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 08-03-2012, 09:17 AM #1 veteran     Join Date: Jan 2010 Location: Maracaibo, Venezuela Posts: 2,650 True ROIs Hi there, im wondering about if anybody has any calculations regarding the relation of sample sizes and "true ROIs" im comparission to our current one, dont know if im making myself clear or even if this is posible to calculate without having to process large amount of data or doing endless correlations calculations but was thinking on knowing the facts of something like this... After X numbers of games we´re X% likely that our ROI its X% within our true ROI If anybody can give me any insight about this topic woud be appreciated...Cheers.
 08-03-2012, 09:42 AM #2 Carpal \'Tunnel     Join Date: Jun 2005 Location: Psychology Department Posts: 7,425 Re: True ROIs If we want to be lazy and ignore population distributions (i.e. prior probabilities of certain win-rates) we can use an X% confidence interval. X% CI = tN-2, alpha * SD / sqrt(N) Where SD is the standard deviation of your sample, N is your sample size and t is given by the t-distribution for N-2 degrees of freedom and a specified alpha level. For example, if you have a sample of 100 and want a 95% confidence interval you want to look up the t-value for 98 degrees of freedom and alpha of 1 - .95 or .05. The easiest way to do this is to use excel: =tinv(.05, 98) Note that for large samples the value of t approaches the value of the normal distribution Z. Again though, the problem with this approach ignore all prior information. Let's say that in your first 10 MTTs you happen to win 2 major events and your ROI is well over 1000%. Your confidence interval will be wide, but still might not contain your true ROI very often. In fact, for MTTs I do not recommend using any equations which assume normality (as these due). Bootstrapping procedures are better. But for STTs these standard equations work pretty well.
08-03-2012, 12:36 PM   #3
veteran

Join Date: Jan 2010
Location: Maracaibo, Venezuela
Posts: 2,650
Re: True ROIs

Quote:
 Originally Posted by Sherman If we want to be lazy and ignore population distributions (i.e. prior probabilities of certain win-rates) we can use an X% confidence interval. X% CI = tN-2, alpha * SD / sqrt(N) Where SD is the standard deviation of your sample, N is your sample size and t is given by the t-distribution for N-2 degrees of freedom and a specified alpha level. For example, if you have a sample of 100 and want a 95% confidence interval you want to look up the t-value for 98 degrees of freedom and alpha of 1 - .95 or .05. The easiest way to do this is to use excel: =tinv(.05, 98) Note that for large samples the value of t approaches the value of the normal distribution Z. Again though, the problem with this approach ignore all prior information. Let's say that in your first 10 MTTs you happen to win 2 major events and your ROI is well over 1000%. Your confidence interval will be wide, but still might not contain your true ROI very often. In fact, for MTTs I do not recommend using any equations which assume normality (as these due). Bootstrapping procedures are better. But for STTs these standard equations work pretty well.

 08-03-2012, 12:38 PM #4 veteran     Join Date: Jan 2010 Location: Maracaibo, Venezuela Posts: 2,650 Re: True ROIs Hahahah seriously i kind of understand what u explain and thank you for takign the time to do so. So, trying to apply that to my question, and asuming these Turbos SNGs sample sizes and your premise above how the calculations would go? 1k games 5k games 10k games 20k games 50k games 100k games
 08-03-2012, 02:43 PM #5 Carpal \'Tunnel     Join Date: Jun 2005 Location: Psychology Department Posts: 7,425 Re: True ROIs For that many games you can use the Z-distribution as an approximation. So for a 95% confidence interval you do this: UL = ROI + 1.96 * SD/sqrt(N) LL = ROI - 1.96 * SD/sqrt(N) Example: Say you have a 5% ROI over 1000 games. You calculate your SD from this data and divide it by the square root of 1000 (i.e, 100). Multiply this result by 1.96. If you add this number to 5% (your observed ROI over the 1000 game sample) you have an upper limit for a 95% confidence interval. If you subtract it from your ROI you have the lower limit. You can then say, "If my true ROI is (whatever your ROI over that sample was), I expect to fall within these limits 95% of the time after playing 1000 games."
 08-03-2012, 03:15 PM #6 veteran   Join Date: Jun 2011 Posts: 2,263 Re: True ROIs And to calculate SD you have to calculate it based on the prize pool payout table and your expected results. An example can be found here. http://forumserver.twoplustwo.com/25...sitngos-91960/

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