There is no such thing as a confidence interval for sit-n-go's.

[RobGW]

Your memory serves you well. I think some people have been misguided by the fact that their distribution of finishes is not normal. You dont need a normal distribution to calculate a confidence interval. As the number of tournaments grows, the results will begin to form a normal distribution. This will give an expected win rate per hour, avg finish, roi, etc. Each with a certain confidence interval. Will this help you in your next tournament? No, but it may help you convince your wife/parents that you can make money. It can help you decide whether to quit your day job.

[rachelwxm]

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Just out of curiosity, what are some examples of data samples that you think can be subject to this sort of statistical analysis?


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Inferential statistics are used to draw inferences about a population from a sample. Many examples would be manufacturing related. For example, the weight or dimensions of any particular widget coming off an assembly line. Also, behavioral studies, such as what does the effect of drinking 12 Heineken's have on one's ability to correctly spell their name in the snow. That's probably a bad example, but you get the idea.

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I think you infer that poker cannot be subject to mean ROI analysis? It is true that your poker skill, along with the slowly improvement of the field do affect your long term trend of your ROI, for example if you play one SNG per day, confidence level can never mean to you. But for guys that play 300-500 game a month assming your skill does not change that dramatically, you can actually infer some meaning results.

[bball904]

Excellent posts! I concur that your method of normalizing the data definitely does produce the desired effect of removing my main objection to the use of confidence intervals.

However, there is still one point that I strongly disagree with you.

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Skill does not need to be analyzed. The basic assumption is that the underlying skill remains constant. A constant variable can be ignored in doing confidence intervals, etc.

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Your basic null assumption is a subjective statement that I do not agree with. If my skill level is a constant, why the heck am I spending time reading books and coming to 2+2? Also, it is not only your skill level that would need to be a constant, but the skill levels of your opponents as well.

I do have 1000 sng's at the 55 level. I will do the analysis for batchs of size 25 and 20 to see how normalized the data becomes with only 40 or 50 data points.

[bball904]

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You dont need a normal distribution to calculate a confidence interval.

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True, only if you want it to mean something.

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As the number of tournaments grows, the results will begin to form a normal distribution.

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Wrong! However, jcm4ccc has shown that manipulating a large number of results into batches can begin to approximate a normal distribution.

[rachelwxm]

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Excellent posts! I concur that your method of normalizing the data definitely does produce the desired effect of removing my main objection to the use of confidence intervals.

However, there is still one point that I strongly disagree with you.

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Skill does not need to be analyzed. The basic assumption is that the underlying skill remains constant. A constant variable can be ignored in doing confidence intervals, etc.

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Your basic null assumption is a subjective statement that I do not agree with. If my skill level is a constant, why the heck am I spending time reading books and coming to 2+2? Also, it is not only your skill level that would need to be a constant, but the skill levels of your opponents as well.

I do have 1000 sng's at the 55 level. I will do the analysis for batchs of size 25 and 20 to see how normalized the data becomes with only 40 or 50 data points.

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Of course there is some long term trending in your ROIs. Just like stock market that I spend a lot of time on, simply because market is trending does not mean you cannot perform reliable statistical analysis on. [img]/images/graemlins/smile.gif[/img]

[stillnotking]

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I simply can't take it anymore. There are so many discussions of statistical measures on this forum that are all completely off based, it is ridiculous.

I remember the first time I opened Aleo's spreadsheet and saw confidence intervals. My initial reaction was to laugh. Results of poker tournaments are not random variables. The data distribution of 1st, 2nd, 3rd, other certainly does not represent a normal distribution. I even believe there is a degree of skill involved in the actual outcome of these poker tournaments. Skill is not really something that statisticians believe they can analyze to any degree of confidence.

A confidence interval can not be computed under the basis of these conditions. Period. The confidence intervals that are being quoted are a lot like saying that based on the last 100 years, I have a 95% confidence that the Chicago Cubs will win between 54 and 111 games this year. It is kinda cute, but means nothing.

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I'm no stats expert (just a few undergrad-level classes for my psych major), but it seems to me that forecasting SNG results is exactly analogous to the following problem:

You have a 10-sided die which is weighted so that certain faces come up more often. The exact amount of the weighting is unknown. The only data you are allowed to collect is by rolling the die over and over. With a sufficient number of rolls, you can have a high degree of confidence in the "weight" of each side of the die. At that point you can make meaningful predictions about future probability.

In the money/out of the money is the wrong way to approach this problem IMO. The die does not "know" which faces are assigned to winning or losing money. But if you know the weight of each face, you can easily make (probabilistic) predictions about the future monetary results.

[for teh win]

The OP has point in a way though. One has to be wary of assuming normal distributions in situations which clearly aren't. As an example, the null hypothesis concerning placings in SNG's must be that there is an equal chance of placing in either of 1st through 10th, hence a uniform distribution and not a normal one. (Aleo's ROI calcs are different though.) Then there are also situations where large samples can be assumed normally distributed by approximation but where smaller samples aren't. There are plenty of nice tests for that but it takes large samples. However, large in this context usually means something like 30 or 40. That's nothing.

Not that any of this would stop you from using stats on your results even in cases where you can't assume a normal distribution. After all, no one except maybe a professional statistician is better prepared for testing non-normal samples or using non-parametric tests than a psych grad. [img]/images/graemlins/wink.gif[/img]

[rachelwxm]

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using non-parametric tests [img]/images/graemlins/wink.gif[/img]

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Gee, we should rename this forum "abstract math" or "applied statistics" or something like that.

honestly, the analysis here always forced me to open some old dusted statistics books. [img]/images/graemlins/laugh.gif[/img]

[microbet]

I think everyone knows that conditions change over time and past performace is not a guarantee of future performance.

I think the bigger misuse of math around here has to do with analyzing individual hands. People routinely quote the EV of certain plays to the hundredth place when part of the calculation is what range of hands you put your opponant on.

[spentrent]

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using non-parametric tests [img]/images/graemlins/wink.gif[/img]

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Gee, we should rename this forum "abstract math" or "applied statistics" or something like that.

honestly, the analysis here always forced me to open some old dusted statistics books. [img]/images/graemlins/laugh.gif[/img]

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The real problem is that I use my old stats and numerical analysis books to prop up my monitor... threads like this force me to pull them out, put them back. Very annoying.