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hahaha Lightwip
+ Show Spoiler +but props for putting in the effort to back up your theories. Now I'm gonna go read it
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On March 29 2012 14:56 Lightwip wrote:Show nested quote +On March 29 2012 14:37 Keone wrote:I am a statistics major, and Lightwip, your statistics are suspect and flawed. Though I somewhat agree with your topic, I don't think your reasoning is very sound. Here's a long-winded explanation of why: --------------------------------------- 1. Specific Starleague SampleYour stats are heavily based on your (13/13/10) race distribution of Terran/Zerg/Protoss. How about a different example, say Incruit OSL 2008? Their race distribution (T/Z/P) was (13/10/17). Here are the new numbers: Terran: 54.40*(10/35) + 47.44*(17/35) + 50*(12/35) = 55.73% Zerg: 54.67*(17/35) + 45.6*(13/35) + 50*(9/35) = 56.35% Protoss: 52.56*(13/35) + 45.33*(10/35) + 50*(16/35) = 55.33% Also, I have a question here: how did you get your numbers? Because with a true binomial distribution P(X >= 16), you shouldn't get those values. Not necessary in my argument, but I don't understand your math, you should go and check, I've included what they should be in spoiler below. + Show Spoiler +
Your values should be:
T: 0.007378994 (AKA .738%)
Z: 0.005479762 (AKA .548%)
P: 0.004825193 (AKA .483%)
Perhaps you forgot that you should not just do the binomial of P(X = 16), which I believe you did. For example, a StarLeague winner might have won all 20 of his matches. This doesn't have any effect on my argument, I'm just letting you know that you probably made a mistake here.
Anyway, the new probabilities for winning: T: 0.02202714 Z: 0.02505878 P: 0.02024176 Scaled & Sorted (Highest to Lowest): Zerg: 37.2%T: 32.7% P: 30.1% Well what do we have here. Zerg comes out on top by nearly 5%. Not as shocking as your 13% T>Z, but I just wanted to show you how the sample set you use affects your result. 2. Questionable Abuse of StatisticsA questionable part is your system of scaling your binomial distributed results. I believe is actually inappropriate given how .166%*13 + .118%*13 + .102%*13 = 5% of ANYONE winning an OSL lol. For your argument to be valid, this should equal 1. Scaling is dangerous: why? I understand your want of scaling, but it's like saying an ant has a 20% better chance of killing an elephant than a gnat, which is abusing statistics. For the statistical test to be sound, the total value must equal to 1; scaling to 1, especially from such a low percentage, is sketch and often leads to untrue answers. Of course, I don't know if that's the case here simply based off the stats, but one thing is for sure; it's not enough to base a conclusion on. To be honest, all this statistical stuff gives us is a completely different conclusion, and that conclusion would be: The winner of the starleague is likely the race that has a lot of its best matchup, and least of its worst matchup. ... No shit, right? Essentially I'm saying that your use of statistics here cannot be used to help your "Terran" argument. 3. Number in RacesAnother important point is the number of people playing a race. If we use your statistics (I don't know how to look up the real numbers): TvZ: 6549-5490 (54.40%) ZvP: 5162-4280 (54.67%) PvT: 4782-4317 (52.56%) Zerg has played the most matches (~12000 TvZs & ~9400 ZvPs = ~21400 games), with Terran in second, and Protoss in third (in non-mirror matches). This is obviously lacking due to the mirror matches... However, it is common knowledge in Korea that Zerg and Terran are the most popular races there. Do you see where I'm going? The conclusion we reached earlier was: The winner of the starleague is likely the race that has a lot of its best matchup, and least of its worst matchup. The point is that there are simply more Zerg and Terran players than there are Protoss players. This has a lot of ramifications. As before, your stats system shows that the winner of the SL is the race which has the most of its ideal matchup, and least of its worst matchup. Therefore, Terran starts out with an already obvious advantage: the lack of Protoss + the popularity of Zergs. This, I believe, is the real driving reason of why Terrans have been so dominant over SCBW's history. 4. Your Valid PointsHowever, this isn't a post just to trash your points. You made several good and valid points. Namely, TvT and mirror matchups. This is very true and a very good reason why elite Z & P players get knocked out so early due to a measure of luck. Jaedong was most definitely an exception in the most volatile of MUs; however, TvT seems to be a more stable mirror, perhaps simply due to the length of the games (thus allowing more skill to matter in the game). To this point, I don't have any real qualms, and I agree that it must play a big factor in the establishment of "Bonjwas". Coupled with the conclusion in Part 3, I can see how Terrans have become so dominant.----------------------------------------- I hope you'll view this post objectively and not subjectively. Thanks! I'll edit for mistakes later, but I think this pretty much shows why your statistics are misleading, yet it leads to reasoning that agrees with your general conclusion. If you could add this to your OP in spoiler tags, people can read both sides to the statistics part; but of course that's up to you =) Of course they aren't perfect. I made this in about 1-2 hours, so I could have made a mistake. 1. generally, P are not as highly represented throughout the SLs. Incruit is pretty much one of the few counter-examples. 2. A 1 - binomcdf(n,p,x). Actually I made a mistake here(16 instead of 15 for x), but that doesn't change the results much. T: 41.7% Z: 31.0% P: 27.3% That doesn't change my point, but thanks. I didn't put enough time into this to re-check my math. I understand I'm doing bad practice here, but it doesn't change the result. The alternative would be to run a few thousand samples, which would be hard given how much effort coding that would take. Also, while it is bad maths, it happens to be pretty consistent with actual titles. T>Z>>P. 3. All of these other factors are true in the pro-scene, and they are further meant to prove my point about bonjwas. Yet even before those, terran has a slight advantage.4. There's a pretty good spread of races played by pros. Z>T>P but they're all in the 300's, according to TLPD. 5. Your Incruit counterexample actually explains the random Z wins pretty well, actually. While a normal SL favors terran, a situation can heavily influence the statistics, suddenly favoring Z for that SL. However, that does not contradict the general trend.
^ That bolded part is what I'm saying isn't proven in your argument. But I could easily believe that.
And I think you've missed the point of my post. I'm not picking on your mistakes. I'm saying your approach is impossible because the simple fact that there are more Zergs & Terrans with fewer Toss makes Terran's situation always more favorable, so if Terran is indeed imba, you can't use those numbers because they have a big advantage already, so your statistical approach doesn't show anything imba about Terran, and instead proves that your argument does not prove imba-ness.
As for the titles; my entire argument is in support of that. Yet it's interesting, doesn't it? How did Zergs get so many titles/runner-ups despite the obvious lack of protoss? Another topic worth looking into... but that I won't look into lol.
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Man. I was reading your post, really getting into it... and then it was over 
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On March 29 2012 15:17 Keone wrote:Show nested quote +On March 29 2012 14:56 Lightwip wrote:On March 29 2012 14:37 Keone wrote:I am a statistics major, and Lightwip, your statistics are suspect and flawed. Though I somewhat agree with your topic, I don't think your reasoning is very sound. Here's a long-winded explanation of why: --------------------------------------- 1. Specific Starleague SampleYour stats are heavily based on your (13/13/10) race distribution of Terran/Zerg/Protoss. How about a different example, say Incruit OSL 2008? Their race distribution (T/Z/P) was (13/10/17). Here are the new numbers: Terran: 54.40*(10/35) + 47.44*(17/35) + 50*(12/35) = 55.73% Zerg: 54.67*(17/35) + 45.6*(13/35) + 50*(9/35) = 56.35% Protoss: 52.56*(13/35) + 45.33*(10/35) + 50*(16/35) = 55.33% Also, I have a question here: how did you get your numbers? Because with a true binomial distribution P(X >= 16), you shouldn't get those values. Not necessary in my argument, but I don't understand your math, you should go and check, I've included what they should be in spoiler below. + Show Spoiler +
Your values should be:
T: 0.007378994 (AKA .738%)
Z: 0.005479762 (AKA .548%)
P: 0.004825193 (AKA .483%)
Perhaps you forgot that you should not just do the binomial of P(X = 16), which I believe you did. For example, a StarLeague winner might have won all 20 of his matches. This doesn't have any effect on my argument, I'm just letting you know that you probably made a mistake here.
Anyway, the new probabilities for winning: T: 0.02202714 Z: 0.02505878 P: 0.02024176 Scaled & Sorted (Highest to Lowest): Zerg: 37.2%T: 32.7% P: 30.1% Well what do we have here. Zerg comes out on top by nearly 5%. Not as shocking as your 13% T>Z, but I just wanted to show you how the sample set you use affects your result. 2. Questionable Abuse of StatisticsA questionable part is your system of scaling your binomial distributed results. I believe is actually inappropriate given how .166%*13 + .118%*13 + .102%*13 = 5% of ANYONE winning an OSL lol. For your argument to be valid, this should equal 1. Scaling is dangerous: why? I understand your want of scaling, but it's like saying an ant has a 20% better chance of killing an elephant than a gnat, which is abusing statistics. For the statistical test to be sound, the total value must equal to 1; scaling to 1, especially from such a low percentage, is sketch and often leads to untrue answers. Of course, I don't know if that's the case here simply based off the stats, but one thing is for sure; it's not enough to base a conclusion on. To be honest, all this statistical stuff gives us is a completely different conclusion, and that conclusion would be: The winner of the starleague is likely the race that has a lot of its best matchup, and least of its worst matchup. ... No shit, right? Essentially I'm saying that your use of statistics here cannot be used to help your "Terran" argument. 3. Number in RacesAnother important point is the number of people playing a race. If we use your statistics (I don't know how to look up the real numbers): TvZ: 6549-5490 (54.40%) ZvP: 5162-4280 (54.67%) PvT: 4782-4317 (52.56%) Zerg has played the most matches (~12000 TvZs & ~9400 ZvPs = ~21400 games), with Terran in second, and Protoss in third (in non-mirror matches). This is obviously lacking due to the mirror matches... However, it is common knowledge in Korea that Zerg and Terran are the most popular races there. Do you see where I'm going? The conclusion we reached earlier was: The winner of the starleague is likely the race that has a lot of its best matchup, and least of its worst matchup. The point is that there are simply more Zerg and Terran players than there are Protoss players. This has a lot of ramifications. As before, your stats system shows that the winner of the SL is the race which has the most of its ideal matchup, and least of its worst matchup. Therefore, Terran starts out with an already obvious advantage: the lack of Protoss + the popularity of Zergs. This, I believe, is the real driving reason of why Terrans have been so dominant over SCBW's history. 4. Your Valid PointsHowever, this isn't a post just to trash your points. You made several good and valid points. Namely, TvT and mirror matchups. This is very true and a very good reason why elite Z & P players get knocked out so early due to a measure of luck. Jaedong was most definitely an exception in the most volatile of MUs; however, TvT seems to be a more stable mirror, perhaps simply due to the length of the games (thus allowing more skill to matter in the game). To this point, I don't have any real qualms, and I agree that it must play a big factor in the establishment of "Bonjwas". Coupled with the conclusion in Part 3, I can see how Terrans have become so dominant.----------------------------------------- I hope you'll view this post objectively and not subjectively. Thanks! I'll edit for mistakes later, but I think this pretty much shows why your statistics are misleading, yet it leads to reasoning that agrees with your general conclusion. If you could add this to your OP in spoiler tags, people can read both sides to the statistics part; but of course that's up to you =) Of course they aren't perfect. I made this in about 1-2 hours, so I could have made a mistake. 1. generally, P are not as highly represented throughout the SLs. Incruit is pretty much one of the few counter-examples. 2. A 1 - binomcdf(n,p,x). Actually I made a mistake here(16 instead of 15 for x), but that doesn't change the results much. T: 41.7% Z: 31.0% P: 27.3% That doesn't change my point, but thanks. I didn't put enough time into this to re-check my math. I understand I'm doing bad practice here, but it doesn't change the result. The alternative would be to run a few thousand samples, which would be hard given how much effort coding that would take. Also, while it is bad maths, it happens to be pretty consistent with actual titles. T>Z>>P. 3. All of these other factors are true in the pro-scene, and they are further meant to prove my point about bonjwas. Yet even before those, terran has a slight advantage.4. There's a pretty good spread of races played by pros. Z>T>P but they're all in the 300's, according to TLPD. 5. Your Incruit counterexample actually explains the random Z wins pretty well, actually. While a normal SL favors terran, a situation can heavily influence the statistics, suddenly favoring Z for that SL. However, that does not contradict the general trend. ^ That bolded part is what I'm saying isn't proven in your argument. But I could easily believe that. And I think you've missed the point of my post. I'm not picking on your mistakes. I'm saying your approach is impossible because the simple fact that there are more Zergs & Terrans with fewer Toss makes Terran's situation always more favorable, so if Terran is indeed imba, you can't use those numbers because they have a big advantage already, so your statistical approach doesn't show anything imba about Terran, and instead proves that your argument does not prove imba-ness.
I think the parameters themselves are proof of it, really. ~1% isn't large, but I'd say it's pretty statistically significant. In a fairly weighted contest, the hypothetical terran is the best.
But, to be fair, by not all that much. The slight imbalance really adds up with the circumstances of SL's and the mirror to make more bonjwas.
As for runner-ups: meh. Too many runner-ups are fluke players. There are very few fluke wins, and I'd say July is the only really important one. There's more than one fluke runner-up.
I haven't seen any reason to believe that less P in the scene total has any measurable effect on their performance. It's mostly that they have a harder time qualifying.
The P-less situation is simply further in T's favor. It alone doesn't make T the best.
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I haven't thought this through very deeply, but I'm afraid it might be a bit difficult to attribute small differences to game balance, as external factors may provide a similar result. General player population (more terran players than protoss players), for example, can cause the difference in winrates I'd think. Elimination type tournaments can cause some distortions as well (I think that has traditionally been the format?).
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Seems like we need a better proof of the most statistically likely breakdown of a SL's participation numbers by race given its importance to the other results. A simple average of the SL's to date maybe?
It might also be interesting to see the correlation between terran players' proficiency in other matchups and their win-rate in TvT.
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On March 29 2012 13:49 Mortality wrote:
2) As has been pointed out numerous times, winning a boX is not the same as bo1 records.
If player A wins against player B 2/3 of the time, then the chance that player A wins a bo3 against player B is 74%. Much, much higher.
How'd you calculate that? If A has 2/3 win ratio vs B, doesn't A have a 89% chance (8/9) to win a bo3? (This would be either 2-0 or 2-1, it doesn't change the odds)
Chance of B to win is 1/3, and B has to win 2 games to win the bo3, so (1/3)^2 is 1/9.
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On March 29 2012 15:44 Demonhunter04 wrote:Show nested quote +On March 29 2012 13:49 Mortality wrote:
2) As has been pointed out numerous times, winning a boX is not the same as bo1 records.
If player A wins against player B 2/3 of the time, then the chance that player A wins a bo3 against player B is 74%. Much, much higher.
How'd you calculate that? If A has 2/3 win ratio vs B, doesn't A have a 89% chance (8/9) to win a bo3? (This would be either 2-0 or 2-1, it doesn't change the odds) Chance of B to win is 1/3, and B has to win 2 games to win the bo3, so (1/3)^2 is 1/9.
Mortality is right. It's a binomial distribution scenario.
Given 2/3 winrate, you have a 74.1% chance of not getting less than 2 wins.
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On March 29 2012 15:44 Demonhunter04 wrote:Show nested quote +On March 29 2012 13:49 Mortality wrote:
2) As has been pointed out numerous times, winning a boX is not the same as bo1 records.
If player A wins against player B 2/3 of the time, then the chance that player A wins a bo3 against player B is 74%. Much, much higher.
How'd you calculate that? If A has 2/3 win ratio vs B, doesn't A have a 89% chance (8/9) to win a bo3? (This would be either 2-0 or 2-1, it doesn't change the odds) Chance of B to win is 1/3, and B has to win 2 games to win the bo3, so (1/3)^2 is 1/9.
But B can win 2-0 or 2-1, so B's chance is > 1/9
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Your mirror matchup explanation for why there are more terran bonjwas than zerg/protoss bonjwas is legitimate for Jaedong, but not Bisu. Whereas Jaedong would have at least 2 more OSL/MSL wins if ZvZ were skill based like TvT, almost all of Bisu's eliminations were at the hands non protoss. Ever since Bisu came to prominence in 2007 he has been eliminated by a protoss only 5 times. 3 of those times were by Stork, a comparably talented player. Thus, only twice has Bisu been eliminated by inferior players due to bad luck, and that's assuming he actually was unlucky and not just having a bad day.
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Very interesting post, i had never thought of that. Even tho i don't trust those statistics too much, you do raise a good point : in mirror matchups, the best player comes out on top more often in TvT than ZvZ or PvP, which " filters " the lesser players. While a good Zerg or Protoss player will can more easily drop games to a lesser player, the better player is more likely to win the game in a terran mirror. This theory can be applied to everyone, not only the very best players of each race.
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hooray, another opportunity for me to link to this
:<
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tanks man. seriously if you think about it, the tank is arguably what makes the terran so menacing and impenetrable. yeah sure dark swarm is really OP too! But it is much more difficult to use, it is tech 3 and it is a spellcaster with no auto attack.
every unit in this game is vital, but anyone who has played BW fears the tank. whether you are P, T or Z.
The tank is holy fking sweet by itself, but in the hands of someone like Flash, you will surely shed much blood or blue goo trying to kill one. He will complement the weakness of the mighty tank with a defense of vultures, mines and goliaths. He will have them on high ground, he will kite, he will never leave a tank out of supporting range of other tanks. The tank puts pressure on the enemy and forces you to kill it or lose your expo. But you better have a beautiful counter ready to get past the bunker and minefield that awaits you ahead.
come on you know u guys all have nightmares of getting terran steeled by flash. scariest army in the game..and it aint cuz of the goliaths.
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United Kingdom1666 Posts
On March 29 2012 13:28 1004 wrote:
honestly
if you had time to think hard about this and to write up this entire post
you have too much time on your hands...
go read a book
kiss a girl
play starcraft
SOMETHING other than just trying to do math to say terran is imbalanced.
"you shouldn't tell me what to do"
okay, then heed them as suggestions... but seriously, you clearly stated that it is completely irrelevant outside of the pro scene. not one person on these forums is a pro, therefore you merely just told everyone a cool story bro.
User was warned for this post
It's called a theory, and discussion, which is interesting to many people. Don't see any value in intelligent thinking+discussion? You won't make it very far in life.
OP- I'm not educated enough in statistics etc to have any meaningful input on your methods, but the responses of others will interest me.
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Keone did an excellent job describing a few of the fallacies of the statistics (that are nonetheless interesting and somewhat fair, I'm shocked Lightwip, shocked).
The one thing I think you are missing though is map balance. The thing is BW is a horribly unbalanced game at its core to take a clear example from the release:
Blood Bath
Essentially any of the original blizzard maps would result in horrible imbalances and 90+% win rates at the pro level. Just going back a few years and using maps that haven't been made in response to new strategies such as enabling Forge expand, an easily blockable choke, or bad mineral placement for muta harass would completely throw the current balance in tatters.
So What is essentially happening is that map makers are trying to use map features to correct the slight imbalances that exist, sometimes successfully; Fighting Spirit and sometimes unsuccessfully; Central Plains
Any map can be constructed to be favourable for any race and I think any imbalances can be discovered there.
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On March 29 2012 12:18 1a2a3aPro wrote:
Finally, how much skew is there, really? Winning 16 in a row is ridiculous, and is not a fair judge of a players ability. A player with 70% across all matchups would not only be S class, they would be as good as Flash. This means a player can do WWLWWLWWLW, repeat, for their entire career, and always win Bo3s and have a great win rate in proleague. Why is it necessary to have such ridiculous streaks? I feel that you have some selection bias here, you are selecting a statistic that will of course heavily favour Terran, due to the volatility of PvP and ZvZ maches.
Sorry, but from mathematical point of view, if you have winning chance 70%, it is extremely likely (if you play enough games) that you will have a long winning streak (and pretty short lose streak). I am too lazy to calculate it now  .
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Why do you use dropships to get to that cliff when there is a ramp next by?
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I like the part about the mirror matches.
Begone, Terran!
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On March 29 2012 18:15 zlosynus wrote:Show nested quote +On March 29 2012 12:18 1a2a3aPro wrote:
Finally, how much skew is there, really? Winning 16 in a row is ridiculous, and is not a fair judge of a players ability. A player with 70% across all matchups would not only be S class, they would be as good as Flash. This means a player can do WWLWWLWWLW, repeat, for their entire career, and always win Bo3s and have a great win rate in proleague. Why is it necessary to have such ridiculous streaks? I feel that you have some selection bias here, you are selecting a statistic that will of course heavily favour Terran, due to the volatility of PvP and ZvZ maches.
Sorry, but from mathematical point of view, if you have winning chance 70%, it is extremely likely (if you play enough games) that you will have a long winning streak (and pretty short lose streak). I am too lazy to calculate it now .
Even with 70% winning chance, longer streaks with no loss are not too likely. The probability to win two games in a row is just 50%, to win three games in a row is roughly 1/3. With 50% winning chance it's only 1/8, so 70% winning ratio gives you longer streaks but they are still probably not too long.
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On March 29 2012 13:56 Lightwip wrote:Show nested quote +On March 29 2012 13:49 Mortality wrote:So much of this was already talked about in the other thread and largely ignored it seems. 1) Individual league performance post-Savior does not support this. Even with Flash at the helm, Terran is behind Zerg. 2) As has been pointed out numerous times, winning a boX is not the same as bo1 records. If player A wins against player B 2/3 of the time, then the chance that player A wins a bo3 against player B is 74%. Much, much higher. 3) Historical X-factors cannot be ignored. Pre-Boxer, Terran sucked. Post Boxer, many players were converted to Terran including the random player NaDa and the Zerg player Oov. Maybe they wouldn't have been as dominant with other races, but there's no denying the impact these players had on Terran and on Starcraft and its development. A player doesn't just produce a win rate... he influences other players! 4) If you browse this forum, a long time ago someone made a thread explaining why Z > P being the least balanced match up indicates Terran dominance. See here: http://www.teamliquid.net/forum/viewmessage.php?topic_id=61932 1. Not by much. Post-Savior could honestly be considered an arbitrary cutoff point to justify cherry-picking, because it's not like there weren't other significant innovations in terran's favor as well throughout BW history. 2. True, but why is this relevant? It just stacks terran's advantage even more. 3. Pre-Boxer was pretty much pre-1.08. Terran was aided quite a bit by 1.08. Over time, Boxer's influence becomes less relevant. 4. Implicitly, my post addressed this issue. It further aids bonjwa-creation.
1. Certainly Savior is far from the only innovator. Nevertheless, this change towards Zerg favor can't really be ignored. I'd be more interested in the stats of "who eliminates who" in post-Savior era Starcraft.
2. Because your methodology assumes that the chance player A beats player B is always the average and does not take into account the confidence of victory a higher tier player (say top 5) has against a lower tier player (say below top 30). Moreover, the number of games played will skew towards the higher tier players. So what really matters is which race has the most higher tier players which is not exactly the same issue as racial balance as it is a much smaller sample and is influenced by the X-factors in (3).
3. How can the fact that so many players who went on to do great things switching to Terran be irrelevant in this discussion? NaDa was already a top player on ladders as random. Just by taking NaDa out of the equation alone you don't just lose a player with 6 trophies for Terran -- you lose EVERY INNOVATION that he made!!!! Of course eventually someone would figure out those innovations, but it could have been years! Meanwhile, even if you assume he wouldn't be as good with either Zerg or Protoss, and even if you assume that the reason why he wouldn't be as good is due purely to racial balance, it's hard to imagine that he wouldn't earn some significant accomplishments and push the metagame no matter which race he played. And he who controls the metagame controls the tournaments.
4. Although it does aid in Bonjwa creation, the point is that it's not actually Terran imbalance that produces this result, but actually Zerg imbalance against Protoss! This would also lend itself to explaining why Zerg is now the dominant race in Starleague since ZvP results were much worse pre-Bisu than they are now.
Conclusion: You're inferring too much from too little. The Terran Empire was built on the backs of giants and I don't think that can be ignored.
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EPT
