# Calculate Error in VPIP!

• Bronze
Joined: 11.05.2008
I've heard people say countless times: "Your sample size is too small" then all your stats have to be thrown out the window. But now there is a way to use your stats well without a large sample size! Hooray!

What can I use it for?
With this formula you can calculate the error in VPIP, so you will get a minimum possible VPIP and a maximum VPIP, specified for a certain confidence interval. Given VPIP you can calculate a range of VPIP.

Formula:
95% Confidence Interval

Let n represent sample size
Let dVPIP represent the error in VPIP

dVPIP = 1.960*sqrt( VPIP*(100-VPIP)/n )

I don't get it , show me examples!

You are at a table someones VPIP shows 25% in your HUD and you have 100 hands on them. Then:

VPIP = 25.0%
n = 100

dVPIP = 1.960*sqrt(25.0*(100-25.0)/100)
dVPIP = 1.960*sqrt(25.0*(75.0)/100)
dVPIP = 1.960*sqrt(18.75)
dVPIP = 8.49

You can be 95% confident that:
His actual VPIP is 25.0% +/- 8.49%
His minimum VPIP is 16.51%
His maximum VPIP is 33.49%

How can I use this?
1) When imputing hand ranges into equilator, ensure you are +EV for all handranges in this range.
2) Getting a better idea of handranges with small samples.
3) I dunno you tell me!

Discuss
• 2 replies
• Bronze
Joined: 01.04.2009
Using a stats calculator I get:
LB: 5.158%
UB: 44.842

Which is pretty much expected for a sample size of 100 into an infinite data set.

In any case VP\$IP isn't normally distributed anyway. Any thinking player is going to be adjusting their range based on position.

If you wanted to model VP\$IP confidence interval ranges I would at least separate them into blinds, late, middle, and early position.

Ultimately it's just a whole lot easier to wait for their stats to converge in the position you are interested in.
• Bronze
Joined: 11.05.2008
I modeled this like this:

player has a probability, p, to play or not play. Either a success or a failure, in this way it is normally distributed.

And yes, people are adjusting their ranges, but then your VPIP stats are junk anyway

if they eventually going to converge, then it could be useful to see vpip_min and vpip_max.

I personally havnt used this in a game, only on my own stats.