Balance and Bonjwas: A Statistical Analysis - Page 2

On March 29 2012 13:39 Obelisco wrote:
On your statistics:
An observation I will make is that you only included 10 Protosses compared to 13/13 TZ, therefore you make T% a bit higher by reducing the amount of un favored matches he is playing by 2 and the P % a bit lower by reduing the favored matches he is playing by 2.
My opinion:
As I havent been followed BW for only recently (yes i regret), i think it is important that you consider the changes in playstyle over time. Pre-Savior, a lot terrans had an insane vZ record, and before Bisu, zerg was heavily favored against protoss. I think the switch in playstyle has balanced a little bit. Maybe Terran wasnt affected because there was not a heavily imbalanced matchup against them? ( I dont know)

On March 29 2012 13:27 Lightwip wrote:

16/20 is arbitrary, but an accurate simulation is a coding nightmare. At the same time, I don't see how 16/20 would differ too much in results from a standard probable starleague.

I think it's universally accepted that PvP and especially ZvZ can be coinflips.

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

On March 29 2012 13:47 Lightwip wrote:

1. That's the point. Protoss is actually less in most SL's, which further supports terran victory.
2. As an aggregate, changes in playstyles become irrelevant. Every innovation Bisu or Savior made is compensated for by another event, or just the general trend. It's similar to aggregate supplies in relation to inflation in macroeconomic theory.

On March 29 2012 14:27 Scarecrow wrote:
Essentially it's a really longwinded attempt to explain why bisu isn't a bonjwa

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:

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1. Specific Starleague Sample
Your 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 +

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 Statistics

A 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 Races

Another 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 Points

However, 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.

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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 =)

4. It would be neither viable nor useful to look at non-pro games. At any level other than pro, the balance is irrelevant because players simply aren't good enough. If you're not a pro, you pretty much lose only because the opponent played better. Balance is more significant at a higher level, in general (the same rule applies for chess, where white is imba).

On March 29 2012 15:07 archonOOid wrote:


Could you please develop this point a bit further as it seems quite compact. Especially the second and third sentences could use more thorough analysis.
Is the pros a homogeneous group and if not how is that taken into consideration,
To what degree does macro and strategy constitute the wins within and below the pro scene and
how is a good player defined?