Hamilton County judges try thousands of cases per year. In an overwhelming majority of the cases disposed, the verdict stands as rendered. However, some cases are appealed, some of the cases are reversed. The Enquirer conducted a study of cases handled by Hamilton County judges over a three$-$ year period. Shown in the below links are the results for $182,908$ cases handled $($disposed$)$ by $38$ judges in Common Pleas Court, Domestic Relations Court, and Municipal Court. Two of the judges $($Dinkelacker and Hogan$)$ did not serve in the same court for the entire three$-$year period.

Common Pleas Court

Domestic Relations Court

Municipal Court

The purpose of the newspaper's study was to evaluate the performance of the judges. Appeals are often the result of mistakes made by judges, and the newspaper wanted to know which judges were doing a good job and which were making too many mistakes. You are called in to assist in the data analysis. Use your knowledge of probability to help with the ranking of the judges. You also may be able to analyze the likelihood of appeal and reversal for cases handled by different courts.

Prepare a report with your rankings of the judges. Also, include an analysis of the likelihood of appeal and case reversal in the three courts. At a minimum, your report should include the rank of the judges within each court. State the criteria you used and provide a rationale for your choice. Which court shows a better quality performance.