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08-10-2019 , 01:17 AM

ToiletBowler

adept

Join Date: May 2016 Posts: 1,144

Our HUD stats say an opponent 3bets 6/30 (20%) in a specific spot.
What potential 3bet ranges (as a %) could we assign them with a degree of 70% confidence? 95%?

What if I then said that the pool 3bets 10% in that specific spot? How would this change the info?

Would love to do the math myself but I don't know how, and have no clue how to google this to find the right answer. Is anyone able to help with the math / the formula that would inform this?

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08-10-2019 , 11:57 AM

statmanhal

Pooh-Bah

Join Date: Jan 2009 Posts: 4,987

The 30 sample data is just about big enough to use the normal approximation to the binomial. The variance of a binomial where p is the estimated success probability from a sample of n is p*q/n. Then an approximate confidence interval is

P +/- z.c* sqrt(pq/n), where z.c is the standardized normal deviate for C% confidence

For the example, p = 0.20, n = 30, z.70 =1.04, z.90 = 1.645

Std dev = sqrt(0.2*0.8/30) = 0.073

The 90% C.I. is (0.20-1.645*0.073, 0.20+1.645*0.072) = (0.08, 0.32)

There are more exact ways but this should suffice.

Use of the pool data is not particularly relevant IMO if your opponent is known and you have good data on him.

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08-11-2019 , 02:07 AM

ToiletBowler

adept

Join Date: May 2016 Posts: 1,144

Thanks a lot!

Where do you get the z.70 =1.04, z.90 = 1.645 figures from?
How will I be able to work it out for other sample sizes and probabiilities?

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08-11-2019 , 02:36 AM

whosnext

Carpal \'Tunnel

Join Date: Mar 2009 Posts: 6,733

These are often called "critical values" of the standard normal variate.

Here is a link to the values of the most common Confidence Intervals.

http://www.math.armstrong.edu/statsonline/5/5.3.2.html

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08-11-2019 , 08:08 PM

statmanhal

Pooh-Bah

Join Date: Jan 2009 Posts: 4,987

Quote:

Originally Posted by ToiletBowler

Thanks a lot!

How will I be able to work it out for other sample sizes and probabiilities?

My post has the equation for sample of at least 30.

P +/- z.c* sqrt(pq/n), where z.c is the standardized normal deviate for C% confidence

To make it real easy, Google "Binomial Confidence Calculator" and you will have a number of choices.

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