Polygamy:
Some men having a chance at a huge family. Most women having a chance at a family, but with a shared husband. Many men having no chance at a family at all.
Monogamy:
Most men having a chance at a family. Most women having a chance at a family.
Now consider that the more one has to lose, the better behaved one is. When men have a chance for a family, they'll do what is needed to make the attempt for a family (normally being productive members of society), after which they get far more needs met than when alone (consider that loneliness is quite dangerous for a person) and they likely have more to lose (especially if they have children). Thus they are more behaved.
But in a polygamous society, there is far less of a chance. So more men decide to not play by the rules. They will seek out more dangerous means to meet their immediate needs.
All this being said, it isn't the marriage that matters. It is the family that does. A society that only allows monogamy on paper, but which allows a polygamous marriages, and where a divide begins to exist meaning that you have many men without a chance of having a family will have the same issues.
Also, I'm not to sure what happens when many women don't have a chance for a family. While one might think it would work the same, there are a few key differences. A man can be responsible for multiple simultaneous pregnancies, but a woman cannot. A woman has, historically, had a level of assurance of the legitimacy of their children that a man does not, and on average men tend to be more physically powerful than women. Also of note is that those last two factors stop being a significant difference with technology (paternity tests and guns being respective examples), so historic data may not fit what trends we will see in a technologically advanced society. (To say nothing of technology increasingly being able to meet a person's needs, which will increasingly make it harder to plot future events based on past data.)