Your Dodge bonus is a component of your Defense - for a character that has bought nothing by Defense figuring out the dodge bonus is a simple matter of dividing their defense bonus by 2 and rounding down.
Knowing the dodge bonus is important for two reasons.
The Dodge bonus doesn't apply doesn't apply when stunned, flat-footed, etc, so the character is basically stuck with half their defence. In a lot of ways, think of it like d20's Dex bonus to defense
A character can spend a hero point to double their dodge bonus (see page 121, bottom left column), basically increasing their defense bonus by half.
The fifty-fifty split can get skewed when a character buys ranks in Dodge Focus, which essentially gives them an additional +1 dodge bonus per rank.
Quick example:
Kung Pow, the martial arts hero, buys Defense +10. Whens surprised, stunned or otherwise unable to defend himself, his defense against attacks is 15. When aware and fighting in most situations, his defense is 20. When he spends a hero point to dodge, his defense is 25.
Lizard Man, whose defense usually relies on agility rather than competent combat technique, buys Defense +4 and 6 ranks of Dodge Focus. WHen surprised, stunned or otherwise unable to defend himself, his defens against attacks is only 12. When aware and fighting normlaly, its 20. When he spends a hero point to dodge, his defense goes to a whopping 28.
