled from your PSP, but that is not gonna happen. 

I won't bore you with details. But with some assumption (independence, i.e. getting one UR in the first slot won't affect your chance of getting a 2nd UR), reporting the total number of URs one get from multiple packs would suffice. Let p be the drop rate from PSP for one individuals, Then you could just average p for multiple individuals. A 95% CI based on standard normal distribution is ok since I think we have a large enough sample. (Again, even if you know clt the ordinary one won't hold since the distributions here are not i.i.d. I won't bore you with the details. But rest assured, normal would suffice)

For SP, it's much easier since the outcome is binary, you can just calculate the drop rate and averge them, build a CI based on normal dist as well.

If you could provide me with data, I could do some more stuff with it, poke around to see what happens. That actually sounds fun.

Hope I didn't bore you guys to death.

Here's some references:
http://en.wikipedia....on_distribution 
http://en.wikipedia....al_distribution 
http://en.wikipedia....al_distribution 
http://en.wikipedia....m#Lindeberg_CLT 
http://en.wikipedia....n_limit_theorem 


TL;DR version:

Instead of doing (total number of UR got for everybody)/(total number of PSP bought), do average(drop rate for each individual)

Modifié par wngmv, 23 juillet 2012 - 05:47 .

[CHAw]

wngmv wrote...

I won't bore you with details. But with some assumption (independence, i.e. getting one UR in the first slot won't affect your chance of getting a 2nd UR), reporting the total number of URs one get from multiple packs would suffice. Let p be the drop rate from PSP for one individuals, Then you could just average p for multiple individuals. A 95% CI based on standard normal distribution is ok since I think we have a large enough sample. (Again, even if you know clt the ordinary one won't hold since the distributions here are not i.i.d. I won't bore you with the details. But rest assured, normal would suffice)

For SP, it's much easier since the outcome is binary, you can just calculate the drop rate and averge them, build a CI based on normal dist as well.

If you could provide me with data, I could do some more stuff with it, poke around to see what happens. That actually sounds fun.

Parts of your explanation went over my head, but point 3 clearly demonstrated why drop rates do not follow a Poisson distribution. I didn't get a couple of your acronyms (clt and i.i.d.) though.

However, I do have another question. Do we actually want to calculate drop rates for each individual data set and then average them to obtain the aggregate? Wouldn't that unduly bias the calculated rate towards the smaller data sets?

Or did you mean a weighted average? In which case, wouldn't the total count divided by the total sample size yield the same result?

In any case, the readily available data is what has already been listed. I don't personally have each individual data set logged somewhere, as the thread was initially created by acturater. As far as I know, all of the data he used came from posts to this thread, or posts to other threads on this forum (listed and linked to on his original post). The rest of the data that I added on to this came from this thread, so everything should be here somewhere. But the totals are all that I have readily available.

[bigfutus]

50 PSP
9 UR

[UnknownMercenary]

31 SPs, 3 URs
9 PSPs, 2 URs

[CHAw]

I apologize for neglecting this thread these past several days, but I appear to have angered the Random Number Gods (for constantly resuscitating this thread?) and they required a sacrifice of 13,662,000 Credits (not to mention 138 prize Fereldan sheep) before they would grant me my N7 Typhoon I. And then, of course, I had to show them my gratitude for their benevolence by slaughtering hundreds of Reaper thralls with it.

Anyway, since my last post, I got:

12 Ultra-Rares in 85 Premium Spectre Packs

Probably do another summary of results this weekend. Will continue to calculate rates by percentage of aggregate rather than by individual sample size unless wngmv, or someone else well versed in statistics, provides further guidance.

Modifié par CHAw, 02 août 2012 - 11:19 .

[bigfutus]

Little off topic, are spectre packs the best choice for unlocking uncommon gear?

[Siran]

Before Earth DLC I'd have said go for PSP every time as you'll most likely max out everything else before you max out on UR. Now with the new "rare" and "uncommon" gear I'm not so sure, as their drop-rates seem to be even lower than UR, especially the uncommon ones...

[Renku]

Post Resurgence: 43 PSP - 6 UR
Post Rebellion: 268 PSP - 54 UR
Post Earth: 40 SP - 0 UR
Post Earth: 51 PSP - 7 UR

Most of the Pre-Rebellion data is unusable because of inaccurate documentation. Data listed before can be backed with screenshots. Always buy in bulk (3M+) and the 40 SP was a mistake.

[CHAw]

bigfutus wrote...

Little off topic, are spectre packs the best choice for unlocking uncommon gear?

I can't say for certain, as I haven't purchased anything other than Premium Spectre Packs for months, but I would hazard a guess that Veteran Packs are the best choice for unlocking uncommon gear equipment like Structural Ergonomics or Thermal Clip Storage, as Veteran Packs guaruntee an uncommon card and cost much less than Spectre Packs.

But I'm assuming that uncommon gear, like rare gear in (Premium) Spectre Packs, can appear in the guarunteed slot in the Veteran Pack. Otherwise, it'll depend on a number of factors (most importantly, whether or not they can even appear in a Veteran Pack at all).

Wait, I just remembered. During the first week after the release of Earth, there were reports that the new uncommon gear was only available from Veteran Packs. This appears to have been fixed since then, but I'd take that as confirmation that they do appear in Veteran Packs. So those are probably your best bet.

Modifié par CHAw, 02 août 2012 - 11:30 .

[UnknownMercenary]

35 SPs, 2 URs
15 PSPs, 3 URs.

Had a pretty bad UR drop rate for the week buying SPs until switching to PSPs for the weekend. Got 3 URs in short order and a bunch of Earth gear.

[Grotaiche]

11 PSP, 3 UR

[Havok1369]

This is fuel for the fire but it is a odd note. Bought 12 PSP the other day. No drops. Bought 20 SP. one UR.
Spent 1600 MS points. Bought 4 PSP and 4 SP. 4 UR.
Had never spent real money but was very curious to see if there would be a significant delta with real cash.
My own drop rate with credits has been somewhere around 7% between both packs once all is averaged out.
Interesting that with real money the rate increased significantly. Chance, maybe.

[Shampoohorn]

24 PSP, 3 UR, post Earth DLC.

Modifié par Shampoohorn, 08 août 2012 - 06:27 .

[artificial-ignorance]

Hello!  As listed on this thread:  social.bioware.com/forum/1/topic/343/index/13527160/1

#SP's = 34 giving 2 UR's
#PSP's = 33 giving 2 UR's

BTW Great data pool!

If you want more data, check out randomfoo's online spreadsheet:  docs.google.com/spreadsheet/ccc
If you want to contribute to his spreadsheet, drop randomfoo a private BSN msg - He will give you a dedicated sheet to record your unlocks.

Good work people! 

[skiadopsendow]

18 psp's and 3 sp bought between monday and tuesday

3 UR's all of them in psp's

[trjdmc]

I bought 7 PSP's and got 6 UR's. My luck finally turned