Welcome Guest
( Log In | Register )
The time is now 6:51 am
You last visited January 23, 2017, 5:30 am
All times shown are
Eastern Time (GMT-5:00)

partial credit filtering: part two

Published:

Part 1 (Entry #10) explained how to use this concept with independent filters that all had about the same success rate. This part will show how to do so with filters that have different success rates from each other. Since the setup math is more involved, fewer filters are used in the example. I'm using 3 filters total. Their success rates are: 80/20, 75/25, and 70/30

   

Step 1 set up a "truth table" 1 column for each filter and 2^filters rows (2^3 = 8), thus...

                                                                                                    
filter 1 filter 2 filter 3
80/20 75/25 70/30
pass pass pass
pass pass fail
pass fail pass
pass fail fail
fail pass pass
fail pass fail
fail fail pass
fail fail fail

 

step 2: substitute the "pass" and "fail" spaces with your pass/fail ratios...

then multiply across (I added a column for "totals")

filter 1 filter 2 filter 3  
80/20 75/25 70/30
80% 75% 70% 42.0%
80% 75% 30% 18.0%
80% 25% 70% 14.0%
80% 25% 30% 6.0%
20% 75% 70% 10.5%
20% 75% 30% 4.5%
20% 25% 70% 3.5%
20% 25% 30% 1.5%

Now you have all eight possible outcomes, and their expected rate of occurence.

What happens if you decide you want to drop a filter?

Here's how. Dropping filter 3 and marking out all redundancies in cols 1 and 2 gives this table.

Two filters gives only four possible outcomes. You would call the third filter a "don't care" condition. 

filter 1 filter 2 filter 3  
80/20 75/25 70/30
80% 75%   60.0%
       
80% 25%   20.0%
       
20% 75%   15.0%
       
20% 25%   5.0%
       

Entry #23

Comments

This Blog entry currently has no comments.

You must be a Lottery Post member to post comments to a Blog.

Register for a FREE membership, or if you're already a member please Log In.