There is part of the Amalek encounter which is rarely considered but forever re-enacted. It may have been carefully crafted by Moshe Rabbeinu but seems to have spontaneously unfolded. It certainly paints a remarkable picture.
Our snapshot of that battle has Yehoshua leading the soldiers under the watchful and worried eye of Moshe Rabbeinu, who is praying intensely for their welfare. The mishna further describes how his prayers inspired faith and courage among the soldiers and that faith won for them victory. However there is another part of the story recorded in the Pirkei D'rabi Eliezer (quoted by the Ramban 17:9.)
This is the story reserved for oral mesorah: somehow, drawn from their tents and seeing Moshe davening, every Jew began to daven as well. Soon every Jew bowed down in synchrony with Moshe. When Moshe proceeded to entirely prostrate himself, so did they and when he spread his hands upward in prayer, they followed suit. Communal prayer, as we know it now - tefilah betzibur - came into its own, to forever become a part of our people.[1]
Ramban focuses on Moshe's personal prayer and emphasizes the deep concern that Moshe had for his people, now entirely untested in battle and pitted against a people whose prophetic destiny is symbolized by the sword. Accordingly, his fear for their safe return and his anxiety over their bravery pushed him to daven with unprecedented intensity. Furthermore, the Ramban intimates that Moshe was laying the groundwork for the redemptive prayers of Eliyahu and Moshiach. Similar to chet ho'egel, the Amalek episode highlights the power of prayer even as it introduces public prayer into our story.
No doubt Esther and Mordechai learned well from their forebears and before they battled Amalek, they called upon all Jews to daven together. Esther and Mordechai also highlight these prayers as they refer to the Megillah as "words of fast days and supplication".
That the institution of prayer became strengthened during our battle with Amalek underscores the fact that tefillah is our most articulate denial of the G-dlessness and randomness which Amalek strove to spread. By attacking our people who were nourished by bread from heaven found at our campsite every morning and were snatched from suffering through the miracles of the plagues and the Yam Suf, Amalek wanted to rebuff the awe that we had garnered from all around us. A victory for Amalek would teach that our wheel of fortune is like all the others and would turn our history into the lore of an ancient people. Prayer is the refutation of randomness. The absolute synchrony of our military success and Moshe's prayers corroborated all at once the uniqueness of our people, the power of prayer and the designed control that belongs to our creator.
But there is another part to the story. Amalek, we are told in Parshas Ki Teitzei, infiltrated us via the weak and unaccompanied. Our people as a whole became threatened from without when there were Jews at the back of the camp, who may have felt abandoned but most certainly felt unnecessary. As a reaction, Moshe's public prayer, that indeed came forth from the hearts of the entirety of our people, welcomed every Jew and spoke to the precious place that every Jew has among us.
Thus Moshe's prayers focused the heart of every soldier on Hashem in their time of need even as he made every Jew share in those prayers and feel connected and elevated through them. In some way the tefilas hatzibur elevated every Jew to feel empowered to daven like Moshe Rabbeinu!
[1]This comment of the Pirkei D'rabi Eliezer becomes an important support for the oft quoted insight of the Rov that public prayer is more than a tool to aid individuals in fulfilling their mitzvah. Carefully reading the precise language of Rambam, the Rov pointed out that it is a prayer form of its own.