One never insists on the originality of Shakespeare's plots, but wonders at the alterations he wrought to such serendipitous effect. Yes, Shakespeare used formulas and stock characters, even in Hamlet, whose underpinnings spell out the Senecan revenge "formula" with a ghost, a dumb show, vengeance, delayed action, madness, and so forth. In Hamlet, however, Shakespeare integrates the ghost and dumb show into the hero's motivations. No mere spectator, King Hamlet's ghost imposes revenge on his son; no set piece, the dumb show is the "mousetrap" by which Hamlet "catch[es] the conscience of the king" (2.2.605).
For the rest, the Bard tenders a "two'fer": two revenge tragedies, each with vengeance, delayed action, and madness, suffered by two families, each with a slain father, an avenging son, and a female of compromised virtue. One father expires mysteriously before the play opens; the other falls midway. One compromised woman is Gertrude, whose incestuous marriage Hamlet seeks to avenge; the other is Ophelia, whose chamber he has entered "unbraced" and "ungarter'd" (2.1.75-77).
Hamlet is the fulcrum for both plots. In the process of reconciling ghost-messages, Christian doctrine, and general reluctance to perform violence, the prince, newly certain of his father's poisoner, unwittingly becomes the murderer of Polonius. He thus incurs two burdens: avenging his father's death and requiting Polonius's.
Delay is another part of the formula, and Hamlet duly hesitates to kill Claudius. But Shakespeare gives Hamlet reasons, besides his overwhelming melancholy, for delay. First, ghosts are not necessarily reliable messengers; Hamlet wants surety of Claudius's guilt. Second Claudius at prayer gives pause to the Christian prince, whose father's ghost laments departing life "with all my imperfections on my head" (l.5.79). Third, Hamlet is conscious throughout of the eternal penalties for slaughter and self-slaughter, the frightening unknowns that may follow death, and the dreadful finality of worm-eaten flesh.
In contrast, no mystery enshrouds Polonius's death. Laertes rushes home from France to avenge both his father and his sister. Ironically, his revenge is delayed by Claudius in deference to Hamlet's "madness," and Laertes lives to repent his own rashness.
Finally, the requisite madness is likewise divided between the families. Hamlet claims to be "but mad north-north-west" (2.2.378), and he instructs his mother "that I essentially am not in madness, / But mad in craft" (3.4.l87-88). Some critics believe he protests his own madness; but he seems sane against Ophelia's mad songs and "self-slaughter." Interestingly, in Polonius's family, madness and revenge are disjointed; no questions arise about Laertes' sanity.
In a play like Titus Andronicus, the madness and vengefulness centered in Titus march inexorably, and slowly, toward a single revenge. In Hamlet, Shakespeare gives us, not merely a sub-plot, but a parallel plot which backlights the principal characters against an aura of universality, creating the illusion that Hamlet is "Everyman." Dividing the burdens of the revenge plot humanizes the protagonist and universalizes the plot. Dividing in two equals multiplying by infinity. Arithmetic doesn't work that way; Shakespeare does.