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Calculate Error in VPIP!

    • Optroot
      Optroot
      Bronze
      Joined: 11.05.2008 Posts: 250
      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
    • tokyoaces
      tokyoaces
      Bronze
      Joined: 01.04.2009 Posts: 1,883
      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.
    • Optroot
      Optroot
      Bronze
      Joined: 11.05.2008 Posts: 250
      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.