Confidence interval for hourly rate, how does this look..

[brendons31]

win rate (a) - true hourly rate off pokertracker (PT)number of hours (b) - number of hours off PT
standard deviation (c) - standard dev of hourly rate off PT
condidence level (d) - Insert a level of confidince ie. 95%
Normsinv (e) - Normsiv of confidence level (d)
sqrt (f) - Square root of number of hours (a)

Upper bound - =a+(e*(c/f))

Lower Bound - =a-(e*(c/f))

[BruceZ]

[ QUOTE ]
win rate (a) - true hourly rate off pokertracker (PT)number of hours (b) - number of hours off PT
standard deviation (c) - standard dev of hourly rate off PT
condidence level (d) - Insert a level of confidince ie. 95%
Normsinv (e) - Normsiv of confidence level (d)
sqrt (f) - Square root of number of hours (a)

Upper bound - =a+(e*(c/f))

Lower Bound - =a-(e*(c/f))

[/ QUOTE ]

There are a couple of issues here.

First, if you are using the Excel function =NORMSINV, that gives you a 1-sided confidence interval, and you need 2-sided here. For example, if you put in =NORMSINV(95%) you get 1.64 standard deviations, but you want this to be 2 standard deviations. To correct this, you need to give NORMSINV a number halfway between your desired confidence and 1, so for 95% that would be 97.5%. In general for confidence d, you give NORMSINV the value (d+1)/2. Note that not all tables of the normal distribution work this way, so if you are not using Excel, you need to determine how your table works.

The second issue you may be doing exactly right except for the terminology. You don't want c to be the standard deviation of your hourly RATE, you want it to be the standard deviation of your win for 1 hour, and then when you divide this by sqrt(hours), that gives you the standard deviation of your hourly RATE. The distinction is confusing because PT gives you something called the standard deviation in units of /hr, so it might look like the standard deviation of your hourly RATE, but it really means your standard deviation for exactly 1 hour, and the units are a misnomer. The way to tell these apart is by their magnitude, so for example, if c is a number like 10 bb/hr, then 10 bb is the standard deviation of your win for 1 hour, and it doesn't mean that the standard deviation of your hourly rate is 10 bb/hr. You must divide this by sqrt(hours played) to get the standard deviation of your hourly RATE, which would be a fraction of 1 bb/hr if you have played more than 100 hours in this case. Or if PT already gives you the standard deviation of your hourly RATE (I don't know that it does), then you could use that directly instead of dividing by sqrt(hours).