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War_Minister
Canada86 Posts
If all maps were perfectly balanced, we could expect a mirror match-up ratio close to 33%. I understand that maps cannot be perfectly balanced but, after doing a quick survey all of scheduled games in October, I found that exactly 50% of all games were mirror match-ups (13% PvP, 18% TvT and 19% ZvZ)! This seems very far from the 33% perfection… I just wonder (I ask to the most veteran fans among you), is this usual in the ProLeague or is October simply an unlucky month? | ||
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zulu_nation8
China26351 Posts
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lazz
Australia3119 Posts
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BanZu
United States3329 Posts
PvP TvT PvZ ZvT TvP 6 match-ups, half are mirrors. Is there something wrong with my logic? | ||
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Ideas
United States8097 Posts
you think 50% is bad? Just look at the SPL 08 season before they had the at least 1 of each race every match rule. | ||
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haxorz
United States138 Posts
On October 26 2009 08:34 BanZu wrote: ZvZ PvP TvT PvZ ZvT TvP 6 match-ups, half are mirrors. Is there something wrong with my logic? Other people have pointed out that it should actually be 1/3 mirror matches. This logic is only correct if we assume that coaches choose which race to send for a game at random (i.e., in the ideal case). Suppose a team's best players are Protosses (Khan!?!?!?!). Suppose another team's best players are Zergs. Their coaches will be more inclined to send their better players, so in this example a mirror match is less likely than 1/3. edit: clarified my point | ||
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huameng
United States1133 Posts
Or think of it this way: you pick any race. your opponent can pick any 3 races, and 1 of those 3 will be the same as yours. so 1/3 matchups are mirrors. | ||
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Deleted User 48059
86 Posts
ZvZ PvP TvT PvZ ZvT TvP ...you need to add ZvP PvT TvZ to that list (order matters; player A can play zerg, and player B terran, OR the other way round) Or, to put it a little differently: player A can be P, T or Z. Whatever player A's race is, there is a *1 in 3* chance that player B will be playing the same race. Hope that helps; I'm not the best at explaining things sometimes Kev edit: yah, I was too slow. stupid long post and slow typing... | ||
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ploy
United States416 Posts
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motbob
United States12546 Posts
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. | ||
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hellokitty[hk]
United States1309 Posts
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Nouar
France3270 Posts
Could some people put in their heads a little bit of common sense... Player A, whatever race he plays, has 1/3 chance to play a mirror. You don't have to calculate any further. | ||
Hot_Bid
Braavos36374 Posts
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lone_hydra
Canada1460 Posts
Seriously, whoever wins, help me with my STAT 230 course T-T | ||
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haxorz
United States138 Posts
On October 26 2009 09:18 Nouar wrote: My god will there ever be a consensus about those statistics ? Could some people put in their heads a little bit of common sense... Player A, whatever race he plays, has 1/3 chance to play a mirror. You don't have to calculate any further. I just want to clarify for everyone - this is true in the ideal case (see my previous post). Of course, pro SC irl is NOT the ideal case. | ||
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cascades
Singapore6122 Posts
How were the statistics for the previous seasons anyway? | ||
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Arrian
United States889 Posts
On October 26 2009 09:37 Hot_Bid wrote: Maps are almost never balanced through all three non mirror matches, PvT TvZ PvZ. They are usually slanted toward two races or one race. All teams know this, so obviously there will be far more mirror matches because the teams know to send a Z on outsider and tornado, a T on match point, etc. Hot_Bid hit the nail on the head. The key word in the whole equation is random, and what race coaches choose to put on certain maps is demonstrably not random, for a slew of reasons. | ||
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Wilko
Germany470 Posts
On October 26 2009 08:40 weepingblades wrote: Yes. ZvZ PvP TvT PvZ ZvT TvP ...you need to add ZvP PvT TvZ to that list (order matters; player A can play zerg, and player B terran, OR the other way round) Or, to put it a little differently: player A can be P, T or Z. Whatever player A's race is, there is a *1 in 3* chance that player B will be playing the same race. Hope that helps; I'm not the best at explaining things sometimes Kev edit: yah, I was too slow. stupid long post and slow typing... Shouldn't mirrors also be counted twice? Like: T1 vs T2 T2 vs T1 Z1 vs Z2 Z2 vs Z1 P1 vs P2 P2 vs P1 | ||
Heyoka
Katowice25012 Posts
On October 26 2009 08:30 zulu_nation8 wrote: theres always been a lot of mirrors, dont know if October has had more than usual. Look at last year's proleague playoffs, almost every match was a mirror. Its been way more than usual. I have the actual numbers in the latest PL article, there have been twice as many mirrors so far this month as compared to last year's maps. | ||
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cascades
Singapore6122 Posts
On October 26 2009 13:47 Wilko wrote: Shouldn't mirrors also be counted twice? Like: T1 vs T2 T2 vs T1 Z1 vs Z2 Z2 vs Z1 P1 vs P2 P2 vs P1 Yes. So it is still 1 in 3. | ||
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jalstar
United States8198 Posts
T1 vs P2 T1 vs Z2 P1 vs T2 P1 vs P2 P1 vs Z2 Z1 vs T2 Z1 vs P2 Z1 vs Z2 | ||
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Wilko
Germany470 Posts
Yes | ||
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29 fps
United States5724 Posts
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TheYango
United States47024 Posts
On October 26 2009 13:47 Wilko wrote: T1 vs T2 T2 vs T1 Z1 vs Z2 Z2 vs Z1 P1 vs P2 P2 vs P1 T1 v T2 is the same as T2 v T1, but P1 v T2 is different from T1 v P2. Let's call our players Movie and Skyhigh. Movie P v Skyhigh P is the same matchup as Skyhigh P v Movie P, but Movie P v Skyhigh T is different from Movie T v Skyhigh P. | ||
p4NDemik
United States13896 Posts
![[image loading]](http://www.teamliquid.net/staff/p4NDemik/TableorGraph/foridiots.jpg) There's 9 possible outcomes. 1/9 (11%) chance of each one happening. As you can see each type of mirror only occurs once, each type of non-mirror occurs twice. Thus there is 3/9 chance (33.3%) for mirrors, 6/9 (66.6%) chance for non-mirrors. | ||
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wswordsmen
United States987 Posts
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baubo
China3370 Posts
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Avidkeystamper
United States8552 Posts
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Heyoka
Katowice25012 Posts
On October 26 2009 14:28 wswordsmen wrote: Conclusion: We observe that 50% of PL matches are mirrors, while if the races were randomly selected due to map balance we would expect 33% mirrors. Therefore the maps are not perfectly balanced but if fact skewed towards one race resulting in more mirror matches than expected. What we're actually measuring here is the coach's perception of the maps, not some intrinsic value they have | ||
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Jyvblamo
Canada13788 Posts
+ Show Spoiler + | ||
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ShadowDrgn
United States2497 Posts
On October 26 2009 14:37 heyoka wrote: What we're actually measuring here is the coach's perception of the maps, not some intrinsic value they have I don't know how many progamers there are, but I think it's around 250 when you combine 12 teams' A and B teams. They all practice 12 hours a day, and with a conservative guess of 2 games/hour, that's 24 games a day. Even if all the pros play one another instead of non-pros on iccup, that's still 3000 games total a day between them. Given a few months to practice new maps, I think the coaches have a very good idea which races are better on certain maps. | ||
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economist_
Vietnam719 Posts
50% would be indicating that something is imbalanced only if the coach were making perfectly random decision (assuming that he makes final decision). If there were something like a coach perceives that some maps are more favorable to certain race and send that race out (in addition to other factors which might kick in), whatever the (conditional) probability you get, it says nothing about imbalance, anything at all p4NDemik, name of your matrix is lol | ||
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Heyoka
Katowice25012 Posts
On October 26 2009 14:39 Jyvblamo wrote: In this thread, we learn that human brains are horribly wired for understanding statistics and probability. + Show Spoiler + If you read Nassim Taleb's books he blames Descartes specifically for how people have difficulty understanding statistics. I get the feeling its something that makes him very angry. On October 26 2009 14:59 ShadowDrgn wrote: I don't know how many progamers there are, but I think it's around 250 when you combine 12 teams' A and B teams. They all practice 12 hours a day, and with a conservative guess of 2 games/hour, that's 24 games a day. Even if all the pros play one another instead of non-pros on iccup, that's still 3000 games total a day between them. Given a few months to practice new maps, I think the coaches have a very good idea which races are better on certain maps. Doesn't change the fact that we are not measuring an actual quality of the maps. The distinction is necessary. | ||
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Highways
Australia6103 Posts
I've actually been complaining about the mass mirrors during last seasons proleague. I think there should just be race restrictions on maps. | ||
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Syntax Lost
Finland86 Posts
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prOxi.swAMi
Australia3091 Posts
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JohannesH
Finland1364 Posts
And as said theres more than just maps simply favoring a race or 2. Some players' style might be more suited for a certain map than another player of same race. Different people have different matchups as their strongest. Some map might have some viable strategies for a race thought weak on it, but those strategies just arent figured out instantly... etc etc. Oh and I like mirrors... Both players having the same weapons in their arsenal is interesting. | ||
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Signet
United States1718 Posts
On October 26 2009 14:01 TheYango wrote: T1 v T2 is the same as T2 v T1, but P1 v T2 is different from T1 v P2. Let's call our players Movie and Skyhigh. Movie P v Skyhigh P is the same matchup as Skyhigh P v Movie P, but Movie P v Skyhigh T is different from Movie T v Skyhigh P. This is true. However, in practice, Movie plays P and Skyhigh plays T. So Movie P vs Skyhigh T is the only matchup that should get counted here. Since each progamer plays one race professionally - with extremely rare exceptions - the theoretical 1/3 mirrors is an asymptotic limit, not the true expected value. | ||
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sovietico
Spain17 Posts
On October 26 2009 14:04 p4NDemik wrote: Reading this thread is downright enfuriating. Such a simple concept takes 20 replies for some to understand. Here's a table for matchups in a totally random situation. There's 9 possible outcomes. 1/9 (11%) chance of each one happening. As you can see each type of mirror only occurs once, each type of non-mirror occurs twice. Thus there is 3/9 chance (33.3%) for mirrors, 6/9 (66.6%) chance for non-mirrors. I think this logic is ok if we have 33% protosses 33% terrans and 33% zergs. Wich is not the case, we should see the number of terran protoss and zerg players to calculate in an apropiate way the "ideal" number of mirror matchups that should be. For ex: if there are 98 terrans 1 protoss and 1 zerg in the rosters of the PL teams, near 99% of the games will be mirrors and not 33%. at least thats what i think :S | ||
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HopLight
Sweden999 Posts
On October 26 2009 14:04 p4NDemik wrote: Reading this thread is downright enfuriating. Such a simple concept takes 20 replies for some to understand. Here's a table for matchups in a totally random situation. There's 9 possible outcomes. 1/9 (11%) chance of each one happening. As you can see each type of mirror only occurs once, each type of non-mirror occurs twice. Thus there is 3/9 chance (33.3%) for mirrors, 6/9 (66.6%) chance for non-mirrors. I love the table name! | ||
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Aphelion
United States2720 Posts
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. Oh god, this is just bad. | ||
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shurgen
350 Posts
ALso, I'm not totally sure, but it may be that because its the beginning of the season, optimal strategies and whatnot have not been made on each of the maps, so they are just sending out what at first glance appears to be the best race on w.e map.. i'm not 100% sure but i think the # of mirrors could possibly go down on some of the maps as time goes on | ||
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Manit0u
Poland17255 Posts
Hot_Bid has already nailed the OP dillema but I guess that most people in this thread didn't bother to read it so I'm going to put this in front of your faces once again: On October 26 2009 09:37 Hot_Bid wrote: Maps are almost never balanced through all three non mirror matches, PvT TvZ PvZ. They are usually slanted toward two races or one race. All teams know this, so obviously there will be far more mirror matches because the teams know to send a Z on outsider and tornado, a T on match point, etc. /thread | ||
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Zato-1
Chile4253 Posts
On October 26 2009 20:34 sovietico wrote: I think this logic is ok if we have 33% protosses 33% terrans and 33% zergs. Wich is not the case, we should see the number of terran protoss and zerg players to calculate in an apropiate way the "ideal" number of mirror matchups that should be. For ex: if there are 98 terrans 1 protoss and 1 zerg in the rosters of the PL teams, near 99% of the games will be mirrors and not 33%. at least thats what i think :S The problem with your logic is that teams must field at the very least 1 player of each race in the first 4 sets. Once you fulfill the requirement of having 1 player of each race, you have one more slot to add a player, as well as a possible fifth slot if the match goes to ace. If coaches were indifferent whom to fill up their lineups slots with (Protoss, Terran or Zerg players) AND all maps gave roughly the same winrate across all matchups, you could expect to see 33% mirror matchups. If, given the relative power of the races and the map pool, coaches tend to favor some races more than others (if you noticed, there were significantly more ZvZ and TvT mirrors than PvP) and/or tend to favor some races for some maps, then you can expect a higher than 33% mirror matchup rate. And to the people who say there are 6 matchups and therefore mirror matchup rate should be 50%: You fail. The error of your ways is this: Yes, there are 6 matchups. However, some matchups are more likely to happen than others: Take, for example, the ZvZ matchup. In order for it to occur, Player 1 must choose zerg (33% chance) AND Player 2 must choose zerg (33% chance). This gives you an 11% chance of a ZvZ matchup assuming races are chosen randomly. Now, take PvT. In order for it to occur, Player 1 must choose protoss (33% chance) AND Player 2 must choose terran (33% chance), OR Player 1 must choose terran (33% chance) AND Player 2 must choose protoss (33% chance). There's an 11% chance you'll get PvT, and another 11% chance you'll get TvP. If you count it as the same matchup, it adds up to 22% chance. Do this exercise for all 6 matchups and you'll get 33% chance of mirror and 66% chance of non-mirror. | ||
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FirstBorn
Romania3955 Posts
Thread should be closed imo. | ||
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Zato-1
Chile4253 Posts
On October 26 2009 21:38 FirstBorn wrote: All the fancy probability discussed in this thread isn't accurate because maps aren't prefectly balanced. As Hot_Bid already said, most teams will choose to send the race that does better on a certain map. Thread should be closed imo. Some of the fancy probability in this thread is accurate given some assumptions. Whether or not those assumptions are accurate or not will impact those probabilities. Refer to my post above for more details. | ||
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okum
France5778 Posts
On October 26 2009 21:38 FirstBorn wrote: Isn't that EXACTLY the problem the OP points at? If maps were perfectly balanced, we'd have 1/3 mirrors. We aren't having 1/3 mirrors, so it seems that the maps aren't perfectly balanced.All the fancy probability discussed in this thread isn't accurate because maps aren't prefectly balanced. As Hot_Bid already said, most teams will choose to send the race that does better on a certain map. | ||
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JohannesH
Finland1364 Posts
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Manit0u
Poland17255 Posts
On October 26 2009 22:10 okum wrote: Isn't that EXACTLY the problem the OP points at? If maps were perfectly balanced, we'd have 1/3 mirrors. We aren't having 1/3 mirrors, so it seems that the maps aren't perfectly balanced. Have PL maps EVER been perfectly balanced? This is the real question and the answer might be disappointing for some... | ||
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Kaniol
Poland5551 Posts
On October 26 2009 13:47 Wilko wrote: Shouldn't mirrors also be counted twice? Like: T1 vs T2 T2 vs T1 Z1 vs Z2 Z2 vs Z1 P1 vs P2 P2 vs P1 No. Statistically it's the same event. Player 1 picks T and Player 2 picks T. That's 1 event, not 2 events. But when we have tvz and zvt you have: 1. Player 1 picks T and Player 2 picks Z 2. Player 1 picks Z and player 2 picks T | ||
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ploy
United States416 Posts
HOW DOES ORDER MATTER WHEN YOU ARE OBSERVING A GAME? A ZvT is the same as a TvZ for the spectator. It is the same matchup, please explain the absurd logic in that when you are WATCHING a game, ZvT and TvZ are two different matchups? Fact: There are only six types of games you can watch: ZvT ZvP PvT ZvZ PvP TvT 3/6 or 50% mirrors. So you could expect to watch a mirror 50% of the time of a game selected at random. | ||
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QuakerOats
United States1024 Posts
On October 27 2009 10:21 ploy wrote: Talk about getting mobbed by a bunch of idiots. HOW DOES ORDER MATTER WHEN YOU ARE OBSERVING A GAME? A ZvT is the same as a TvZ for the spectator. It is the same matchup, please explain the absurd logic in that when you are WATCHING a game, ZvT and TvZ are two different matchups? Fact: There are only six types of games you can watch: ZvT ZvP PvT ZvZ PvP TvT 3/6 or 50% mirrors. So you could expect to watch a mirror 50% of the time of a game selected at random. Definitely trolling. But I'll bite anyway and show how dumb your argument is. Fact: There are only 3 outcomes if you flip two coins. 2 heads 1 heads 1 tails 2 tails Thus the chance of getting 2 heads is 33%. | ||
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Signet
United States1718 Posts
On October 27 2009 07:45 Kaniol wrote: No. Statistically it's the same event. Player 1 picks T and Player 2 picks T. That's 1 event, not 2 events. But when we have tvz and zvt you have: 1. Player 1 picks T and Player 2 picks Z 2. Player 1 picks Z and player 2 picks T Progamers don't pick races like that. Flash plays Terran and Terran only. Bisu plays Protoss and Protoss only. You're never going to have a situation where Flash picks Zerg and Bisu picks Terran, which would be different than Flash picking Terran while Bisu picks Zerg. Flash (T) vs Bisu (P) is the same thing as Bisu (P) vs Flash (T) | ||
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ploy
United States416 Posts
HH TT HT TH So the chance of getting 2 heads is 25%. However, the chance of getting HH or TT (which would represent any mirror matchup) is 50%. Please try again. | ||
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StRyKeR
United States1739 Posts
On October 27 2009 10:21 ploy wrote: Talk about getting mobbed by a bunch of idiots. HOW DOES ORDER MATTER WHEN YOU ARE OBSERVING A GAME? A ZvT is the same as a TvZ for the spectator. It is the same matchup, please explain the absurd logic in that when you are WATCHING a game, ZvT and TvZ are two different matchups? Fact: There are only six types of games you can watch: ZvT ZvP PvT ZvZ PvP TvT 3/6 or 50% mirrors. So you could expect to watch a mirror 50% of the time of a game selected at random. Agreed with QuakerOats. If this isn't a troll... Anyway, in case it isn't, you have to realize that if all those cases were equally likely, then yes, you could expect a mirror 50% of the time, but those cases aren't equally likely. Define a mirror as 1 head 1 tail. Then you can say you get a mirror "one-thirds of the time because there are only three possibilities HH, TT, HT". Yes, to the viewer, there's only three possibilities, 2 heads, 1 head and 1 tail, or 2 tails, but each case has a different probability of occurring. 1/4, 1/2, and 1/4 respectively. As you said, ZvT and TvZ are the same, right? So why should HT and TH be different? Both teams are "sending out" a player, H or T. If a "mirror" is one head, one tail, then your reasoning implies that there's a 1/3 chance of getting 1 H 1 T. Also, as noted by many others in this thread, given that one person has race X, if the map was balanced and the other team was indifferent as to which race it sent out, so each race has 33% chance of occurring, then clearly there's only one possible way to get a mirror, so the chance is 33%. | ||
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TheYango
United States47024 Posts
On October 27 2009 10:32 ploy wrote: First off you can't even get the scenario right. There are 4 outcomes if you flip two coins: HH TT HT TH So the chance of getting 2 heads is 25%. However, the chance of getting HH or TT (which would represent any mirror matchup) is 50%. Please try again. So by your logic, HT and TH are different scenarios but TvZ and ZvT are the same? On October 27 2009 10:31 Signet wrote: Progamers don't pick races like that. Flash plays Terran and Terran only. Bisu plays Protoss and Protoss only. You're never going to have a situation where Flash picks Zerg and Bisu picks Terran, which would be different than Flash picking Terran while Bisu picks Zerg. Flash (T) vs Bisu (P) is the same thing as Bisu (P) vs Flash (T) Progamers don't pick races, but COACHES DO. Lets say Coach Park has Bisu, Fantasy, and Hyuk. Coach January has Stork, Firebathero, and Great. Bisu v Great is different from Stork v Hyuk, but Fantasy v Firebathero is the same either way you slice it. The possible matches you get then are: Bisu v Great Bisu v Stork Bisu v Firebathero Fantasy v Great Fantasy v Stork Fantasy v Firebathero Hyuk v Great Hyuk v Stork Hyuk v Firebathero 33% of those matches are mirrors. | ||
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haster27
Taiwan809 Posts
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Signet
United States1718 Posts
On October 27 2009 10:34 TheYango wrote: Progamers don't pick races, but COACHES DO. Lets say Coach Park has Bisu, Fantasy, and Hyuk. Coach January has Stork, Firebathero, and Great. Bisu v Great is different from Stork v Hyuk, but Fantasy v Firebathero is the same either way you slice it. This I agree with. The coaches are drawing from a limited pool of players. It's selection without replacement. That's why I said (on another page) that the 1/3 probability is an asymptotic limit. If each team had an infinite number of P/T/Z players, the theoretical probability of a mirror match would be 1/3. Since they don't, there is a "defect" which we have to calculate based on the rosters. (also taking into account the players which the coach is actually willing to send out) It also amplifies the effect of even one map being imbalanced. For example, when Battle Royal was in the map pool, both teams would usually send out a Z on that map. That means all of the other maps are more likely to get a T or a P sent out, even if they are balanced, because the teams have each already sent a Z already. | ||
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timmeh
Austria177 Posts
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TheYango
United States47024 Posts
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. | ||
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Signet
United States1718 Posts
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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timmeh
Austria177 Posts
On October 27 2009 10:57 TheYango wrote: 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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StarBrift
Sweden1761 Posts
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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Gustav_Wind
United States646 Posts
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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BluzMan
Russian Federation4235 Posts
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StarBrift
Sweden1761 Posts
On October 26 2009 09:10 motbob wrote: 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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StarBrift
Sweden1761 Posts
On October 27 2009 21:28 Gustav_Wind wrote: 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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TheYango
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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Gustav_Wind
United States646 Posts
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. 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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JohannesH
Finland1364 Posts
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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Highways
Australia6103 Posts
It is : -33% Mirror -67% Non-Mirror It is basic probability. | ||
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timmeh
Austria177 Posts
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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okum
France5778 Posts
How about a simulation?
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maneatingshoe
Canada484 Posts
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Gustav_Wind
United States646 Posts
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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Trang
Australia324 Posts
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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kOre
Canada3642 Posts
On October 27 2009 22:25 okum wrote: This thread is making me lose faith in humanity. How about a simulation?
The easiest method to proving mirrors = 33% lol | ||
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Jumbalumba
Australia118 Posts
On October 27 2009 21:40 StarBrift wrote: 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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Fwmeh
1286 Posts
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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]343[
United States10328 Posts
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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siv00
261 Posts
You're playing WarCraft II Orcs and Humans, and playing as Humans. What are the odds of a mirror opponent? 1 in 2, or 50% What are the odds in StarCraft which has an extra race? Clearly not 50%. | ||
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diehilde
Germany1596 Posts
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okum
France5778 Posts
You are the coach of SKT T1, and it's near the end of the season. The last match of the season is between your team and eSTRO. Since your teams are currently tied for the last playoff spot, the outcome of this match is extremely important and every game is a matter of life and death. By Kespa rules, both teams are required to field one player of each race on the first three maps. You know you're going to play Bisu, fantasy and Hyuk. Bisu and fantasy have been doing equally well all around recently, so the big question mark is Hyuk. Hyuk is invincible in his mirror matchup with a 22-0 season record, but miserable against both other races, having lost all 18 games since the beginning of the season and showing no sign of improvement (the closest to a victory this year being a 5 pool that almost, but not quite, worked against Frozean's 14CC on Battle Royal). The eSTRO coach reveals to you that he has already picked his slots and won't change them. Aware of your dilemma and feeling sorry for your team's lackluster performance this season, he decides to give you what might be a small handicap: if you guess a map for the zerg, he will reveal the placement of one of his non-zerg players on the other two maps. You tentatively put Hyuk on map #1, which is Monty Hall. When you tell the other coach about this, he reveals that he will play his terran on map #2, Paradoxxx. Now, to maximize your chance of getting Hyuk a mirror match, should you stay with #1 or switch to #3? | ||
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QuakerOats
United States1024 Posts
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ZeaL.
United States5955 Posts
On October 28 2009 03:22 okum wrote: Let's consider a slightly modified problem. You are the coach of SKT T1, and it's near the end of the season. The last match of the season is between your team and eSTRO. Since your teams are currently tied for the last playoff spot, the outcome of this match is extremely important and every game is a matter of life and death. By Kespa rules, both teams are required to field one player of each race on the first three maps. You know you're going to play Bisu, fantasy and Hyuk. Bisu and fantasy have been doing equally well all around recently, so the big question mark is Hyuk. Hyuk is invincible in his mirror matchup with a 22-0 season record, but miserable against both other races, having lost all 18 games since the beginning of the season and showing no sign of improvement (the closest to a victory this year being a 5 pool that almost, but not quite, worked against Frozean's 14CC on Battle Royal). The eSTRO coach reveals to you that he has already picked his slots and won't change them. Aware of your dilemma and feeling sorry for your team's lackluster performance this season, he decides to give you what might be a small handicap: if you guess a map for the zerg, he will reveal the placement of one of his non-zerg players on the other two maps. You tentatively put Hyuk on map #1, which is Monty Hall. When you tell the other coach about this, he reveals that he will play his terran on map #2, Paradoxxx. Now, to maximize your chance of getting Hyuk a mirror match, should you stay with #1 or switch to #3? Far too much effort for an obscure joke lol. | ||
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okum
France5778 Posts
On October 28 2009 03:39 ZeaL. wrote: This is what the internet is all about.Far too much effort for an obscure joke lol. | ||
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TheYango
United States47024 Posts
On October 28 2009 03:22 okum wrote: Now, to maximize your chance of getting Hyuk a mirror match, should you stay with #1 or switch to #3? The real question is why you played Hyuk on Monty Hall in the first place, given it's anti-zerg statistics slant.  + Show Spoiler + Yes I get the reference. | ||
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Keniji
Netherlands2569 Posts
On October 28 2009 03:22 okum wrote: Let's consider a slightly modified problem. You are the coach of SKT T1, and it's near the end of the season. The last match of the season is between your team and eSTRO. Since your teams are currently tied for the last playoff spot, the outcome of this match is extremely important and every game is a matter of life and death. By Kespa rules, both teams are required to field one player of each race on the first three maps. You know you're going to play Bisu, fantasy and Hyuk. Bisu and fantasy have been doing equally well all around recently, so the big question mark is Hyuk. Hyuk is invincible in his mirror matchup with a 22-0 season record, but miserable against both other races, having lost all 18 games since the beginning of the season and showing no sign of improvement (the closest to a victory this year being a 5 pool that almost, but not quite, worked against Frozean's 14CC on Battle Royal). The eSTRO coach reveals to you that he has already picked his slots and won't change them. Aware of your dilemma and feeling sorry for your team's lackluster performance this season, he decides to give you what might be a small handicap: if you guess a map for the zerg, he will reveal the placement of one of his non-zerg players on the other two maps. You tentatively put Hyuk on map #1, which is Monty Hall. When you tell the other coach about this, he reveals that he will play his terran on map #2, Paradoxxx. Now, to maximize your chance of getting Hyuk a mirror match, should you stay with #1 or switch to #3? did you just put the monty hall problem(paradox - i love your second map choice) in a starcraft scenario? awesome! In school it would be much easier to understand it this way. | ||
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OpticalShot
Canada6330 Posts
STA101 The difference between 33% and 50%. Includes: 20 different examples for the same problem. | ||
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Drakonis
Canada97 Posts
Player A / Player B 1) T ---- vs---- T 2) T ----vs---- P 3) T ----vs---- Z 4) P ----vs---- T 5) P ----vs---- P 6) P ----vs---- Z 7) Z ----vs---- T 8) Z ----vs---- P 9) Z ----vs---- Z As you can see, there are 9 different matchup possibilities, 3 of which are mirrors. Therefore, 3/9 = 1/3 = 33.33333333333% chance of a mirror matchup. | ||
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Signet
United States1718 Posts
On October 28 2009 00:18 ]343[ wrote: 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 Nicely written, this is the right way to do the calculation of this real-world scenario. I think it still needs to account for the 1 player of each race rule. I would make each team a vector of [1 1 1] + [(Ti-1)/(Xi-3) (Pi-1)/(Xi-3) (Zi-1)/(Xi-3)] to represent the expected number of players of each race that that team will send out for its first 4 matches. Then do vector cross for teams i=1 and i=2. It would end up being exactly 1/3, like you said, if Ti=Pi=Zi and the 4th player is equally likely to be any race (ie, the races have the same skill distribution). | ||
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