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Hm, just doing vector crosses, if two teams both choose their repeated race randomly, and each slot/map had players randomly assigned, then we'd expect:
Four game series:
* Games where both teams have same repeat race (ie, PTZZ vs PTZZ): 37.5% mirrors
* Games where the teams have different repeat race (ie, PTZZ vs PTTZ): 31.25% mirrors
Therefore, within the first four games, anything above 37.5% cannot be attributed to randomness within the asymptotic limits.
Trying to calculate the ace match is less theoretical, since each team's ace player is nonrandom. For example, Oz sends out Jaedong basically 100% of the time, SKT would typically send out Bisu or fantasy, etc. I'm going to estimate that ace matches would be less than 10% of the total PL matches, and that the limits for mirrors should be within 25-40%.
So it looks like 38% is the most mirror matches we could attribute to chance and team distribution alone. (in practice it would be less than that, since not every team is going to have the same racial distribution of their top players)
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On October 27 2009 10:57 TheYango wrote:Show nested quote +On October 27 2009 10:52 timmeh wrote:
Make them choose line-up order before revealing map order. Make map order random. That just turns proleague into more of a coin toss. Whereas right now coaches can pick and counterpick based on the expected opponent on a given map, having the map order be random could result in a situation where a coach neither made good picks for his players, nor did any of the players play better than their opponents--but simply the maps worked out in their favor. In professional play, it's desirable for such random factors to be eliminated. Personally, I'd rather watch a good mirror match, than a complete rape non-mirror that abuses map imbalance.
May give an advantage to a player. But in the long run it equals out for everyone. It also promotes players being good on all maps, not just on maps favouring their race. And having random factors may actually increase (spectator) excitement.
I'd rather see someone overcome a map "imbalance" than seeing the 3rd "good" ZvZ of the day.
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What the hell is the problem with people in this thread. There are 6 matchups. 3 of them are mirrors. Thus 50% of the games should be mirrors. What is this crap about TvZ and ZvT being different matchups? it's the same matchup people! The only difference is that you chose a player to call player 1 and one to call player 2. It sure as hell does not make the game consist of 9 matchups.
From a players perspective sure he can play 9 matchups but a viewer can ONLY watch 6. There is no way around this. When we're talking about the ammount of games in proleague that are mirrors matchups there should be 50%.
Example for those still not grasping the simple idea of this:
Hwasin(T) plays against Luxury(Z). For those of you who claims there is a TvZ matchup and a ZvT matchup which is this? Is it TvZ because I chose to type Hwasins name first? Obviously NO. TvZ is allways one matchup. There are 6 matchups in this game. If you are one of the players there is 9. But when we're talking about proleague none of us here is a player are we?
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On October 27 2009 21:25 StarBrift wrote:
What the hell is the problem with people in this thread. There are 6 matchups. 3 of them are mirrors. Thus 50% of the games should be mirrors. What is this crap about TvZ and ZvT being different matchups? it's the same matchup people! The only difference is that you chose a player to call player 1 and one to call player 2. It sure as hell does not make the game consist of 9 matchups.
From a players perspective sure he can play 9 matchups but a viewer can ONLY watch 6. There is no way around this. When we're talking about the ammount of games in proleague that are mirrors matchups there should be 50%.
Example for those still not grasping the simple idea of this:
Hwasin(T) plays against Luxury(Z). For those of you who claims there is a TvZ matchup and a ZvT matchup which is this? Is it TvZ because I chose to type Hwasins name first? Obviously NO. TvZ is allways one matchup. There are 6 matchups in this game. If you are one of the players there is 9. But when we're talking about proleague none of us here is a player are we?
Haha. What the hell is the problem with people in this thread indeed.
Since you don't understand the argument from concepts of probability, try this thinking about this -
Let's say you are a Terran and your opponent picks Random. How often do you expect to play a mirror?
What about if you are a Protoss?
What about if you are a Zerg?
So, how often do you expect to play a mirror when it's Random vs Random?
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Russian Federation4235 Posts
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On October 26 2009 09:10 motbob wrote:Show nested quote +On October 26 2009 09:04 ploy wrote:
Uh no thats not right. Order does not matter in this situation. Banzu is right - 50% of the matchups you can watch are mirrors, so it's to be expected that about 50% of the matchups that you see are mirrors. You're wrong. If a team sends out a zerg, it's a 33% chance the match will be mirror if the other team sends out a random player. Thus, mirror matches "should" occur 33% of the time.
So you're gonna base your statistics on half of the information? You're assuming that the choice of the first coach is not part of the statistics. Why not? The coaches send outj their picks simultaneously.
You're saying: IF one of the players races are pre determined then it's a 33% chance that there will be a mirror match. By including only half of the information you have narrowed it down to 3 possibilities.
I'm saying: SINCE we know that none of the players races are pre determined then its a 50% chance that there will be a mirror match. By including all the information I have kept the possible matchups at 6.
Both of our statements are statistically sound. But you are talking about some kind of wierd format when one team gets to know the others pick before hand and I'm talking about pro league.
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On October 27 2009 21:28 Gustav_Wind wrote:Show nested quote +On October 27 2009 21:25 StarBrift wrote:
What the hell is the problem with people in this thread. There are 6 matchups. 3 of them are mirrors. Thus 50% of the games should be mirrors. What is this crap about TvZ and ZvT being different matchups? it's the same matchup people! The only difference is that you chose a player to call player 1 and one to call player 2. It sure as hell does not make the game consist of 9 matchups.
From a players perspective sure he can play 9 matchups but a viewer can ONLY watch 6. There is no way around this. When we're talking about the ammount of games in proleague that are mirrors matchups there should be 50%.
Example for those still not grasping the simple idea of this:
Hwasin(T) plays against Luxury(Z). For those of you who claims there is a TvZ matchup and a ZvT matchup which is this? Is it TvZ because I chose to type Hwasins name first? Obviously NO. TvZ is allways one matchup. There are 6 matchups in this game. If you are one of the players there is 9. But when we're talking about proleague none of us here is a player are we? Haha. What the hell is the problem with people in this thread indeed. Since you don't understand the argument from concepts of probability, try this thinking about this - Let's say you are a Terran and your opponent picks Random. How often do you expect to play a mirror? What about if you are a Protoss? What about if you are a Zerg? So, how often do you expect to play a mirror when it's Random vs Random?
Are you discussing the chances of a mirror game occuring on ICCUP or are you talking about proleague? Because I'm pretty sure the OP was talking about proleague. Read my previous post please as I don't want to type the exact thing twice in a row on a forum board.
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United States47024 Posts
On October 27 2009 21:25 StarBrift wrote:
Hwasin(T) plays against Luxury(Z). For those of you who claims there is a TvZ matchup and a ZvT matchup which is this? Is it TvZ because I chose to type Hwasins name first? Obviously NO. TvZ is allways one matchup. There are 6 matchups in this game. If you are one of the players there is 9. But when we're talking about proleague none of us here is a player are we?
Read my previous example. Hyuk v Stork is different from Great v Bisu. WHICH TEAM fields the Zerg matters. In a mirror though, both teams field 1 race. You're right, the order they pick doesn't matter. Firebathero vs Fantasy is the same as Fantasy v Firebathero. But the first team's Zergs are different from the 2nd team's Zergs.
If team A and B each have 33% of each race, TvT only occurs when they both choose a Terran, but a TvZ occurs in two cases: when team A chooses a Terran and team B chooses a Zerg, and when team B chooses a Terran and team A chooses a Zerg. The probability of a TvT is then half that of a TvZ.
On October 27 2009 21:37 StarBrift wrote:
So you're gonna base your statistics on half of the information? You're assuming that the choice of the first coach is not part of the statistics. Why not? The coaches send outj their picks simultaneously.
Yes. And that works out:
Chance of ZvZ = (Chance 1st coach sends a zerg) * (Chance 2nd coach sends a zerg) = (1/3) * (1/3)
Chance of TvT = (Chance 1st coach sends a terran) * (Chance 2nd coach sends a terran) = (1/3) * (1/3)
Chance of PvP = (Chance 1st coach sends a protoss) * (Chance 2nd coach sends a protoss) = (1/3) * (1/3)
Chance of mirror = ZvZ + TvT + PvP = 1/3
He assumed a zerg first for simplicity, because it results in the same result. Apparently you didn't get it.
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On October 27 2009 21:37 StarBrift wrote:Show nested quote +On October 26 2009 09:10 motbob wrote:On October 26 2009 09:04 ploy wrote:
Uh no thats not right. Order does not matter in this situation. Banzu is right - 50% of the matchups you can watch are mirrors, so it's to be expected that about 50% of the matchups that you see are mirrors. You're wrong. If a team sends out a zerg, it's a 33% chance the match will be mirror if the other team sends out a random player. Thus, mirror matches "should" occur 33% of the time. So you're gonna base your statistics on half of the information? You're assuming that the choice of the first coach is not part of the statistics. Why not? The coaches send outj their picks simultaneously. You're saying: IF one of the players races are pre determined then it's a 33% chance that there will be a mirror match. By including only half of the information you have narrowed it down to 3 possibilities. I'm saying: SINCE we know that none of the players races are pre determined then its a 50% chance that there will be a mirror match. By including all the information I have kept the possible matchups at 6. Both of our statements are statistically sound. But you are talking about some kind of wierd format when one team gets to know the others pick before hand and I'm talking about pro league.
Ok, since you're not getting it, let's throw in some names and see if it helps any.
SKT and CJ are separately deciding which player to send in.
SKT will send in either Bisu (P), Fantasy (T), or Hyuk (Z), chosen at random.
CJ will send in either Movie (P), Skyhigh (T), or Effort (Z), chosen at random.
Each of these outcomes are equally likely.
Bisu vs Movie (PvP)
Bisu vs Skyhigh (PvT)
Bisu vs Effort (PvZ)
Fantasy vs Movie (TvP)
Fantasy vs Skyhigh (TvT)
Fantasy vs Effort (TvZ)
Hyuk vs Movie (ZvP)
Hyuk vs Skyhigh (ZvT)
Hyuk vs Effort (ZvZ)
9 equally likely outcomes, 3 mirror matches. 1/3 chance.
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I cannot believe people are still arguing about the % of mirrors there would be on random player picking... Everyone should either get it or realize that they suck at math and stfu, but too much to ask it seems.
I play 1 race, theres 3 possible races i can face, if each has equal chances to come up its mirror 1/3 of time, nuff said... or not :/
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I remember someone saying TL has a higher than average IQ. After reading this thread there is no way.
It is :
-33% Mirror
-67% Non-Mirror
It is basic probability.
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On October 27 2009 21:25 StarBrift wrote:
What the hell is the problem with people in this thread. There are 6 matchups. 3 of them are mirrors. Thus 50% of the games should be mirrors. What is this crap about TvZ and ZvT being different matchups? it's the same matchup people! The only difference is that you chose a player to call player 1 and one to call player 2. It sure as hell does not make the game consist of 9 matchups.
From a players perspective sure he can play 9 matchups but a viewer can ONLY watch 6. There is no way around this. When we're talking about the ammount of games in proleague that are mirrors matchups there should be 50%.
Example for those still not grasping the simple idea of this:
Hwasin(T) plays against Luxury(Z). For those of you who claims there is a TvZ matchup and a ZvT matchup which is this? Is it TvZ because I chose to type Hwasins name first? Obviously NO. TvZ is allways one matchup. There are 6 matchups in this game. If you are one of the players there is 9. But when we're talking about proleague none of us here is a player are we?
You're trolling, right?
Example with Terran:
A player can only play 2 TYPES (note how I am reiterating TYPE) of matchups:
(a)Mirror => TvT
(b)Non-mirror => TvZ or TvP
The chances of getting (b) is twice as high as getting (a)
But he can face 3 different races:
(a) TvT
(b) TvZ
(c) TvP
If you consider each race, then you have to do the statistics with each race and add it all up. It will still give you 33% mirror.
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This thread is making me lose faith in humanity.
How about a simulation?
Python 2.6.2 (release26-maint, Apr 19 2009, 01:58:18)
[GCC 4.3.3] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> from random import choice
>>> race = ["T", "Z", "P"]
>>> N = 1000000
>>> mirrors = 0
>>> for n in range(N):
... p1 = choice(race)
... p2 = choice(race)
... mirrors += (p1 == p2)
...
>>> print float(mirrors) / N
0.333159
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I love that I'm sitting in a class about probability RIGHT NOW....and this made my day. People have the most interesting approaches to math. 1/3 mirrors is legit lol.
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On October 27 2009 22:27 maneatingshoe wrote:
I love that I'm sitting in a class about probability RIGHT NOW....and this made my day. People have the most interesting approaches to math. 1/3 mirrors is legit lol.
I'm sure anyone who gives the 1/3 answer could give the straightforward approach.
It's just that the people who say 50% don't understand the straightforward approach... so...
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On October 27 2009 22:25 okum wrote:
This thread is making me lose faith in humanity.
I hear ya.
I was thinking of posting at the 2nd page, but I decided not to because I thought it had already been settled and made unequivocal that the chance of a mirror was 1/3. Apparently it hadn't. It's demoralising to see people spouting this type of thing time and time again.
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On October 27 2009 22:25 okum wrote:This thread is making me lose faith in humanity. How about a simulation?
Python 2.6.2 (release26-maint, Apr 19 2009, 01:58:18)
[GCC 4.3.3] on linux2
Type "help", "copyright", "credits" or "license" for more information.
>>> from random import choice
>>> race = ["T", "Z", "P"]
>>> N = 1000000
>>> mirrors = 0
>>> for n in range(N):
... p1 = choice(race)
... p2 = choice(race)
... mirrors += (p1 == p2)
...
>>> print float(mirrors) / N
0.333159
The easiest method to proving mirrors = 33% lol
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On October 27 2009 21:40 StarBrift wrote:Show nested quote +On October 27 2009 21:28 Gustav_Wind wrote:On October 27 2009 21:25 StarBrift wrote:
What the hell is the problem with people in this thread. There are 6 matchups. 3 of them are mirrors. Thus 50% of the games should be mirrors. What is this crap about TvZ and ZvT being different matchups? it's the same matchup people! The only difference is that you chose a player to call player 1 and one to call player 2. It sure as hell does not make the game consist of 9 matchups.
From a players perspective sure he can play 9 matchups but a viewer can ONLY watch 6. There is no way around this. When we're talking about the ammount of games in proleague that are mirrors matchups there should be 50%.
Example for those still not grasping the simple idea of this:
Hwasin(T) plays against Luxury(Z). For those of you who claims there is a TvZ matchup and a ZvT matchup which is this? Is it TvZ because I chose to type Hwasins name first? Obviously NO. TvZ is allways one matchup. There are 6 matchups in this game. If you are one of the players there is 9. But when we're talking about proleague none of us here is a player are we? Haha. What the hell is the problem with people in this thread indeed. Since you don't understand the argument from concepts of probability, try this thinking about this - Let's say you are a Terran and your opponent picks Random. How often do you expect to play a mirror? What about if you are a Protoss? What about if you are a Zerg? So, how often do you expect to play a mirror when it's Random vs Random? Are you discussing the chances of a mirror game occuring on ICCUP or are you talking about proleague? Because I'm pretty sure the OP was talking about proleague. Read my previous post please as I don't want to type the exact thing twice in a row on a forum board.
This made me laugh.
Probabilities (theoretically) of certain matchups happening on ICCUP is different than it in proleague now?
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It would depend on the sizes of population, obviously. If we have n progamers, with n/3 of each race, we can show that the number of possible matches would be n!/2(n-2)!. And with n/3 numbers of every race, we get (n/3)!/(2(n-3)/6)! of each mirror matchup. The ratio would then be the probability of a mirror match happening. ((n/3)!/(2(n-3)/6)!) / (n!/2(n-2)!) which we can simplify to (n-3)/9(n-1), which for larger values of n will be about 1/9. And since we have 3 mirror matchups we get 3/9=1/3.
If we wanted, we could also look at it this way. Consider that we have a big urn, filled with n progamers. Let us also assume that that they are many enough so that 1/ n=0, and let us also assume that they are evenly distributed, just to make things simpler. A mirror matchup occurs exactly when we draw two of the same in a row. The P of drawing either a P or a T or a Z is 1. The P of drawing the same as the first, given the above assumptions, is 1/3. The probability of this happening in a row is 1*1/3=1/3. Thus the probability that we get a mirror matchup from the assumed pool of progamers must be 1/3. I honestly prefer a more combinatorics focused approach, but this might be more clear if you are not used to math.
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United States10328 Posts
hahahahaha oh god this is so lulzy
p4ndemik's table is the easiest way to see it... 3x3 possibilities (each side can pick 3 races), 3 mirrors
and to address the "more of some race" issue:
say team 1 has T1 terrans, P1 protosses, Z1 zergs, and let X1 = T1+P1+Z1 then the total # of ways is
say team 2 has T2 terrans, P2 protosses, Z2 zergs, and let X2 = T2+P2+Z2
PROBABILITY = TOTAL # OF DESIRABLE / TOTAL #
(but if permutations matter on top, they must matter on the bottom!... using combinations is the same; you just cancel)
Total #: X1*X2
Total # desirable (i.e. mirror): T1T2 + P1P2 + Z1Z2
So the probability of a mirror in this match is (T1T2+P1P2+Z1Z2)/[ (T1+P1+Z1)(T2+P2+Z2) ]
in the case where T1=T2=P1=P2=Z1=Z2 (i.e., the ideal world where every team has equal numbers of T/P/Z and equal number of players), this evaluates to (1+1+1)/[ (1+1+1)(1+1+1) ] = 1/3
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EPT
