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  1. brokenball is offline
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    #1

    Handicap table


    Above is a handicap table for games to 11 for 3 games out of 5 type matches.
    Assuming there is player A with a USATT rating 40 point higher than player B, then player B would start with a 1 ball handicap in games to 11. The right hand column is the point difference. The left hand column is the handicap or lead the weaker player should get. This handicap should result in the weaker player having approximately a 50-50 chance of winning. If player A's rating is 150 points higher than player B's rating then player B would start with a 3 ball handicap.

    The information in the other columns was calculated out of curiosity and shows the probability of the better player winning each ball game and match as a function of the ratings difference

    Like anything, this table could be improved but it is accurate since it is based on probabilities and math and not a guess or estimate, with no real justification, like other tables I have seen.

    One problem is that there is a lot of chance for fluke wins by weaker player if the handicap is high. A weak player could win 3 games in a row if he starts with a 10 ball handicap and gets 3 edge or nets balls. A cure for this problem would be to make another version of this table where the stronger player starts with a negative score instead of the weaker player starting with a positive score. This would mean the weaker player still must win 11 points. This would give the stronger player more time to recover should the weak player get some lucky breaks.

    Another thing that can be done is to vary the handicap if the rating difference is between two ratings difference. For instance, if the ratings difference between two players is 125 then the weaker player could get a two ball handicap the first game and a three ball handicap the second game then back to a two ball handicap the third game.
    I would do the calculations that show how to vary the handicap between two levels based on the ratings difference.

    I developed this table about 10 years ago. My tables, I have more, are the only ones I have seen that are based on math and not just guesses or estimates. I could show the math but it would probably not help.

    A couple of years ago, forum member Emrathich wanted to "improve" the rating system by making each game significant, not just the whether one won or lost the match. I did the math using the technique I used to make the table above and concluded that if each game was significant then a player with a much higher rating would need to win by scores of 3 to 1 or 3 to 0 to not lose points, A 3 to 2 win was not good enough. I posted this info an NO ONE liked this idea because they said they like to take it easy when playing weaker players. I saved Emrathich a lot of time.

    This table could also be used to estimating ratings if either player's rating is known. For instance, my third coach had a rating of 2500 or a little more. I would play handicap games with him to put pressure on him because he would screw around otherwise. I would always win matches when I started with a 6 ball handicap but I would lose matches with a 5 ball handicap.

    I tried posting this before but I couldn't see it posted so I am doing it again.












  2. IB66 is offline
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    #2
    Quote Originally Posted by brokenball

    Above is a handicap table for games to 11 for 3 games out of 5 type matches.
    Assuming there is player A with a USATT rating 40 point higher than player B, then player B would start with a 1 ball handicap in games to 11. The right hand column is the point difference. The left hand column is the handicap or lead the weaker player should get. This handicap should result in the weaker player having approximately a 50-50 chance of winning. If player A's rating is 150 points higher than player B's rating then player B would start with a 3 ball handicap.

    The information in the other columns was calculated out of curiosity and shows the probability of the better player winning each ball game and match as a function of the ratings difference

    Like anything, this table could be improved but it is accurate since it is based on probabilities and math and not a guess or estimate, with no real justification, like other tables I have seen.

    One problem is that there is a lot of chance for fluke wins by weaker player if the handicap is high. A weak player could win 3 games in a row if he starts with a 10 ball handicap and gets 3 edge or nets balls. A cure for this problem would be to make another version of this table where the stronger player starts with a negative score instead of the weaker player starting with a positive score. This would mean the weaker player still must win 11 points. This would give the stronger player more time to recover should the weak player get some lucky breaks.

    Another thing that can be done is to vary the handicap if the rating difference is between two ratings difference. For instance, if the ratings difference between two players is 125 then the weaker player could get a two ball handicap the first game and a three ball handicap the second game then back to a two ball handicap the third game.
    I would do the calculations that show how to vary the handicap between two levels based on the ratings difference.

    I developed this table about 10 years ago. My tables, I have more, are the only ones I have seen that are based on math and not just guesses or estimates. I could show the math but it would probably not help.

    A couple of years ago, forum member Emrathich wanted to "improve" the rating system by making each game significant, not just the whether one won or lost the match. I did the math using the technique I used to make the table above and concluded that if each game was significant then a player with a much higher rating would need to win by scores of 3 to 1 or 3 to 0 to not lose points, A 3 to 2 win was not good enough. I posted this info an NO ONE liked this idea because they said they like to take it easy when playing weaker players. I saved Emrathich a lot of time.

    This table could also be used to estimating ratings if either player's rating is known. For instance, my third coach had a rating of 2500 or a little more. I would play handicap games with him to put pressure on him because he would screw around otherwise. I would always win matches when I started with a 6 ball handicap but I would lose matches with a 5 ball handicap.

    I tried posting this before but I couldn't see it posted so I am doing it again.

    Hi BB, table only reveals itself when I reply to your post, Der is having similar issues when posting photos, gotta be some sort of glitch going on with the system!!


  3. brokenball is offline
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    #3
    Quote Originally Posted by IB66

    Hi BB, table only reveals itself when I reply to your post, Der is having similar issues when posting photos, gotta be some sort of glitch going on with the system!!

    Yes, I see or don't see. I am using another computer, a mac instead of a Win PC, and I cannot see the picture either. Here is a link to my site.
    https://deltamotion.com/peter/TableT...%20to%2011.png

    I don't like the fact I must upload my pictures to another site to use a URL on this site. I can simply post a link to the other site.
    The attach files feature didn't work either.

    The + at the top right of this forum for creating new topics doesn't seem to be working right.

  4. IB66 is offline
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    #4
    I’m using an iPad, I don’t have any issues using the ‘+’ icon when starting threads, but sometimes when attaching photos form the iPads gallery there are issues getting them to load up properly, I use the ‘photo’ icon, just a pain having to keep repeating the process until the photos eventually load!!!

  5. Brs is offline
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    Oct 2015
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    #5
    Giving the stronger player negative points works better. Winning on three net balls isn't a good deal for the weaker player because what they really want is to play many points against someone better. So instead of starting 10 to 0, if it starts 3 to -7, they are guaranteed at least 18 points played per set even if they win none, which is unlikely.

    Another problem with starting at 9 or 10 is that is stops the better player from playing normally because one error loses the game. That defeats the purpose of the hanidcap match for the weaker player, which is to feel how it is to play against the stronger when they are playing for real.


  6. brokenball is offline
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    #6
    Quote Originally Posted by Brs
    Giving the stronger player negative points works better. Winning on three net balls isn't a good deal for the weaker player because what they really want is to play many points against someone better. So instead of starting 10 to 0, if it starts 3 to -7, they are guaranteed at least 18 points played per set even if they win none, which is unlikely.
    I like the idea of splitting the difference and adding points to the weaker player and subtracting some points from the stronger player. I would change a 10 point handicap to -5 for the stronger and 5 to the weaker so the total number of points that can be played without winning is still 20. However, it isn't that simple. The ratings difference will column will change a little and there will be more rows because now there can be more initial starting scores. For instance,

    initial starting score
    weaker stronger
    Code:
    0                  0
    1                  0 this could be 0 and -1 both may be an option.
    1                 -1
    2                  -1 this could also be 1 and -2
    2                  -2
    You can see this is more complicated to compute but I think it would provide more difference is rating categories. The games would stay at a consistent length which is also good.
    Another problem with starting at 9 or 10 is that is stops the better player from playing normally because one error loses the game. That defeats the purpose of the hanidcap match for the weaker player, which is to feel how it is to play against the stronger when they are playing for real.
    Agreed. The stronger player would probably just push waiting for the weaker player to screw up. You must take into consideration that a 10 point handicap would mean a 2500 player would be playing a <500 player. <500 players have a hard time with the basics and make lots of errors.

    Let me think about this. I did this 10 years ago and need to refresh my brain on the techniques I used. I remember the tricky part was figuring out the probability at 10-10.
    Last edited by brokenball; 07-11-2021 at 05:37 PM. Reason: formatting

  7. brokenball is offline
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    #7
    https://deltamotion.com/peter/TableT...ap%20Table.pdf
    I updated the handicap table. This table divides the handicap between starting the weaker player with a positive score and/or starting the stronger player with a negative score. This provides 3 ways to start a game when there is a 2 ball handicap. It also provides 3 different rating bands since the 3 ways of providing a 2 ball handicap are not equal. Dividing the handicap between the weaker and stronger player keeps the games almost the same length. Notice I eliminated some options like starting the weak player with a huge handicap and the stronger player with 0. This will avoid cases where a few lucky balls will tip the outcome. Penalizing the stronger player makes the game longer so I avoided only penalizing the stronger player..

    My thanks to Brs for joggin' my noggin into looking for a better way. Feel free to use the table. Now that I have this table I can make others but I see no point in making a table for 4 out of 7 matches or longer games. Perhaps one for hard bat 2 out of 3 games to 21 would be useful but few play hard bat now.

    I had made the original table over 10 years ago. The only tricky part is figuring out what happens at deuce. I had to think like Ramanujan to figure it out.



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