Alpha males don't lack faults - often their faults include arrogance and overconfidence - but the smart author twists things. Some of the sexiest alphas I've read about are the ones who doubt themselves. They doubt their worthiness and they view themselves as weak. Often, their arrogance arises out of their self-doubt. Those are the kind of alphas I like to read about and write about. Invariably, it's the strong heroine who bares their doubt and helps them heal.
I even have a favorite kind of alpha hero - the warrior. Why is this character archetype my favorite? Whether he's a knight or a cop, he is a protector who stands for the defenseless and he brings the villain to justice. A warrior is a man with a core of decency and a sense of justice. For the warrior, it's all about doing what's right. He will never be the good man who does nothing and lets evil flourish. These traits are very attractive to me. They are also wonderful to write about.
A warrior isn't just a tough fighter. He's so much more, because his every virtue-tenacity, principle, and decency-can be turn 180 degrees to create his vices-stubbornness, rigidity, and self-righteousness. Chivalry can be followed so blindly by your hero, it can become a detriment in his own life. It's a wonderful twist on the warrior archetype.
A few years ago, I discovered The Complete Writer's Guide to Heroes and Heroines by Cowden, LaFever, and Viders. They offer some wonderful perspective on creating the Warrior hero in their book. To create an outstanding alpha hero, I'd encourage writers to use this excellent book as a writer's bible. I've mined it for tons of ideas when I write and it's helped me to create interesting, complex heroes and I look forward to creating a few more wonderful warriors in my writing future.