One Pocket Handicaps

The rating differences below are on a scale where a player who
plays twice as well as another player will be rated 100 points
higher.  You can figure spots between two players from the spots
they got from a common opponent, assuming the games were fair.

Example: A gives B 9-7, so he is 37.8 rating points better than B.
B gives C 9-6 so he is 61.2 points better than C. A is then 99.0
points better than C and the closest spot listed is 14-7, which
requires a lot of ball spotting.  An option would be to alternate
between 9-5 and 10-5 for an average spot of 97.1.

You can also use the table below to see how different two spots
are.

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Rating  Ball
Diff.   Spot

  11.0  14-13
  11.9  13-12
  12.9  12-11
  14.2  11-10
  15.7  10-9
  17.7   9-8
  20.1   8-7
  22.8  14-12
  23.4   7-6
  24.8  13-11
  27.1  12-10
  28.0   6-5
  29.9  11-9
  33.4  10-8
  34.7   5-4
  35.7  14-11
  37.8   9-7
  39.0  13-10
  42.9  12-9
  43.6   8-6
  45.7   4-3
  47.6  11-8
  49.9  14-10
  51.4   7-5
  53.6  10-7
  54.7  13-9
  60.5  12-8
  61.2   9-6
  62.7   6-4
  65.7  14-9
  67.1   3-2
  67.8  11-7
  71.5   8-5
  72.4  13-8
  77.0  10-6
  80.4   5-3
  80.7  12-7
  83.4  14-8
  86.1   7-4
  89.2   9-5
  91.2  11-6
  92.5  13-7
 103.5  14-7
 104.1  12-6
 105.0  10-5
 106.2   8-4
 108.4   6-3
 112.9   4-2
 116.0  13-6
 119.1  11-5
 123.9   9-4
 126.9  14-6
 127.2   2-1
 131.8   7-3
 132.1  12-5
 139.7  10-4
 143.9  13-5
 147.6   5-2
 152.0   8-3
 153.9  11-4
 154.9  14-5
 166.8  12-4
 169.7   9-3
 175.6   6-2
 178.6  13-4
 185.4  10-3
 189.6  14-4
 194.4   3-1
 199.0   7-2
 199.6  11-3
 212.5  12-3
 219.1   8-2
 224.4  13-3
 235.3  14-3
 236.8   9-2
 240.2   4-1
 252.6  10-2
 266.8  11-2
 275.0   5-1
 279.7  12-2
 291.6  13-2
 302.5  14-2
 303.0   6-1
 326.4   7-1
 346.6   8-1
 364.3   9-1
 380.0  10-1
 394.3  11-1
 407.2  12-1
 419.1  13-1
 430.0  14-1