If you read the speech in your head, and try and do it without hearing any music or pauses, it seems like an extremely short, effectless 7 sentences.
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Wallace: I see a whole army of my countrymen here in defiance of tyranny. You have come to fight as free men, and free men you are. What would you do with that freedom? Will you fight?
Veteran soldier: Fight? Against that? No, we will run; and we will live.
Wallace: Aye, fight and you may die. Run and you'll live -- at least a while. And dying in your beds many years from now, would you be willing to trade all the days from this day to that for one chance, just one chance to come back here and tell our enemies that they may take our lives, but they'll never take our freedom!!!
Wallace and Soldiers: Alba gu bra! (Scotland forever!)
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So why does it work so well?
One, story buildup. Randall Wallace did a great job of making this speech a turning point by building up the scenes of scottish resistance to this point. If William can't turn the army around, then their cause will end there. So our minds give the speech gravity, because we know it's an important moment.
Two, direction. Gibson is many things including a master filmmaker. He knows just where to put beats in a scene to make it effective. Just how to cut it. And since he was doing the acting himself, he knew just how to play the scene.
Three, and this is the most important, music. Steven Spielberg has said that music is 50% of the movie. And it's true. And there has not been a contemporary film composer that could top James Horner for emotional impact. Glory, Avatar, Field of Dreams, Legends of the Fall, Titanic. The man was a master at enhancing the feelings of screen story. His passing is a great loss to cinema. But at least we can enjoy his masterworks such as this for years to come.
And these three aspects really encapsulate the essence of film craft.