Most Judges will agree that once a jury gets a case, they make decisions not based upon law, but upon personality: who do they like and who do they believe? The legal questions are all decided before trial. The jury is left only to decide matters of fact, based upon their own determination on credibility, and often, likability.
The motivation for bringing a legal action, will almost always reveal critical keys for unlocking it. If, for example, the aggrieved party is acting because he wants to prove that he was right, sometimes money alone can't do that: an acknowledgement, public exposure, an agreement to take steps to prevent such misconduct in the future may be necessary. If, on the other hand, the lawyers have become passionately embroiled in a contest of strength and skill between them, sometimes a few rounds of litigation, or even a concession or two may be what's needed to empower the advocate to recommend settling the lawsuit at any amount.
The cautious mediator will give voice to every participant's true objectives by asking them probing questions early on which are designed to dig deeper than the initial demands or offers and to uncover the true motivations for moving forward or pushing back. It is only after this initial sensitive work is done that the process of negotiation can begin in earnest.