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T v Z &P Relative Advantage Comparisons between NA

Forum Index > SC2 General
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travy
Profile Joined April 2010
United States14 Posts
August 18 2010 17:28 GMT
#1
TLDR Summary :

Terran’s relative racial advantage of being placed in the top 50 and top 100 on the ladders in Korea and the US is 1.6-1.9 times (or 60%-90%) greater than what be expected given race choice base rate differences in diamond ladders. This suggests that for some reason, regardless of differences in regional race preference, Terran is just shy of being twice as likely as the average of zerg and protoss to be in the top 50 or top 100.

However, and more interestingly, zerg and tosses representation in the top 50 and 100 differ CONSIDERABLY based on whether or not you look at Korea or NA ladders. In fact, they more than reverse their statistics. Whereas toss in NA is right around what would be expected in both top 50 and top 100. Zerg has a major relative disadvantage in NA, being around 40-50% less likely to be placed in the top 50/100 when compared to Korea where zerg has a 60-70% advantage of being placed in the top 50 or 100 controlling for how many people play each race. This is pretty interesting given that Korea plays zerg the least of any of the major regions. Toss’s disadvantage in korea (.57), is almost as great as zerg’s disadvantage in NA (.44).

Read long post below for more details, caveats, limitations, and practical implications.

Original Post:
Below is an analysis that I did using relative risk ratios to account for the fact that 1.) different numbers of people play different races, 2.) that different numbers of races are represented differently in different countries, and finally 3.) that different numbers of races are differentially represented in the top 50 and top 100 by region. I did this because a recent post by a blizzard employee addressed that there are balance differences across regions and should be considered in discussions of who or who is not OP/IMBA. Another poster posted a different analysis that was also interesting (http://www.teamliquid.net/forum/viewmessage.php?topic_id=144694), but didn’t really get at what I was curious about, and is confounded by the fact that win % is screwy because blizzard tries to force your win% to 50%. There are several decent posts on that thread btw, so check it out. I used a simple statistical procedure called relative risk analysis.

The procedure I used is modified slightly from most text book explanations to accommodate the question that I had. It is very simple and explained below. I have included a summary (above) for people that feel this is TLDR. For people that are interested, want to argue, correct me, or replicate after patches etc., I have explained why I used relative risk and how I used this statistic.

What is Relative Risk?
Relative Risk is a statistic that is used in psychology and medical science to identify risk (e.g. smokers are 20 times as likely as non smokers to develop cancer), disproportionate representation (e.g. African Americans are twice as likely to be identified as having an emotional disturbance in the pre-school public education system as their white counterparts), or athletic advantage (e.g. players are 1.5 times as likely to win against a particular team on their home field when compared to away games).

What is my question?
I was interested to see, controlling for differences in representation by region, what is the statistical likelihood that a given race would be represented in the top 50 and top 100 players in North America and Korea. Specifically, I hypothesized that Terran would be overrepresented in the top 50 and top 100, controlling for the differences in base rates of diamond play (i.e. controlling for the fact that terran/toss are overrepresented and zerg is underrepresented), and that zerg would be underrepresented in diamond controlling for the fact that not many people play zerg. I thought that these would be consistent across regions. Data suggests that I was right about the first hyp, and wrong about the second .

Method & Results:
I calculated relative risk (hereafter called relative advantage) of diamond level players being represented in the top 100 and top 50, controlling for differences in the race representation of all diamond players. This allows me to answer the question “How each race does, controlling for the fact that some races (e.g. terran & protoss) will be overrepresented by the diamond base rate, affect probability of being represented in the top 100 and 50 players on the ladder”. I chose diamond as my base rate because diamond suggests there is at least some skill or knowledge of competitive play. I used the web page http://rts-sanctuary.com/ to get data.

To calculate a relative advantage I first find the percent of players playing a particular race in the diamond level within a region. So for example, a few days ago (when I did these analyses)in NA it is ~34% toss, 29%terran, and ~23% zerg. I’ll call this base rate. I then divide the diamond top 50&100 percentage by this base rate (so top50%/baserate%). In NA, the top 50 representation is ~36% toss,~48 terran, and 14%~zerg.

I can then calculate a ratio that will tell me whether or not a race is over or underrepresented in the top 50&100, based on what would be expected given their base rate. A value of 1 using this statistic tells me that the race is represented as would be expected given the races diamond level base rates. For example, in NA if I divide the top 50 zerg % (which was %14 when I did this) by the base rate of 23%, I get the number .6, which suggests that zerg is 40% less likely (or .4 times as likely) to be represented in the top 50 than what would be expected given their overall Diamond representation. Terran’s value of 1.6 suggests that this race is 1.6 times as likely (or 60% more likely) to be placed in the top 50 given their overall representation in diamond. (toss’s value of 1 indicates they are represented around what would be expected).

Finally, I can get a relative advantage statistic by dividing a target race by the comparison races. If I divide terran’s relative representation statistic by the AVERAGE zerg and toss statistic, I can get the relative advantage statistic I’m interested in. In NA, this value is 1.9, which suggests that compared to toss’ and zerg’s base rate, terran is almost twice as likely to be represented in the top 50 players. You could reverse this and put terran and protoss’ average in the denominator and zerg in the numerator and get the relative disadvantage for zerg, which would be .44.

I can do the same thing in Korea too. In Korea, terran’s relative advantage statistic is lower, but around the same magnitude—1.5. HOWEVER, if you look at zerg and toss you find something interesting: their relative representation statistic are practically reversed, with toss at around 50% less likely to be represented in the top 50, and zerg 60% MORE likely to be represented in the top 50. In fact, zergs relative advantage statistic is 1.7, which suggests they are 1.7 times as likely to be represented in top 50 controlling for base rates, than the average of Terran and protoss in Korea.

Despite these results being pretty interesting, I was worried that they may have been due to the fact that top 50 provides too small of a sample size to get stable estimates, so I re-did this in the top 100, which should provide more stable estimates. To do this my denominator will stay the same in the relative representation statistic, but my numerator will change to include the next 50 people. Top 100 race percentages in NA are .31, .45, and .22 for toss, terran, zerg. In korea they are .29, .42, and .27 for toss, terran, zerg. Doing the same statistics as above, a similar trend holds. Terran holds a slight advantage in both countries, whereas in NA (1.6X)this advantage is larger than in korea (1.3X). As in the top 50, zerg and toss’s representation is drastically different (and therefore their relative advantage/disadvantage statistic differ also), when comparing NA (.77) to Korea (1.25).

Limitations:

I’m unaware how accurate RTS sanctuary’s data is compared to what Blizzard has in their data base.
While these statistics are useful for examining representation, they do not provide the ability to make accurate causal inferences. I also didn’t calculate confidence intervals or p values, so generalizability is weakened. Granted these estimates will change frequently. We can simply say that, on average, across America and Korea, Terran is overrepresented in the top 100. We can also say that the relative advantage or disadvantage of zerg and protoss depends on the region that you are from, with NA’s placing relatively more toss in the top 50/100 and Korea placing a shockingly high amount of zerg in the top 50/100.

It is noteworthy that this is even more shocking given that Korea has the LOWEST base rate of diamond zerg players in all of the major regions (only bested by LA). The reason why these statistics are the way they are will be left to speculation/opinion/or anecdotal observation unless blizzard allows us to data mine other statistics, as there is no hard and fast way to “prove” why this is. Some reasons are probably more plausible than others, but I am prefer not to make these implications.


Practical Implications for NA Ladderers:
If you are a pragmatist and do not necessarily care why these statistics are the way they are, yet want practical implications for laddering, here are some:

1.) Play terran instead of the race you are playing

2.) If you are a zerg and do not want to play terran, watch Korean replays instead of American replays

3.) You will probably be better off watching Korean replays regardless of the race you play .
travy
Profile Joined April 2010
United States14 Posts
August 18 2010 17:41 GMT
#2
Title was supposed to be T v Z &P Relative Advantage Comparisons between NA and Korean Ladders

TLOBrian
Profile Blog Joined March 2010
United States453 Posts
August 18 2010 17:50 GMT
#3
On August 19 2010 02:41 travy wrote:
Title was supposed to be T v Z &P Relative Advantage Comparisons between NA and Korean Ladders



Wouldn't it be better to just be comparisons between countries?

An interesting read OP, I still don't think that it has anything to do with balance per say, but It does reinforce the fact that overall zerg is not played that much.
Steven Bonnell II is the friggin man.
jp_zer0
Profile Joined July 2010
Canada48 Posts
August 18 2010 17:52 GMT
#4
You haven't explained how the ladder's top 100 is relevant.
tacrats
Profile Joined July 2010
476 Posts
August 18 2010 17:55 GMT
#5
I think the style difference is greater for terran between the regions. Zerg seems pretty similar to me.
Toadily
Profile Blog Joined April 2010
United States837 Posts
August 18 2010 18:13 GMT
#6
If I had to guess the reason why theres way more zergs in the top 50/100 as compared to the abysmal small number of zergs in the entire diamond league in Korea would be that those are the good/pro zerg players who stuck with it since BW/Phase 1 beta. So regardless of whether there is race imbalance or not they would have no trouble placing high on the ladder. While the rest of the ok/mediocre/bad zerg has way more trouble and is either doing badly or switched to another race.
travy
Profile Joined April 2010
United States14 Posts
August 18 2010 18:26 GMT
#7
On August 19 2010 02:52 jp_zer0 wrote:
You haven't explained how the ladder's top 100 is relevant.



jp_zer0, brings up a good point questioning the validity of the top 50 and 100 as a measure of performance. Building the case for the validity of this would be more discussion based than data based. Would be interesting to do some correlations between ladder rank and tournament success, though.

rai
Profile Joined August 2010
United States2 Posts
August 18 2010 18:31 GMT
#8
So in a nutshell, Korea is better at zerg than us noob americans. Anyone know any good Korean replay sites?
TurpinOS
Profile Joined February 2010
Canada1223 Posts
August 18 2010 18:35 GMT
#9
Again, a well thought out paragraph that actually just end up proving absolutely nothing because of the value of the top 50-100, the way matchmaking works and the fact that a whole lot of other factors need to be considered.
http://eve.znaor.hr/pimpmydomi/
travy
Profile Joined April 2010
United States14 Posts
Last Edited: 2010-08-18 18:46:42
August 18 2010 18:46 GMT
#10
On August 19 2010 03:35 TurpinOS wrote:
Again, a well thought out paragraph that actually just end up proving absolutely nothing because of the value of the top 50-100, the way matchmaking works and the fact that a whole lot of other factors need to be considered.



Friend, there is very little in this life that you can provide a proof for-- data suggest, they don't prove. Top 50/100 is far from a an adequate measure of performance, but it is interesting to consider these differences.
GagnarTheUnruly
Profile Joined July 2010
United States655 Posts
August 18 2010 22:43 GMT
#11
I think it's interesting that as race statistics are springing up on TL.net, signs are pointing towards things being very even everywhere but the very apex of player abilities. It makes me wonder what's going on in the top 100 or so.
Jermstuddog
Profile Blog Joined June 2010
United States2231 Posts
August 18 2010 22:52 GMT
#12
I would say top 100 in each country is a fair number to look at for balance.

You are pulling all the pros, even if they're screwing around and not playing their perfect tourney game.

You are pulling the top amateurs, all those people who might go pro, but for some reason don't. They definitely know the game, but maybe their play just isn't quite refined enough or have RL issues holding them back.

Nothing wrong with top 100 IMO.
As it turns out, marines don't actually cost any money -Jinro
rai
Profile Joined August 2010
United States2 Posts
August 18 2010 23:34 GMT
#13
At the very least this information shows that Terran is less difficult to play because successful Zerg players are rarer. I'm sure everyone already knew that though.
MamiyaOtaru
Profile Blog Joined September 2008
United States1687 Posts
August 18 2010 23:39 GMT
#14
On August 19 2010 07:43 GagnarTheUnruly wrote:
I think it's interesting that as race statistics are springing up on TL.net, signs are pointing towards things being very even everywhere but the very apex of player abilities. It makes me wonder what's going on in the top 100 or so.
What's going on in the top 100 is automatic match making can't place people any higher. Everyone below that gets matched up with who they need to be matched up with to maintain ~50% win ratio, even if it means playing people of lesser skill in an OP race (or people of grater skill in a UP race). At the top, there is nowhere higher to go, so that is the only place you are going to see win ratios that don't make things appear even.
travy
Profile Joined April 2010
United States14 Posts
August 19 2010 01:19 GMT
#15
On August 19 2010 08:39 MamiyaOtaru wrote:
Show nested quote +
On August 19 2010 07:43 GagnarTheUnruly wrote:
I think it's interesting that as race statistics are springing up on TL.net, signs are pointing towards things being very even everywhere but the very apex of player abilities. It makes me wonder what's going on in the top 100 or so.
What's going on in the top 100 is automatic match making can't place people any higher. Everyone below that gets matched up with who they need to be matched up with to maintain ~50% win ratio, even if it means playing people of lesser skill in an OP race (or people of grater skill in a UP race). At the top, there is nowhere higher to go, so that is the only place you are going to see win ratios that don't make things appear even.



Would be interested to see how represented the top pro's or competitive players are in the top 50/100. Would lend more credibility imo.
Mantikor
Profile Joined August 2010
United States68 Posts
Last Edited: 2010-08-19 01:33:21
August 19 2010 01:31 GMT
#16
On August 19 2010 03:26 travy wrote:
Show nested quote +
On August 19 2010 02:52 jp_zer0 wrote:
You haven't explained how the ladder's top 100 is relevant.



jp_zer0, brings up a good point questioning the validity of the top 50 and 100 as a measure of performance. Building the case for the validity of this would be more discussion based than data based. Would be interesting to do some correlations between ladder rank and tournament success, though.


I always find it amusing when people just jump to questioning the relevence of stats. I might be on a limb here... but, you guys play terran right? If these stats were reversed and showed terran as underplayed or even, completely balanced, the replies from you guys would praising these numbers.

Fact is, doesnt matter what stats you pull, everywhere you look, its the same. blizz top 200, these stats, gosugamers top50, hell.. look at tournaments. Even the intel tourney has 50% terrans. Dare i mention... percentage of forum threads, rofl.
wat
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