The statistics on how often a trial court judge's decisions are reversed on appeal are not routinely compiled, the first step is to search for all appellate court opinions in which the judge's decisions were appealed. This can be done on the fee-based Westlaw systems. In Westlaw you would search the Syllabus field. Since middle initials are sometimes left out, it is usually better to search for John /2 Doe (where /2 means the words must appear within two words of one another) rather than "John P. Doe" (where the quotations marks tell the system to search for the words as a phrase.) Of course, if there are many John Does, the quotation marks may work better. In Westlaw it would be sy(john /2 doe). Westlaw is available for public use at no charge in the Law Library.
Unfortunately, the opinions coming straight from the appellate courts do not include the name of the trial court judge, so a search of the appellate court archive on this Web site would not be successful.