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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.