When you read a play, you are not getting the complete product as imagined by the playwright. Plays, even though they are considered a form of literature are created to be brought to life on the stage. So a play is not actually complete until living breathing actors speak the text aloud, and move through space. When you read a play you have to create the world of the play, the characters, and all of the action only in your imagination. But when you watch a live theatre production, the directors, designers, actors, and technicians have done much of the work for you already. And with a stage production, you have multiple interpretations of the play's text (actors, designers, director), and on multiple levels: visual, audio, kinesthetic. Whereas simply reading a play on your own means there is only one interpretation; yours, and unless you are reading aloud, you only see words written on a page. Studying and analyzing a play text is still important, so we can understand how they work but since plays are meant to be performed, live theatre productions are the essential final step to bringing a play to life.
Aristotle's six elements still hold true when analyzing a live theatrical production, but some of the elements take on more of a significant role because they claim more of our attention. For example, while reading a play, Plot and the Central Idea are really important, but in a live stage production, elements such as Spectacle and Music naturally take precedence. A genius designer can make the element of Spectacle actually embody the play's Central Idea, while demonstrating Character, and moving the Plot forward. There are a few more additional elements that also need to be considered when we are discussing Performance Analysis. Obviously the Story, Character, Central Idea are still essential but how those elements are expressed by the "Style" of the production i.e. the dramatic/theatrical style used, the overall design, materials used, acting style etc. is also really significant. The "Conventions" of the production i.e. acting conventions, scenic conventions, the use of musical or movement conventions. Finally, the "Audience" also comes into consideration i.e. are the audience intended to be participants in the play or observers? How do the actors interact with the audience? How does the audience respond? How do the audiences' responses fit with my own?
As an example of how the performance elements of Character and Spectacle can impact the balance of a play, watch the following video of U of S Associate Professor, Natasha Martina in the Department of Drama discussing the impact of movement within a theatrical performance.