Hi guys, long-time occasional lurker and first-time poster. 
I was a team captain for two APA teams for a while. 8-ball and 9-ball. I kept progressively increasing statistics about the players on my team. It started out as a small list of who played most recently so I wouldn't skip a player twice in a row. Then I started keeping track of win percentages and other basic stuff.
Then I wrote a computer program to do my statistics automatically and that increased the amount that I could do since I no longer had to do it by hand.
I gradually had the idea to keep track of how each player was "really" playing, which is pretty easy for 9-ball. For example:
- If a 5 loses a match but got 31 points, that means he played like a 4 for that match.
- If a 5 wins a match against a 4 and the 4 got 25 points, that means the 5 was on track to get 47.12 points by the time the 4 would have finished the match at 31 points. That means the 5 was playing a little better than a 6.
So I would take all these numbers and average them together and I could tell each player "you've been playing like a 5.3" or whatever.
Unfortunately the same method can't be used for 8-ball since the numbers often go off the charts. It's not uncommon for, say, a 5 to beat a 4 4-1. That means the 5 would be on track to win 12 games, which means he played twice as well as a 7, which doesn't seem like very useful (or accurate) information.
Last week I cracked this mathematical nut though. The trick is to be able to calculate the probability of a certain rating having a certain win-loss record. Basically it's the same as calculating the odds of a coin toss experiment, e.g., what are the odds that you get 6 heads if you toss a coin 10 times. Tossing a head would be like winning. And you can figure out the odds of one rating "tossing a head" vs. another rating from the APA 8-ball handicap table.
Once you can calculate the probability of a certain rating having a certain record, it's not a leap to find the most likely rating to have that record.
So, I present to the community a web page that I made where you can put in a player's win-loss record and the page tells you the most probable rating that matches that record. Basically it tells you how well you have "really" been playing if you have a certain record.
http://www.tckerrigan.com/Misc/Pool/
I hope some of you find this as interesting and amusing as I have.
I was a team captain for two APA teams for a while. 8-ball and 9-ball. I kept progressively increasing statistics about the players on my team. It started out as a small list of who played most recently so I wouldn't skip a player twice in a row. Then I started keeping track of win percentages and other basic stuff.
Then I wrote a computer program to do my statistics automatically and that increased the amount that I could do since I no longer had to do it by hand.
I gradually had the idea to keep track of how each player was "really" playing, which is pretty easy for 9-ball. For example:
- If a 5 loses a match but got 31 points, that means he played like a 4 for that match.
- If a 5 wins a match against a 4 and the 4 got 25 points, that means the 5 was on track to get 47.12 points by the time the 4 would have finished the match at 31 points. That means the 5 was playing a little better than a 6.
So I would take all these numbers and average them together and I could tell each player "you've been playing like a 5.3" or whatever.
Unfortunately the same method can't be used for 8-ball since the numbers often go off the charts. It's not uncommon for, say, a 5 to beat a 4 4-1. That means the 5 would be on track to win 12 games, which means he played twice as well as a 7, which doesn't seem like very useful (or accurate) information.
Last week I cracked this mathematical nut though. The trick is to be able to calculate the probability of a certain rating having a certain win-loss record. Basically it's the same as calculating the odds of a coin toss experiment, e.g., what are the odds that you get 6 heads if you toss a coin 10 times. Tossing a head would be like winning. And you can figure out the odds of one rating "tossing a head" vs. another rating from the APA 8-ball handicap table.
Once you can calculate the probability of a certain rating having a certain record, it's not a leap to find the most likely rating to have that record.
So, I present to the community a web page that I made where you can put in a player's win-loss record and the page tells you the most probable rating that matches that record. Basically it tells you how well you have "really" been playing if you have a certain record.
http://www.tckerrigan.com/Misc/Pool/
I hope some of you find this as interesting and amusing as I have.
