Two Plus Two Publishing LLC Two Plus Two Publishing LLC
 

Go Back   Two Plus Two Poker Forums > >

Notices

Probability Discussions of probability theory

Reply
 
Thread Tools Display Modes
Old 05-12-2017, 11:47 AM   #1
BirdsallSa
grinder
 
Join Date: Oct 2014
Posts: 670
Probability of Winning a 7 Game Series

I feel like the numbers I'm getting here can't be right. Assuming Team A has a 20% chance to win any given game and Team b is 80%:

1 Scenario of Series ending in 4 - (0.2)^4 = 0.16%
4 Scenarios of Series ending in 5 - (0.8)*(0.2)^4*4 = .48%
10 Scenarios of Series ending in 6 - (0.8)^2*(0.2)^4*10 = 1%
20 Scenarios of Series ending in 7 - (0.8)^3*(0.2)^4*20 = 1.6%

So, by these numbers a team with an average 20% chance of winning a game only has a 3.24% chance of winning a 7 game series? This seems like it can't be right.
BirdsallSa is offline   Reply With Quote
Old 05-12-2017, 11:51 AM   #2
BirdsallSa
grinder
 
Join Date: Oct 2014
Posts: 670
Re: Probability of Winning a 7 Game Series

Actually I think I understand how this could be correct now. Winning this series is essentially asking how often a team with a 20% winning percentage will win at least 57% of its games against a team with an 80% winning percentage. So, this number really should be quite low.
BirdsallSa is offline   Reply With Quote
Old 05-12-2017, 12:04 PM   #3
statmanhal
Pooh-Bah
 
Join Date: Jan 2009
Posts: 3,969
Re: Probability of Winning a 7 Game Series

It's right except for a calculation error for 5 games. Should be .512%, not .48%. Total becomes 3.33%.

Of course this assumes binomial distribution is applicable with a constant and independent win probability, which is probably as good as any other assumption.
statmanhal is offline   Reply With Quote
Old 05-12-2017, 08:49 PM   #4
David Sklansky
Administrator
 
David Sklansky's Avatar
 
Join Date: Aug 2002
Posts: 13,932
Re: Probability of Winning a 7 Game Series

Quote:
Originally Posted by statmanhal View Post
It's right except for a calculation error for 5 games. Should be .512%, not .48%. Total becomes 3.33%.

Of course this assumes binomial distribution is applicable with a constant and independent win probability, which is probably as good as any other assumption.
Actually its not. Because home game advantage means that some games are more than 20% and others are less. And that is worse for the dog.
David Sklansky is offline   Reply With Quote
Old 05-13-2017, 01:18 AM   #5
BirdsallSa
grinder
 
Join Date: Oct 2014
Posts: 670
Re: Probability of Winning a 7 Game Series

Quote:
Originally Posted by David Sklansky View Post
Actually its not. Because home game advantage means that some games are more than 20% and others are less. And that is worse for the dog.
I realize that, but this was about getting the methodology right, so I used a simplified scenario where we assumed no home court advantage, and a standardized win percentage.
BirdsallSa is offline   Reply With Quote
Old 05-19-2017, 03:55 PM   #6
masque de Z
Carpal \'Tunnel
 
masque de Z's Avatar
 
Join Date: Aug 2009
Location: Stanford, CA USA
Posts: 8,722
Re: Probability of Winning a 7 Game Series

Do a tree diagram win-lose branches and account for order of games played to take care of home details etc. That likely requires a computer program to list the correct products because eg 4-1 can happen many different ways but not after 4-0 etc.

You can do one on your own if you select a big piece of paper and start in the middle on the left and do it carefully branching each time in 2 outcomes (draw each branching to take place at given "columns" range eg 1-2 4-5 7-8 etc to account for home advantage also (so list the order first 2 games here then 2 games there etc).


If the paper is big its doable.


The problem of course is to think of a computer program to list it or to see a creative way to do it by hand faster. So challenge yourselves to discover it lol.

If the teams have p1,p2 and q1=1-p1, q2=1-p2 depending where they play then
Eg 4-0 can happen with p1^2*p2^2 but 4-1 can happen as

p1^2*p2*q2*p1 or p1^2*q2*p2*p1 or p1*q1*p2*p2*p1 or q1*p1*p2*p2*p1 etc.


See what i mean? Now try 4-2 outcomes and you will even more complicated sequences. A proper tree diagram will list all of them because you have less than 2^6~64 branches likely as many terminate earlier like 4-0 0-4 4-1, 1-4 etc .

Last edited by masque de Z; 05-19-2017 at 04:12 PM.
masque de Z is offline   Reply With Quote
Old 05-24-2017, 04:07 AM   #7
masque de Z
Carpal \'Tunnel
 
masque de Z's Avatar
 
Join Date: Aug 2009
Location: Stanford, CA USA
Posts: 8,722
Re: Probability of Winning a 7 Game Series

Also if we ignore the difference playing home vs visiting we can see it this way too;

To win you need to win the last of course. That means you need to win from 3-3,3-2,3-1,3-0 in the score before.

Now 3-0 has p^3, 3-1 has 4*p^3*q, 3-2 has 5!/3!/2!*p^3*q^2=10*p^3*q^2 and 3-3 has 6!/3!/3!*p^3*q^3=20p^3*q^3


So overall you have a chance to win that is (p^4+4*p^4*q+10*p^4*q^2+20*p^4*q^2)=

p^4*(1+4*q+10*q^2+20*q^3)

(adding nothing new here just a summary of results for general p/q worth having)

So for example 80-20 is 96.67% to win and 3.33% to lose.

If its 55% vs 45% then the best team has 60.8%.


Playoffs are a massive disgrace to the best team principle everywhere they are applied. They exist only to give inferior teams the chance to win everything and make an entire stellar season irrelevant because of near term volatility and lucky sob accidents or injuries and for ratings and stupid public. They are wasting an entire year of championship effort for almost nothing but a placement and some home advantage edge that is trivial tribute to a potentially massive difference in quality performance between teams.


The only way a team deserves to win a championship is by winning against all the other teams in a year long effort that they play everyone perfectly symmetrically collecting more points.

And a massive F OFF to everything else (when they play each other all year symmetrically anyway. And if they dont bloody make it so).

Last edited by masque de Z; 05-24-2017 at 04:13 AM.
masque de Z is offline   Reply With Quote

Reply
      

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off


Forum Jump


All times are GMT -4. The time now is 03:07 PM.


Powered by vBulletin®
Copyright ©2000 - 2017, Jelsoft Enterprises Ltd.
Copyright © 2008-2010, Two Plus Two Interactive
 
 
Poker Players - Streaming Live Online