I think you might be confusing phalanx:
Each individual hoplite carried his shield on the left arm, protecting not only himself but the soldier to the left. This meant that the men at the extreme right of the phalanx were only half-protected. In battle, opposing phalanxes would exploit this weakness by attempting to overlap the enemy's right flank. It also meant that, in battle, a phalanx would tend to drift to the right (as hoplites sought to remain behind the shield of their neighbour). The most experienced hoplites were often placed on the right side of the phalanx, to avoid these problems. Some groups, such as the Spartans at Nemea, tried to use this phenomenon to their advantage. In this case the phalanx would sacrifice its left side, which typically consisted of allied troops, in an effort to overtake the enemy from the flank. It is unlikely that this strategy worked very often, as it is not mentioned frequently in ancient Greek literature.
During deployment in the Republican era, the maniples were commonly arranged in triplex acies (triple battle order): that is, in three ranks, with the hastati in the first rank (that nearest the enemy), the principes in the second rank, and the veteran triarii in the third and final rank as barrier troops, or sometimes even further back as a strategic reserve. When in danger of imminent defeat, the first and second lines, the Hastati and Principes, ordinarily fell back on the Triarii to reform the line to allow for either a counter-attack or an orderly withdrawal. Because falling back on the Triarii was an act of desperation, to mention "falling on the Triarii" ("ad triarios rediisse") became a common Roman phrase indicating one to be in a desperate situation.