[Tom]

I messed up your example in an attempt to explain why it misses the point (unsuccessfully as it turns out).

I understand exactly what you're saying, but its not the point I am making. Its correct that you don't draw an inference about why a team lost after 1 game. You try as hard as you can to isolate the variable (or variables) to determine what effect they have on the outcome. Think about something as complicated as the health impacts of smoking. Some people smoke their whole life and nothing happens, whilst others appear to develop all sorts of problems. We cannot tell exactly what effect smoking will have on any particular person, because a range of genetic and lifestyle factors also significantly affect the result. But, after looking at millions of smokers, we can confidently state that, generally speaking, smoking is bad for you.

This is why, in looking at Starcraft, you should look at the results of thousands or millions of games, played on a range of maps, at a range of skill levels. If players using one race consistently underperform across these variables, it is fair to draw an inference that race is having some effect on the outcome (even though it would be difficult to use race to predict the outcome in any single case).

I am not going to waste any more time trying to explain it.

*************************

For the same reason that the GMs in this thread refuse to debate balance/gameplay with silver league players, I am no longer going to debate statistics/scientific method with anyone who does not hold (at least) an undergraduate degree in mathematics, engineering or science. Sorry to sound like a douche, but its just not worth the aggravation.

Whilst I am happy to debate genuine methodological flaws, I am getting tired of justifying basic principles of science/statistics over and over. Please read the OP!

[KaiserK]

Re: nGenLight's Rep comment (I don't know how to reply directly to this). I apologise, I admit that my "hate of balance complaints" comment may have been a bit aggressive... but I do intensely dislike statements such as "Unit X is imbalanced" or "Matchup XvY is imbalanced", because such statements are not productive particularly when the game is a year young and the statement to me reflects an unwillingness to figure out a way to beat X unit or X race. Still, I'm a bit hurt that I get a negative rep comment just for stating what I think... just because I dislike balance complaints (note I did not say I dislike the discussion) I can't participate?

Originally Posted by Tom

For the same reason that the GMs in this thread refuse to debate balance/gameplay with silver league players, I am no longer going to debate statistics/scientific method with anyone who does not hold (at least) an undergraduate degree in mathematics, engineering or science. Sorry to sound like a douche, but its just not worth the aggravation.

Whilst I am happy to debate genuine methodological flaws, I am getting tired of justifying basic principles of science/statistics over and over. Please read the OP!

Tom, I read your OP properly this time. I've missed most of the thread cuz I'm late to the party, and it's difficult to understand what alot of people are saying due to misunderstandings about logic and statistics. I see that some of what I said had already been brought up. Now I will state that I have an honours in physics and although my knowledge of statistical methods is limited I understand your basic premise.

Now if I understand correclty, the primary reason you are asking this question is the number of Protoss players at the top level. I again posit that this could be firstly due to a selection bias (i.e. the best players choose not to play Protoss) simply on the basis that Protoss is less interesting to them. A knowledge of the number of players applying for the tourney, the number of players in Code B etc, would allow better analysis of this theory. For now I will drop this proposition, since we can't really assess it.

I also note your comment that in all matchups the global tourney winrates are approaching 50%. Assuming there enough tournaments occuring to provide statistically useful results, such that player skill/dedication/innovativeness is not a significant factor, then this would imply no race is overpowered/underpowered. Of course we cannot make such a drastic assumption about skill etc not being a factor, but I think it is still the most telling piece of information. Even though less players are playing protoss at the top level, they are playing it to an equal level with their opponents, whether this is because of race or skill. I am going to focus on this statistic.

When I think about balance, I think about the "skill ceiling". It is impossible to reach the skill ceiling, because players cannot ever hope to control individual units to conduct perfect execution of strategies. However, I do believe in an approximate physical maximum APM for humans, as well as a maximum to the best decision making and the best APM allocation (spending APM to gain the best advantage). To me, these sorts of things represent a players true skill. They are impossible to evaluate, because APM measures in game do not tell you anything about APM allocation.

Suppose then we explain a players win probability as a combination of skill (or proximity to the skill ceiling) and race. Pretend we could actually make a formula: win probability = skill factor * race factor, where skill factor would account for both player's skill in a game, and race factor would account for each players race.

Now we know win probabilty ~ 50%. Suppose then we answer your question "Is protoss underpowered in high level play?" as "yes". This implies the "race factor" for protoss is lower than that for terran or zerg. That would mean that the "skill factor" for those protoss players is higher, in order for them to achieve the 50% win ratio. The protoss players who are performing so well in tourneys to give a 50% win ratio, are "better" than their terran and zerg counterparts. In part this might be true. I can't say for sure.

What are your thoughts on this analysis? I'm not sure where I'm going with this now...

PS: Like many others in this forum, I believe metagaming comes into it alot. Notice how all players at top level go through trends of playing a certain style. For example in TvZ, 2 rax was all the rage, and now its reactor hellions. Noone is actually sure which is better, but there is a tendency for all players to be a bit sheepish, follow the mainstream strategy because that is working for them now. Then other races adapt to that, and suddenly the strategy is less effective. I believe this affects all levels of play, but the important thing is, it may mean that right now, Protoss have some adapting to do, and when they do the challenge will flip back to T and Z?