RE: Rising in the Rankings
(06-02-2014 12:10 AM)Bbobb555 Wrote: (06-01-2014 03:50 PM)TheGreatErenan Wrote: (06-01-2014 03:31 PM)Bbobb555 Wrote: Ok, so let x be the number of P1 games for any given player. Then the probability that he/she will have no P1 games on some map is about 12*(1-(11/12)^x). So if a player has played 50 games as P1, then there is actually still about a 12% chance that there are no games for some map. Note that only P1 season 5 games should be counted.
Um, wait. Assuming each map is equally likely to appear, the number of possibilities for map distribution over x matches played is 11^x (eleven possible maps for each of x matches). The number of ways you can play x matches without playing a single match on some particular map is (11-1)^x or 10^x. So I would think the actual probability of this happening is (10^x)/(11^x). If you play 50 matches, that's (10^50)/(11^50), which is less than 1% (about 0.8518551%)
Note that you can't simply multiply this number by 11 to get the probability of not getting every map at least once during your match history, as 10^x already includes a lot of scenarios that exclude other maps. For instance, if the map excluded is, say Glitch, that 10^x includes the scenario of getting SFI x times, which excludes every map except SFI.
Actually, you can simply multiply it by 11, the reason being that the probability that two maps have no matches is extremely small. It only makes less than a 2.5% (9^50/10^50 * 10/2 if you are interested) change in the overall result. (Note: I am ignoring the chance that 3 maps have no matchups, etc. because these have almost no effect and furthermore, they actually increase the probability) When the probability is extremely small, terms further in the PIE expansion tend to have next to no effect at all. I was aware of this and that is why I said "about."
Aside from that, I did make 2 stupid mistakes. First, you were right, there should be no subtraction from 1, and that was a silly mistake. Also, I thought there were 12 maps instead of 11.
Revised:
The probability is, as you said, 11*(10/11)^50, which is still about 9.37%. If we include the probability of two maps being the same, it is (11*10^50-55*9^50)/11^50 which is about 9.13%. As you can see, there is a very small difference in the two, simply because the probability of two maps both having no matchups is negligible.
(06-01-2014 08:40 PM)Demon Wrote: Don't over think it. Chance of getting SFI is 1/11, roughly 9%. Chance of not getting SFI is 10/11, roughly 91%. Chance of not getting SFI 50 times in a row is (10/11)^50, so about 0.852%. Very unlikely. Note that while Erenan used different logic, he arrived at the same calculation and is certainly correct 
SFI is just an example, of course, this calculation will work for all maps.
Not different logic, it's the exact same logic. But you have to consider that you can get 0's not only on SFI, but on other maps, too, and the probability that some map has no matchups is over 9%.
The full expression for the probability is (11*10^50-55*9^50+165*8^50-330*7^50+462*6^50-462*5^50+330*4^50-165*3^50+55*2^50-11*1^50)/11^50 = 9.130942597%
Also note that this probability varies a lot as x varies. For example:
p(10) is 1.
p(20) is about 88.72%. I included all the terms in this.
p(30) is about 50.80%. I included 5 terms in this calculation since it is a large probability.
p(40) is about 22.56%.
p(50) is about 9.13%.
p(60) is about 3.58%.
p(70) is about 1.39%.
p(80) is about 0.536%.
p(100) is about 0.0798%.
I think what you actually want here is a Chi Square test. E.g. for Gullsjakal's data on the person who got 471/477 P1 games, the numbers were (50,45,33,36,40,48,42,51,51,52,29). This produces a Chi Square score of 14.773 with 10 degrees of freedom. The p-value here is .14 which is small but isn't statistically significant. Using Chi Square prevents you from having to actually get a 0 on a map, or by making a mistake by doing something like arbitrarily choosing a number after having seen the data (e.g. "Yeah, only 3 games is really low! What are the odds of that?").
(06-02-2014 10:13 AM)lawtai Wrote: However, those map #'s also show a pretty even distribution for the most part. That would seem to indicate that people might start a large number of games in a row, and end up as P1 for all of them, but they're not quitting out and selecting maps.
To make this assertion, I would say you first want to be categorize the games by race. Unfortunately, this will in many cases reduce your sample size to something hard to use. But if somebody plays half Adorables and half Feedback, you definitely don't want their totals mixed; you want the totals for Feedback by map as P1 completely separate from Adorables by map as P1.
(05-31-2014 01:48 PM)game_taker Wrote: (05-31-2014 12:17 PM)Bbobb555 Wrote: (05-31-2014 09:45 AM)SuperDonkey Wrote: (05-31-2014 09:00 AM)jchris98 Wrote: So, I honestly have no idea what you seek to accomplish by this other than to upset the community. I mean, they have already said there would be no new updates.
I did not know this was considered common knowledge. However, I would consider it false. It is directly contradicted both by recent changes to integration with OSN and by the dev's statement that he was seriously considering the creation of a button to make friendly submissions optional. From what I've read in the forums--and I admit I've read only bits here and there--I do not get the impression that there is no chance of any future updates. I'll remain optimistic on this count.
No, jchris is right. There are going to be no new changes except for bugfixes, and even those are rare unless they are major bugs. A fix like this is most likely not going to happen.
This is a bug! A bug of epic proportions that exists solely in the matching system.
Also I would like to point out that the community was not aware of something like this being possible. It was only known that you could take advantage of P1 games by only playing maps which you are strictly good at for whatever reason. Although you can argue that, that knowledge implied that you could do what SuperDonkey has done it was still not known that such a thing is plausible with random game match ups. SuperDonkey proved that it is plausible and for this reason I would argue that if he had not made this post (or instead told AA) then anyone who would find out about this would be able to exploit this bug and never be caught. Furthermore it is possible that there are other people who are currently taking advantage of this bug. By publicly announcing this bug I think it forces AA to fix this bug since there will be people attempting copy what SuperDonkey succeeded in doing.
TL;DR -- This is a bug. I'm glad SuperDonkey posted this. I hope AA fix this bug. Thank you for pointing out this bug and not abusing it.
I'm going to assert that you are 100% correct, game_taker. I estimate my skill level as mid-level Master and doubt I could make SuperTitan in less than 3 or 4 years--and that's with a *lot* of playing. However, by keeping this bug to myself, I estimate I could have reached it in 2-3 months inconspicuously. And by that, I mean even somebody closely watching every game of mine couldn't be certain.
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