Chapter 4
Introduction to Probability
Case Problem: Hamilton County Judges
The data in the table provides the basis for the analysis. We provide notes as a guide to answering
questions 1 through 5.
1. The conditional probabilities of cases being appealed in the three courts are given in the 3 Total rows
in the table. For Common Pleas Court, the probability of an appeal is .0401; for Domestic Relations
2. The probability of a case being appealed for each judge is given in column 5 of the table. Judges
3. The probability of a case being reversed for each judge is given in column 7 of the table. Judges
Winkler, Panioto and Grady/Hair have the lowest probability of reversal for Common Pleas,
4. The probability of a reversal given an appeal for each judge is given in column 9 of the table.
5. We describe here how The Cincinnati Enquirer used this data to rank the judges. Other approaches
may also be valid, but a rationale should be provided. The newspaper provided ranking for each
judge within each of the courts on percentage of cases appealed, percentage of cases reversed and
percentage of appealed cases reversed. Those rankings were the same as the ones we have computed
Domestic Relations Court
Municipal Court
Judge
Total Cases Disposed
Appealed Cases
Reversed Cases
Probability of
Appeal
Rank
Probability of
Reversal
Rank
Conditional
Probability of
Reversal Given
Appeal
Rank
Sum of Ranks
Fred Carto lano 3037 137 12 0.0 4511 14 0.00395 6 0.0 8759 5 25
Thomas Crush 3372 119 10 0.0 3529 4 0.0 0297 4 0.0 84 03 4 12
Patrick Dink elacker 1258 44 8 0.034 98 3 0.00636 12 0.1 81 82 14 29
Timothy Hogan 1954 60 7 0.0 3071 2 0.0 0358 5 0.116 67 9 16
Robert Kraft 3138 127 7 0.04047 10 0.002 23 3 0.05512 2 15
William Math ews 2264 91 18 0.040 19 7 0.007 95 15 0.1 97 80 16 38
William Morriss ey 3032 121 22 0.0 3991 6 0.0 0726 14 0.18182 14 34
Norb ert Nadel 2959 131 20 0.0 4427 13 0.00676 13 0.1 52 67 12 38
Arth ur Ney, Jr. 3219 125 14 0.0 3883 5 0.0 0435 9 0.1 12 00 8 22
Richard Niehaus 3353 137 16 0.0 4086 11 0.00477 10 0.1 16 79 10 31
Thomas Nurre 3000 121 6 0.04033 8 0.00200 2 0.0 4959 1 11
John O’Connor 2969 129 12 0.0 4345 12 0.00404 7 0.0 9302 6 25
Robert Ru ehlman 3205 145 18 0.0 4524 15 0.00562 11 0.1 24 14 11 37
J. Howard Sundermann Jr. 955 60 10 0.06283 16 0.01047 16 0.1 66 67 13 45
Ann Marie Tracey 3141 127 13 0.0 40 43 9 0.0 04 14 8 0.102 36 7 24
Ralph Winkler 3089 88 6 0.028 49 1 0.001 94 1 0.06818 3 5
Total 43 945 1762 19 9 0.0 401 0.0 0453 0.1 1294
Judge
Total Cases Disposed
Appealed Cases
Reversed Cases
Probability of
Appeal
Rank
Probability of
Reversal
Rank
Conditional
Probability of
Reversal Given
Appeal
Rank
Sum of Ranks
Penelope Cun nin gham 2729 7 1 0.00257 2 0.00037 2 0.14286 2 6
Patrick Dink elack er 6001 19 4 0.00317 3 0.00067 3 0.21053 4 10
Deborah Gaines 8799 48 9 0.00546 4 0.00102 4 0.18750 3 11
Ronald Panioto 12970 32 3 0.00247 1 0.00023 1 0.09375 1 3
Total 30499 106 17 0 .0 0348 0.00056 0.16038
Judge
Total Cases Dispos ed
Appealed Cases
Reversed Cases
Probability of
Appeal
Rank
Probability of
Reversal
Rank
Conditional
Probability of
Reversal Given
Appeal
Rank
Sum of Ranks
Mike Allen 6149 43 4 0.006 99 20 0.0 0065 7 0.0 93 02 4 31
Nadine Allen 7812 34 6 0.004 35 9 0.0 00 77 11 0.17647 10 30
Timothy Black 7954 41 6 0.005 15 12 0.0 0075 10 0.14634 6 28
David Davis 7736 43 5 0.005 56 15 0.0 0065 6 0.1 16 28 5 26
Leslie Isaiah Gaines 52 82 35 13 0.00663 19 0.0 02 46 20 0.37143 18 57
Karla Grad y 5253 6 0 0.0 01 14 1 0.0 00 00 1 0.000 00 1 3
Deidra Hair 2532 5 0 0.0 01 97 3 0.0 00 00 1 0.000 00 1 5
Dennis Helmick 7900 29 5 0.003 67 6 0.0 00 63 5 0.172 41 9 20
Timothy Hogan 2308 13 2 0.0 05 63 17 0.00087 13 0.15385 7 37
James Patrick Kenney 2798 6 1 0.0 02 14 4 0.0 00 36 4 0.166 67 8 16
Joseph Luebbers 4698 25 8 0.005 32 14 0.0 0170 18 0.32000 16 48
William Mallo ry 8277 38 9 0.004 59 11 0.0 0109 14 0.23684 14 39
Melba Marsh 8219 34 7 0.004 14 8 0.0 00 85 12 0.20588 13 33
Beth Mattingly 2971 13 1 0.004 38 10 0.0 0034 3 0.0 76 92 3 16
Albert Mestemaker 4975 28 9 0.005 63 16 0.0 0181 19 0.32143 17 52
Mark Painter 2239 7 3 0.0 03 13 5 0.0 01 34 16 0.42857 19 40
Jack Ro sen 7790 41 13 0.005 26 13 0.0 0167 17 0.31707 15 45
Mark Schweikert 5403 33 6 0.006 11 18 0.0 0111 15 0.18182 11 44
David Stockdale 5371 22 4 0.00410 7 0.00074 9 0.1 81 82 11 27
John A. Wes t 2797 4 2 0.001 43 2 0.000 72 8 0.50000 20 30
Total 10 8464 500 10 4 0.0 04 61 0.0 0096 0.20800