The higher variance is caused by a lower win rate (see link below for more details).
So yes, in hypers where win rates are low (ballpark 52-53%) you would need a larger sample to provide the same confidence in your win rate compared to a higher win rate format.
The result of a single trial (game) is binary => you win or you lose.
Wrt to the application of statistics to modeling confidence intervals in HUSNGs, your chance of winning (theoretical win rate) is dependent on your skill relative to your opponent.
The mathematics underlying such random probability distributions are well understood and the properties are summarised quite succinctly (compared to your average textbook lol) in this wiki post:
a little example concerning variance and standard deviation:
say you play an opponent who is equally skilled as you and you play 100 games, of which you expect to win 50, the standard deviation is calculated as follows:
first, we need the variance:
V = N * p * (1 - p)
where N is the amount of games played and p is your probability of winning.
so we have:
V = 100 * 0.5 * (1 - 0,5)
V = 25
now we need the standard deviation σ
the standard deviation is the square root of the variance.
so we have σ = √25 = 5
now we can calculate with what amount of certainty we can expect the match to turn out.
with 68,3% certainty we can expect to win 45 - 55 matches of the 100 we played. (expectation ± 1 σ)
with 95,4% certainty we can expect to win 40 - 60 matches (expectation ± 2 σ)
with 99,97% certainty we can expect to win between 35 and 65 matches (expectation ± 3 σ)
you can see that over just 100 games variance can be extremely cruel.
using those simple formulas you can calculate very easily if you are a winning player at a certain level with close to 100% accuracy.
Mersennary wrote an article about just this chart in 2011:
http://www.husng.com/content/given-my-results-what-should-my-confidence-...
Since it is based on your ITM / Winrate %, it does not matter what speed you play.
Hi.
ok thanks. thought because of the higher variance in these games the samplesize must be larger... sorry for my english :)
The higher variance is caused by a lower win rate (see link below for more details).
So yes, in hypers where win rates are low (ballpark 52-53%) you would need a larger sample to provide the same confidence in your win rate compared to a higher win rate format.
The result of a single trial (game) is binary => you win or you lose.
Wrt to the application of statistics to modeling confidence intervals in HUSNGs, your chance of winning (theoretical win rate) is dependent on your skill relative to your opponent.
The mathematics underlying such random probability distributions are well understood and the properties are summarised quite succinctly (compared to your average textbook lol) in this wiki post:
http://en.wikipedia.org/wiki/Binomial_distribution
a little example concerning variance and standard deviation:
say you play an opponent who is equally skilled as you and you play 100 games, of which you expect to win 50, the standard deviation is calculated as follows:
first, we need the variance:
V = N * p * (1 - p)
where N is the amount of games played and p is your probability of winning.
so we have:
V = 100 * 0.5 * (1 - 0,5)
V = 25
now we need the standard deviation σ
the standard deviation is the square root of the variance.
so we have σ = √25 = 5
now we can calculate with what amount of certainty we can expect the match to turn out.
with 68,3% certainty we can expect to win 45 - 55 matches of the 100 we played. (expectation ± 1 σ)
with 95,4% certainty we can expect to win 40 - 60 matches (expectation ± 2 σ)
with 99,97% certainty we can expect to win between 35 and 65 matches (expectation ± 3 σ)
you can see that over just 100 games variance can be extremely cruel.
using those simple formulas you can calculate very easily if you are a winning player at a certain level with close to 100% accuracy.
"using those simple formulas you can calculate very easily if you are a winning player at a certain level with close to 100% accuracy."
If you keep playing equally strong opponents there is really no need to do the math, you know. ;-)
Hi.
i suppose that´s why mathematicians use variables in their formulas, like "p".