The unassisted triple play is the rarest play in baseball, for which there is a specific statistic and which is actually a single play. The rarest of all is the triple play without assistance from an outfielder, made only once in the history of professional baseball, by Walter Carlisle. This occurs when an outfielder completes all 3 putouts in an inning without the help of his teammates (for example, without throwing the ball to anyone). Unlike most double plays, which are usually made with dirt balls, three-pointers are usually the result of line hits that are caught when runners have left their base, either as a result of a hit and run play, a double steal or a spectacular capture of a ball that runners assumed would fall to the ground. Triple plays, even without assistance, are not extremely difficult for Major League Baseball players to achieve; their rarity is because they depend on the specific circumstances that arise in a game.
Retrosheet maintains a complete database of every triple play made in a major league game, with all the details available, compiled by Chuck Rosciam and Frank Hamilton. There have only been 15 such three-pointers in the regular season in MLB history, one of which took place in the World Series (second baseman Bill Wambsganss of the Cleveland Indians in the fifth game of the 1920 World Series on October 10, 1920 (Boxscore)). To this day, Pignatano remains the only player in major league history to end his career by making a triple play. The rarest of the rare plays, which I'm sure will never really happen but which would be incredible to see, would be one that can only happen under the rules of the National League. But are they all that unusual? We wanted to delve deeper, explore and discover the rarest work in baseball.
As mentioned in the other answer, this would be a situation in which a team turns around what is already a triple play, but must register a “fourth out” to cancel a streak that would otherwise count. The only type of triple play that seems to occur most is in the vicinity of second base, in which an outfielder can catch a lining and step on second base to catch the main runner, and simply mark the other runner when he approaches that same base. However, it turns out that the antithesis of an unassisted triple play (three errors made by a player in play) is even rarer, since it has only happened once, as far as I can see in the history of MLB. A triple play (abbreviated TP) occurs when all three outs in the inning are recorded in the same play. Another common sequence (insofar as these plays can be called common) is an in-line drive to the shortstop or second baseman who is caught without the runners realizing it or after having taken a big advantage (such as in the case of a hit and run), and runners are ejected if they fail to score. A triple play (referred to as TP) is the rare act of making three outs during the same inning, such as a continuous play.