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

[Joboo]

[ QUOTE ]
[ QUOTE ]
I really question all the posters on here that believe 200 SNGs is a blip and may not represent your true capability. I have been playing SNGs for a while, but just created a spreadsheet to actually track my results this weekend. I've played 43 SNGs this weekend, here are some statistics:

Profit/SNG: $30.67
Std. Deviation: $76.63
t-value (95% confidence interval, DOF=42): 2.018

True profitability at SNGs with 95% confidence:

$7.09 <= Profit/SNG <= $54.26

If you see something wrong with my statistical analysis, please feel free to post. If you think statistics are some kind of hokum, and that this can't possibly be correct just because you don't believe it - don't bother to respond.


[/ QUOTE ]

I haven't checked the math in this example because it's not worth my time, but assuming it is correct, and assuming that there is statistical merit in sng confidence interval calculations, we'd have to give this poster the benefit of the doubt and tell him to quit his day job based on 43 tournaments.

[/ QUOTE ]

I'm certainly out of my league as far as statistics knowledge goes, but it would seem to me that the confidence intervals don't mean anything with such a small sample size. It's sort of like a baseball player who hits a homerun on the first day of the season, that would project for him to hit 162 home runs, which is ridiculous. However, if you instead see that he's hit 20 home runs at the halfway mark of the season, then 40 home runs hit for the season is a much more reasonable and and accurate projection.

It would seem to me that your problem doesn't really lie with Aleo's confidence intervals calculations, but more with people's misguided uses of it over laughably small samples. Of course, I could be looking at it too simplistically, but that's the way it seems to me.

[Snoogins47]

[ QUOTE ]
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.

[/ QUOTE ]

I am INTENSELY plebeian as far as stats go. This is more of an inquiry than a criticism...

But wouldn't the comparison to the Cubs record be a fallacious argument? I think the "skill factors" in a baseball situation are much more varied than in poker (considering over the Cubs' tenure, we have not only different teams, but entirely different rules as well), and most importantly, poker results are intrinsically related to the distribution of cards; and baseball does not have any random variable inherent in it (I'm sure I'm struggling with terms here. While the weather, or somebody's injury, may be considered a variable, what I mean is that there is no variable in which a standard distribution can actually be construed)

If I'm way wrong, or correct, I'd like to hear it: this stuff has always interested me, but I know very little about stats.

Another thing: If the results for a SNG can't fit into this realm due to the presence of skill, and tournament places not being "random variables," wouldn't it be silly to calculate a confidence interval for a cash game winrate as well? The distribution of your hands is random, but the results of them are very highly dependent on your skill relative to the field.

I think the general point I'm making here is that the vast majority of these statistical calculations seem to me to be a very interesting approximation, that is often close to correct in practice, but should be treated lightly due to the ever-changing environmental variables.

So, how dumb am I? [img]/images/graemlins/smile.gif[/img]

[rachelwxm]

[img]/images/graemlins/shocked.gif[/img] You must be running badly.

[bball904]

[ QUOTE ]
I think the general point I'm making here is that the vast majority of these statistical calculations seem to me to be a very interesting approximation, that is often close to correct in practice

[/ QUOTE ]

Absolutely! I prefer to think of them as common sense intervals.

[bball904]

On the contrary, I'm running quite well. 26.3% ROI in 285 55's in January. Can someone project how well I'll do if I can get 400 55's played in February? I'm dying to know...

[bball904]

[ QUOTE ]
It would seem to me that your problem doesn't really lie with Aleo's confidence intervals calculations, but more with people's misguided uses of it over laughably small samples.

[/ QUOTE ]

True that the frustration comes with the misguided use, but the fact remains that the calculations themselves are misguided.

[bball904]

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


[/ QUOTE ]

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.

[jcm4ccc]

[ QUOTE ]
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.

[/ QUOTE ]

Initially I agreed with you, but the more I read your comments, the less I agree. You seem to be implying that nothing of value can be predicted from your SnG stats. That is incorrect.

[ QUOTE ]
The data distribution of 1st, 2nd, 3rd, other certainly does not represent a normal distribution.

[/ QUOTE ] Yes, but there are things you can do statistically to get around that fact. You can combine multiple SnGs into a stat that has a normal distribution. You can use binomial distributions for how often you get into the money, or how often you get first place. In other words, there are meaningful predictions you can make.

[ QUOTE ]
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.

[/ QUOTE ] 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. However, if your skill level has been increasing as you play more and more SnGs, then it would be difficult to factor that out in doing confidence intervals, etc.

If you will provide me with the following information, I can produce some stats for you:

1. Number of tournaments played
2. Number of 1st place finishes
3. Number of ITM finishes
4. Amount of money won in your first set of 25 SnGs, your second set of 25 SnGs, your third set of 25 SnGs, etc.

If you have only played a small number of SnGs at a particular level, then you will very large confidence intervals and the data will be less meaningful. But they will be correctly calculated.

[AgentSq]

If I had read this post 20 years ago I would be able to give a proper answer here, but from my fading memory....

There is something called the central limit theorem that is terribly important in most stats but is generally brushed over. What it says is that the distribution of an average is normal irrespective of the distribution it is drawn from.

This is a fairly strange and counter intuitive result but is true.

Applied to SNG's what this means is that the observed average $ rate per game is an estimate for your true average rate. And what's more, this estimate is normally distributed having a mean of the observed average and a standard deviation of the standard deviation of the observed results divided by the square root of the number of obs.

So it is meaningful to construct a confidence interval around an average win rate in order to 'prove' that you are a winning player. If everyone did this then you would never get people posting averages based upon 30 results. The reason for this is that the observed standard deviation is always going to be relatively large compared with the average win. So there needs to be a large number of obs before root n becomes large enough to produce a distribution that is 95% +'ve. When people reply pointing out that you need 200+ results - this is why they are not kidding!

However your last point about things changing is also another much overlooked point. Remember, that your average is only an estimate drawn from an unknowable distribution of your results. I would suggest that this unknowable distribution is quite variant as you and your opponents change through time. What this means is that the confidence interval that is constructed may no longer be relevant as you play today.

Hence someone could calculate that they are 99% sure that they are a winning player. But in the strictest sense they are 99% that they were a winning player. Future results may or may not follow.

So finally to answer your original question, yes confidence intervals can be constructed. However the actual usefulness is, to me at least, marginal and probably more psychological. The amount of games that you would have to put in to get a tight confidence interval would be large. Having played this many you really should know whether you are a winner or loser.

[rachelwxm]

So what make you not confident about "confident level" at all? [img]/images/graemlins/cool.gif[/img]

my game is boring enough that I don't even wonder about those confidence level terms. [img]/images/graemlins/cool.gif[/img]