Rules of the GameUpdated Thursday May 21, 2015 by Ken Labrie.
The word "appeal" is frequently misused. Judgment calls by umpires are not subject to question or objection by a manager or coach.
9.02(a) Any umpire's decision which involves judgment, such as, but not limited to, whether a batted ball is fair or foul, whether a pitch is a strike or a ball, or whether a runner is safe or out, is final. No player, manager, coach or substitute shall object to any such judgment decisions.
The only "appeal" of this nature that a manager may make under the rules is if the manager feels that the umpire has misapplied a playing rule. In this case, rules 9.02(b) and 9.02(c) apply:
9.02(b) If there is reasonable doubt that any umpire's decision may be in conflict with the rules, the manager may appeal the decision and ask that a correct ruling be made. Such appeal shall be made only to the umpire who made the protested decision.
9.02(c) If a decision is appealed, the umpire making the decision may ask another umpire for information before making a final decision. No umpire shall criticize, seek to reverse or interfere with another umpire's decision unless asked to do so by the umpire making it.
Thus, for example, when a manager thinks the base umpire "blew" a safe/out call at first base and goes to the plate umpire saying, "Can I appeal that?" he has no basis under the rules for the request. The safe/out call is a judgment call, and thus not questionable. Even supposing it were, the question should have been directed to the base umpire, not the plate umpire. The plate umpire should, therefore, simply answer "No" to this question.
That being said, if the manager approaches the base umpire and requests that he ask his partner to see if he had a better angle, this is not an "appeal," simply a request. The base umpire is under no obligation to go to his partner, but may do so if he feels that his partner may have information that bears on the call.