Rising in the Rankings

[PETA] Doodat · 06-01-2014, 04:47 AM

Amazing. Such concise much wow.

Chemoeum · 06-01-2014, 06:58 AM

Much post, many fun, is doge

TheGreatErenan · (This post was last modified: 06-01-2014 03:33 PM by TheGreatErenan.)

P.S. A lot of people really seem to have gotten the wrong idea from OML's comments concerning Outwitters being "out of production." OML did not say that there would no new updates for Outwitters. In fact, all they said was that they had moved out of content production on Outwitters and then immediately and explicitly clarified that all this meant was that there would be no new teams or map packs but that they would continue to allot manhours to balancing gameplay issues, implementing bug fixes, and supporting servers and seasons. Preventing players from abusing P1 game cancellation clearly falls into this latter category, so I see no obvious reason to doubt that a fix could be implemented.

P.P.S. I think you can actually make at least some educated guesses at how much people abuse the system by cancelling P1 games, at least with players who play a lot of games. Look at the match histories of as many players as you can find who are known (for sure) not to cancel any games but who play many many games. Check the proportions of their P1 games and what maps they are on. Theoretically, if the map-selection system works the same way for all players, then with a large enough sample there should be some consistency to the proportions (if it's supposed to be roughly even, for instance, then theoretically each map would appear about 9% of the time for every player in your sample). If such a consistency to the proportions does in fact emerge from a large sample, then if you look at a player's history and find that it deviates significantly from the expected norms, it would be plausible that they are cancelling P1 matches on whatever maps appear less often. Some other math guys/gals please check me on this claim if you wish. Analyzing statistical data isn't exactly my special area of expertise (speculating about the correctness of Platonist and Nominalist ontological theories of musical works is Tongue

).

Flarp55 · (This post was last modified: 06-02-2014 12:19 AM by Flarp55.)

Lol how it is all a PS to your original post.

(06-01-2014 03:28 PM)TheGreatErenan Wrote: P.S. A lot of people really seem to have gotten the wrong idea from OML's comments concerning Outwitters being "out of production." OML did not say that there would no new updates for Outwitters. In fact, all they said was that they had moved out of content production on Outwitters and then immediately and explicitly clarified that all this meant was that there would be no new teams or map packs but that they would continue to allot manhours to balancing gameplay issues, implementing bug fixes, and supporting servers and seasons. Preventing players from abusing P1 game cancellation clearly falls into this latter category, so I see no obvious reason to doubt that a fix could be implemented.

P.P.S. I think you can actually make at least some educated guesses at how much people abuse the system by cancelling P1 games, at least with players who play a lot of games. Look at the match histories of as many players as you can find who are known (for sure) not to cancel any games but who play many many games. Check the proportions of their P1 games and what maps they are on. Theoretically, if the map-selection system works the same way for all players, then with a large enough sample there should be some consistency to the proportions (if it's supposed to be roughly even, for instance, then theoretically each map would appear about 9% of the time for every player in your sample). If such a consistency to the proportions does in fact emerge from a large sample, then if you look at a player's history and find that it deviates significantly from the expected norms, it would be plausible that they are cancelling P1 matches on whatever maps appear less often. Some other math guys/gals please check me on this claim if you wish. Analyzing data isn't exactly my special area of expertise (speculating about the correctness of Platonist and Nominalist ontological theories of musical works is ).

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 11*(10/11)^50. So if a player has played 50 games as P1, then there is actually still about a 9.4% chance that there are no games for some map. Note that only P1 season 5 games should be counted.

TheGreatErenan · (This post was last modified: 06-01-2014 03:55 PM by TheGreatErenan.)

(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.

Demon · (This post was last modified: 06-01-2014 08:44 PM by Demon.)

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 Smile

SFI is just an example, of course, this calculation will work for all maps.

Flarp55 · (This post was last modified: 06-02-2014 12:39 AM by Flarp55.)

(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%.

Demon · 06-02-2014, 01:38 AM

Chance of not getting a game on any map (rather than a specific map) is trickier, and your figure of 9.131% checks out as far as I can tell.

Still, that's a fairly small chance.

Flarp55 · 06-02-2014, 02:14 AM

(06-02-2014 01:38 AM)Demon Wrote: Chance of not getting a game on any map (rather than a specific map) is trickier, and your figure of 9.131% checks out as far as I can tell.

Still, that's a fairly small chance.

It might be a small, but it's not too small, and shows that you can't accuse someone of cheating just because they have no games on a map. Don't even think about if they have one match on a map.

If they have 100 games, on the other hand, you can.

TheGreatErenan · (This post was last modified: 06-02-2014 02:32 AM by TheGreatErenan.)

Right, which is why I said you would have to focus on players who had played many many matches. However, intuitively it seems that you'd have to play quite a large number of matches before you could reasonably expect to see a rough evenness among the numbers of times you played on each map. But what you said is true. If a player has played hundreds of P1 matches and absolutely none of them are on a particular map, it seems very likely that they cancelled P1 matches on that map.

In any case, admittedly without having put much thought into it, I am in favor of implementing a hidden ranking penalty when quitting a P1 match prior to being assigned an opponent, and this would make all of the above data analysis unnecessary, since people would presumably stop doing it.

Alternatively, I would be happy with the "can't make a move until both players are in the game" solution as well, but I understand that there are significant downsides to this.