Haggadah is a Midrashic Passage
The Pasover Haggadah is probably the best recognized Jewish text outside of the Bible; it is also one of the least understood. Who has not been frustrated by its apparent lack of clear organization, its seeming jumping from topic to topic, and its many digressions and tangents. One is faced with a collection of disjointed paragraphs that only tenuously connect to one another but without an overall apparent structure. If we recognize it as a midrashic commentary, however, these features, with which we are already familiar from the midrashic literature, become much more intelligible.
The introduction to the Malbim Haggadah includes precisely such an analysis by the 1894 publisher and compiler of this haggadah. For the complete translation see the Malbim's Haggdah (Targum Press, 1993 by J. Taub and Y. Shaw) or an adaptation at http://www.ohr.edu/yhiy/article.php/802.
The source verse for midrashic expansion is: And you shall tell to your son on that day saying, because of this Hashem did for me in my going out of Egypt. (Shemos 13:8). The key words and concepts of each section of the verse are repeated and recombined in the corresponding sections of the Haggadah.
This verse can be seen as containing 6 parts:
1. And you shall tell to your son
2. on that day
4. because of this
5. Hashem did for me
6. in my going out of Egypt
To elaborate (numbers in front of the paragraphs correspond with parts of the above sentence):
1. The first eight paragraphs, beginning with "Avadim Hayinu" and concluding with "The son who does not know how to ask", are an explication of -- And you shall tell to your son. Each paragraph contributes an essential element to describe the words "V'higadta l'vincha", "And you shall tell to your son": the basics information, the importance of telling it, that even the greatest Sages engaged in it, and the role of sons in this process.
2. The next section starts exactly with the words of the verse which it explicates - " (Ykhol M'Rosh Chodesh, Talmud Lomar) Bayom Hahu", on the day, and which describes the proper time for this obligation.
3. The third section corresponds to the third phrase, "Leimor -- saying", and contains the saying of the story of the Exodus. This section of the Haggadah starts with "Mit'chilah Ovdei Avodah Zarah Hayu Avoseinu" and continues with "Tzei u'lmad". These sections are followed by "Kammah Maalos Tovos" and "Al achas kamma v'kamma", which we say as praise.
4. Rabbon Gamliel's explanation of Pesach, Matzah and Marror, containing this part of the verse - because of this.
5. Here we say, "In every single generation one is obligated to look upon himself as if he personally had gone forth out of Egypt." The paragraph "Asah Hashem li -- Hashem acted for me" in the above verse.
6. The sixth section of the Haggadah begins with "L'phichach" "Therefore we are obliged to avow thanks", an introduction to the recital of Hallel, and the first half of Hallel itself. The latter, of course, contains in its second paragraph these very words "B'tseis Beis Yisrael Mimitsraim".
Thus the arrangement of the entire Haggadah turns out to be based on one verse, albeit the key one, that serves as the source of the obligation to retell the story of the Exodus.
I would also like to point out that within the general pattern, there are a number of other midrashic style sub-passages, such as in the third section, the midrashic commentary to Devarim 26: 5-8 or in the second section, the Mekhilta passage on B'Yom Hahu.
These features of the Haggadah would argue for its composition at the same time that the popularity of Midrashic approach was at its zenith, around the time of R. Akiva, R. Yishmael and their disciples. This conclusion is at variance with the one reached by the abovementioned introduction to the Haggadah which, on other grounds, concludes that it was written at the time of Rebbi and organized in its final form by R. Nachman.
Chag Kosher V'Someach.
1 The English adaptation of Malbim's Haggadah is followed by an appendix in which this introduction is ascribed to R. Naftaliben MaskilLeAison. It also argues that the Haggadah commentary was also composed by him "in the style of Malbim".
2 The Haggadah thus serves as a midrashic expansion of the verse; however, it may also be organized around this verse for mneumonic purposes. This arrangement allows everyone, even the not particularly learned members of the Jewish nations, to conduct a roughly the same Seder as everyone else.