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On April 11 2011 06:42 neSix wrote:
Now I'm not math major, and for the record I want to state that this post doesn't actually contribute to the thread in any manner, but I do want to ask...
I think 33% is not what you should be rolling for mirrors as random. I think it would be more like 11%, or 1/3 of 1/3. Allow me to explain:
Assume your possible race is set X, containing A, B, C.
Assume your opponents possible races are set Y, coincidentally also containing A, B, C.
Assuming that a random value is picked from set X to determine your race, you have an approximately 33% chance of rolling any given race. If at the same time, your opponent's race is also determined by randomly pulling a value from set Y, they also have a 33% chance of rolling any given race.
With these assumptions, I think we can state that you are 33% likely to get A from set X, but only 33% of THOSE times that A is pulled from set X will A also be pulled from set Y. Consequently, we must conclude that if you play random you should only be getting mirrors about 1/9 of the time (1/3 * 1/3).
Is that not correct?
Edit:
I'm just pointing this out to say that (as you have correctly noted) if your sample size were big enough to be significant, mirror matchups for random players would be occurring statistically too often if it were more than 11%, not 33%.
Took a while but I think where the error is. Atleast what I think is the error.
Your calculations are correct and thats how you can determine the probablity for an A-A mirror matchup.
But there is also the 1/9th chance of the B-B and the 1/9th chance of the C-C mirror matchup. All of them are part of the set of solutions of the number of mirror matchups. It then becomes 3x1/9th and we are back at 3/9th, 1/3th probability for a mirror matchup as random in a single independent game.
On April 11 2011 06:47 eVolvE342 wrote:
thats wrong nesix because when you enter a game one of the races is already determined. If you are random then at startup screen you have a 33% chance of getting every race still but the opponents race has been determined 100%. However if it is random vs random then your logic would hold.
I don't think you can assume that your race isn't determined during the loading screen but I don't know how that matters either. The knowledge of the race of your opponent doesn't affect the probability for you to get one of the 3 races. All the events are independend and thus there is no conditional probability. And the chance to get the mirror matchup becomes 1/3th. So that is correct, but you are ommiting the possibilities that didn't happen. That your opponent spawned as one of the other races. So in the total sample of possibilities, that 1/3th chance still leads to the 1/9th in total.
Ergo, taking probabilities like this, it doesn't really matter if only you are random or if your opponent is also random. And when we consider your opponents are a certain race, but whom of those you play is also random than everything is the same. Except for a person queing with a certain race. Only that would limit the options to only 3 of the other possible races.
So in terms of chances to get mirror matchups. It's 1/3th for random players and 1/3th for people who que with the same race.
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Not sure what the confusion is about the likelihood of getting a mirror match up as Random.
There are nine match ups as Random, three of them are mirrors. 3/9 = 1/3 = 33.3%
ZvZ
ZvP
ZvT
PvP
PvZ
PvT
TvT
TvZ
TvP
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On April 11 2011 06:42 neSix wrote:
Now I'm not math major, and for the record I want to state that this post doesn't actually contribute to the thread in any manner, but I do want to ask...
I think 33% is not what you should be rolling for mirrors as random. I think it would be more like 11%, or 1/3 of 1/3. Allow me to explain:
Assume your possible race is set X, containing A, B, C.
Assume your opponents possible races are set Y, coincidentally also containing A, B, C.
Assuming that a random value is picked from set X to determine your race, you have an approximately 33% chance of rolling any given race. If at the same time, your opponent's race is also determined by randomly pulling a value from set Y, they also have a 33% chance of rolling any given race.
With these assumptions, I think we can state that you are 33% likely to get A from set X, but only 33% of THOSE times that A is pulled from set X will A also be pulled from set Y. Consequently, we must conclude that if you play random you should only be getting mirrors about 1/9 of the time (1/3 * 1/3).
Is that not correct?
Edit:
I'm just pointing this out to say that (as you have correctly noted) if your sample size were big enough to be significant, mirror matchups for random players would be occurring statistically too often if it were more than 11%, not 33%.
This is only true for specific mirrors, such as the likelihood you'll get PvP or ZvZ specifically, even in RvR. It's also only true when the racial representation for all 3 races is equal.
Think about it:
Let's say your opponent is T. You pick R.
1/3 of the time you'll hit T vs his T. IF the racial representation of players you face is equal (1/3 P, T, Z) then you'll hit T players 1/3 of the time, whic means 1/9 of your matchups should be TvT specifically. This works with any specific matchup in the ideal situation.
Let's say your opponent is R.
1/3 of the time, you hit P. Every time you hit P, 1/3 of those times your opponent will also hit P. Thus, in RvR. You have a 1/9 chance of hitting PvP (or any other matchup, for that matter)
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Since I started using SC2Gears,
41 ZvP
35 ZvZ
21 ZvT
Matches pretty well with the racial distribution.
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SC2Gears
16 PvP
8 PvT
7 PvZ
FML
Doing a 1 stat z test, the p value I got was .015, RAGE
Of course, I'm not random, so do whatever
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On April 11 2011 08:11 Sentient wrote:
Since I started using SC2Gears,
41 ZvP
35 ZvZ
21 ZvT
Matches pretty well with the racial distribution.
On April 11 2011 08:33 pikagrue wrote:
SC2Gears
16 PvP
8 PvT
7 PvZ
FML
Doing a 1 stat z test, the p value I got was .015, RAGE
Of course, I'm not random, so do whatever
Again, two people who did not read the OP, or who just aren't trying to contribute to the thread...
If you aren't playing Random, then your distribution of match-ups is going to be completely dependent on the distribution of the races that people with similar MMR play. Neither of these posts has anything to do with the amount of mirror match-ups that a RANDOM PLAYER would get. All they say is that the # of people who play P > Z > T, which is a topic for a different thread.
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So what's the probability of a random player who hasn't had (or noticed) an unusual number of mirror matchups actually contributing to the thread?
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Okay, I just looked at SC2 Gears. I have not noticed anything weird. However, this includes all of my games since November after I made my switch from Z to random, so take that with a grain of salt. (i.e. it is not exclusive to this season) I also have exactly 12 and 21 extra games as P and T, respectively, because I played that many games as each race to learn them during November/December.
Record as T: 51-26-1 or 78 total. TvT, 18-5 or 23 total. TvZ, 17-11 or 28 total. TvP, 16-10-1 or 27 total.
Record as P: 42-23-1 or 66 total. PvT, 6-8-0 or 14 total. PvZ, 26-6-1 or 33 total. PvP 10-9 or 19 total.
Record as Z: 30-22-4 or 56 total. ZvT, 9-4-1, or 14 total. ZvZ, 11-12-2, or 25 total. ZvP 10-6-1, or 17 total.
All 9 matchups:
200 games total
TvT: 23 games or 11.5%
TvZ: 28 games or 14%
TvP 27 games or 13.35%
PvT 14 games or 7%
PvZ 33 games or 16.5%
PvP 19 games or 9.5%
ZvT 14 games or 7%
ZvZ 25 games or 12.5%
ZvP 17 games or 8.5%
The only thing I notice is that I play a lot of Zergs, and more Protoss than Terran, which perhaps suggests that the number of Zergs near my MMR>the number of Protoss near my MMR>the number of Terrans near my MMR. Everything else is normal, and if you discount my practice custom games you see that I have replays for 167 games with a breakdown of 56 as Z, 54 as P, and 57 as T, which suggests that nothing is wrong with the randomizer.
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Wow this is actually true, I've played 12 PvP's in a row (over three days), and this morning I played 3 ZvZ's when i tried out zerg..
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On April 11 2011 00:54 DarkRise wrote:
I'm low masters protoss and i pretty much get 50% PVTs, 30%PVP, 20% vs Z
i think it depends on your division or league.
Expect more Ps in low league, Zs or Ts in mid and a mix in upper league
same, but i get like 50% pvp 49% zerg and once a month i might play a terran
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Here are my stats when I play random:
Replays: 99
PvP: 10
ZvZ: 6
TvT: 6
PvZ & ZvP: 30
PvT & TvP: 25
ZvT & TvZ: 22
Mirror matchup: 22.22%
Non-Mirror matchup: 77.77%
Protoss Stats for reference (different account and I realize you are not asking for this):
PvP: 247
Non-PvP: 210
Mirror Matchup: 54%
Non-Mirror matchup: 46%
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On April 11 2011 10:17 PokePill wrote:
Here are my stats when I play random:
Replays: 99
PvP: 10
ZvZ: 6
TvT: 6
PvZ & ZvP: 30
PvT & TvP: 25
ZvT & TvZ: 22
Seems normal to me, looks like more Ps near your MMR (while there are more Zs near mine)
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I get too many Random vs. Random match ups...which then turn into PvP or ZvZ. I haven't gotten Terran in ages.
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So many people doing complex maths. Pretty sure it's quite straight forward.
Let P(z), P(t), P(p) be the probability that you roll either zerg, terran or protoss.
Let P(oz), P(ot), P(op) be the probability that your opponent is zerg, terran or protoss.
Let P(mm) be the probability of a mirror match
P(mm) = P(z)*P(oz)+P(t)*P(ot)+P(p)*P(op)
now P(z)=P(t)=P(p)=1/3
therefore you get P(mm) = 1/3(P(oz)+P(ot)+P(op))
but P(oz)+P(ot)+P(op) = 1 since your opponent can only be 1 or 3 races (unless I've been out of the loop for too long).
so P(mm) = 1/3*1 = 1/3 i.e. irrespective of the distribution of races being played. If you are a random player you should get a mirror match 1/3 of the time. Sure you might get more PvPs than other mirror match ups but still 1/3 mirror matchups.
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If you are in a higher league and you play as Protoss or Zerg, you should have more mirrors, as there is less Terran players in those leagues. Protoss is the most played race overall, so if you're a protoss player you better start liking PvP  Also, map downvotes might have something to do with it too.
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On April 11 2011 09:30 wherebugsgo wrote:
Okay, I just looked at SC2 Gears. I have not noticed anything weird. However, this includes all of my games since November after I made my switch from Z to random, so take that with a grain of salt. (i.e. it is not exclusive to this season) I also have exactly 12 and 21 extra games as P and T, respectively, because I played that many games as each race to learn them during November/December.
Record as T: 51-26-1 or 78 total. TvT, 18-5 or 23 total. TvZ, 17-11 or 28 total. TvP, 16-10-1 or 27 total.
Record as P: 42-23-1 or 66 total. PvT, 6-8-0 or 14 total. PvZ, 26-6-1 or 33 total. PvP 10-9 or 19 total.
Record as Z: 30-22-4 or 56 total. ZvT, 9-4-1, or 14 total. ZvZ, 11-12-2, or 25 total. ZvP 10-6-1, or 17 total.
All 9 matchups:
200 games total
TvT: 23 games or 11.5%
TvZ: 28 games or 14%
TvP 27 games or 13.35%
PvT 14 games or 7%
PvZ 33 games or 16.5%
PvP 19 games or 9.5%
ZvT 14 games or 7%
ZvZ 25 games or 12.5%
ZvP 17 games or 8.5%
The only thing I notice is that I play a lot of Zergs, and more Protoss than Terran, which perhaps suggests that the number of Zergs near my MMR>the number of Protoss near my MMR>the number of Terrans near my MMR. Everything else is normal, and if you discount my practice custom games you see that I have replays for 167 games with a breakdown of 56 as Z, 54 as P, and 57 as T, which suggests that nothing is wrong with the randomizer.
Can you please give me your season 2 stats only because that's what I'm trying to analyze. Its relatively easy to do with sc2gears. Just only highlight the games from 1.3.1 patch for analyses. Thanks a lot, the more data I can get the better.
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On April 11 2011 10:50 NinjaDrone wrote:Show nested quote +On April 11 2011 09:30 wherebugsgo wrote:
Okay, I just looked at SC2 Gears. I have not noticed anything weird. However, this includes all of my games since November after I made my switch from Z to random, so take that with a grain of salt. (i.e. it is not exclusive to this season) I also have exactly 12 and 21 extra games as P and T, respectively, because I played that many games as each race to learn them during November/December.
Record as T: 51-26-1 or 78 total. TvT, 18-5 or 23 total. TvZ, 17-11 or 28 total. TvP, 16-10-1 or 27 total.
Record as P: 42-23-1 or 66 total. PvT, 6-8-0 or 14 total. PvZ, 26-6-1 or 33 total. PvP 10-9 or 19 total.
Record as Z: 30-22-4 or 56 total. ZvT, 9-4-1, or 14 total. ZvZ, 11-12-2, or 25 total. ZvP 10-6-1, or 17 total.
All 9 matchups:
200 games total
TvT: 23 games or 11.5%
TvZ: 28 games or 14%
TvP 27 games or 13.35%
PvT 14 games or 7%
PvZ 33 games or 16.5%
PvP 19 games or 9.5%
ZvT 14 games or 7%
ZvZ 25 games or 12.5%
ZvP 17 games or 8.5%
The only thing I notice is that I play a lot of Zergs, and more Protoss than Terran, which perhaps suggests that the number of Zergs near my MMR>the number of Protoss near my MMR>the number of Terrans near my MMR. Everything else is normal, and if you discount my practice custom games you see that I have replays for 167 games with a breakdown of 56 as Z, 54 as P, and 57 as T, which suggests that nothing is wrong with the randomizer. Can you please give me your season 2 stats only because that's what I'm trying to analyze. Its relatively easy to do with sc2gears. Just only highlight the games from 1.3.1 patch for analyses. Thanks a lot, the more data I can get the better.
Okay, I just did it again. Apparently I hadn't been auto-saving my replays until very recently (lol) so the data didn't change much.
154 games total.
TvX 75 games = 48.7% (I just remembered I practiced with T for a couple dozen games, particularly TvP. This is why T is overrepresented here)
TvT 21 games = 13.6%
TvZ 27 games = 17.5%
TvP 27 games = 17.5%
PvX 45 games = 29.2% (also practiced 5-6 PvPs. Damn my PvP is only 50% ;/ )
PvT 9 games = 5.8%
PvZ 20 games = 13%
PvP 16 games = 10.4%
ZvX 34 games = 22%
ZvT 7 games = 4.5%
ZvP 10 games = 6.5%
ZvZ 17 games = 11%
Total mirrors: 54 games = 35%
Nothing weird. Seems like a low number of Ts and a large number of Zs at my MMR.
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Okay I'll jump in, for maybe someone that wants to compile the people their stats here.
Race: Zerg
Total games: 116
Game distribution:
vsZerg: 51
vsProtoss: 45
vsTerran: 20
Mirrors: 44%
Yes I realize it's not a lot of games, but it's still a good amount above the "normal" number of 33%
Maybe it's basicly just caused by the lack of terrans, and it's just "luck" that I get more Zergs then protoss.
Win/Loss/Draw/percentage
vsZerg 26-25-0 50%
vsProtoss 20-23-2 46%
vsTerran 16-4-0 80%
Overall: 54%
I added the win percentages because I feel like something very strange is going on with terran, I do have to say that I played a lot of terran towards the end of season 1 because I got tired of zerg, and the MU I practiced the most is ZvT, but still.
(and 2 of those losses were against that fast, ton of rax, pull all scv's and marines allin after)
I'm absolutely destroying terrans for some reason, my initial thought was that it just tried to find terrans in the hope of balancing out the race distribution for my games played, and the most of them were just much lower then me, but I didn't get anything special in terms of points, all between 9 and 12
So it kinda boggles my mind why I get paired up against terrans that seem to be below my skilllevel.
And it's not really me playing great, but just the terrans playing very poorly.
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(mathcrafting o_O)
I'm a random player and I've went through my records but they seem pretty balanced. No oversaturation of mirror matchups.
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On April 11 2011 05:50 AmericanUmlaut wrote:Show nested quote +On April 11 2011 05:37 shinarit wrote:On April 11 2011 04:56 AmericanUmlaut wrote:On April 11 2011 04:30 shinarit wrote:On April 11 2011 04:14 Klive5ive wrote:
Random numbers are never actually "random" for computers so it's not inconceivable that there's something slightly wrong for random players. Yeah, pseudo-random is much more evenly distributed than real random... So it would be surprising to find anything wrong with it... though we dont know the exact algorithm (or at least i dont, point me somewhere if i can find it there, straight from Blizz possibly). This whole thread is incredible, but as a programmer, this post is my favorite. d Pseudo-random, by definition, is not random but statistically cannot be distinguished from random. A pseudo-random number generator that created numbers more evenly distributed than real random numbers would by that very fact reveal itself as non-random and could then be predicted to some extent without knowledge of the algorithm used ot generate the numbers. Thus, the generator would not be pseudo-random. Thus, you are full of crap. QED. I think you will be surprised and your world will be crushed: pseudo random generators are not random generators. They are ofcourse cannot be distinguished, but thats because random generator cannot be identified in a finite sample. But what we were talking about were the random generators of our computers. And if you ever tried one of them (as a programmer you should have, i know i did), they produce a very even distribution, even in low size sample. Real random CAN produce it as well, but it tends not to. So whats with the crap and all the crunchertalk? You demonstrate nothing, just throw in stuff everyone knows and which are irrelevant to the topic. I was pointing out that your comment on pseudorandom algorithms was logically contradictory, because a pseudorandom generator that could be shown to have a more even distribution of values than a truly random source of numbers would by definition not be pseudorandom. This demonstrates that you either don't understand the words that you are using, or you're intentionally saying things that aren't true. Your comment about pseudorandom behavior producing a very even distribution, "even in a low size sample," is a perfect example of the silliness of this entire thread, which probably only hasn't been closed yet because the mods were enjoying the TSL. No statistical observation based on a low sample size has any significance.
Once again. Read what i wrote and think again. Also, sit down and try flipping a coin and generating random 1/2-1/2 chances with your favourite compiler's random generator. Or if its not enough for a show, try with a d20 die. I know what im talking about, i know that random cannot be proved to be random, and that pseudo random generators are KNOWN to NOT be random (thats why we call them pseudo, they just look like one), if you know the seed you can tell the whole series, but thats not the point. The point is, usually they generate more even distribution. If you dont beleive me, try it. If you dont try it, hold back your "arguments".
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EPT
