In Missouri,  first degree murder is defined as knowingly causing the death of another person after deliberation. Second degree murder is defined as knowingly causing the death of another person. The sole distinction is the element of deliberation.  Second degree murder is, therefore, a "lesser included offense." meaning that if the judge or jury found that the defendant had satisfied all the elements except for deliberation, the proper verdict would have been second degree murder.  So if the prosecutors overcharged, it would not have been to their detriment, except morally.