This is way too serious a question for an off-the-cuff response, and anything more meaningful would require a lot more information. If you have an attorney, your attorney can give you a good answer, if not, I strongly suggest you DO NOT attend a mediation without one. Good luck!
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There are no "caps" in New York (yet) so the max you can settle for is the best offer the defendants are willing to make. Apparently your lawyer has not told you what to expect at the mediation, which is actually a good thing. It's never a good idea for the client to ask an attorney what has been demanded, or for an attorney to offer an opinion on the value of a case before there is money on the table. There are just too many variables involved.
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Since you are dealing with a minor, a Judge will have to approve any settlement that you agree to. They Judge who approves the settlement will understand that malpractice cases are expensive to try, and difficult to win, and that a settlement is definite. What is fair depends on the injury and what will be required in the future. This needs to be addressed with your lawyer and the mediator. You certainly do not give enough information here.
If you have an attorney you should direct your question there. If not, I STRONGLY suggest consulting an attorney RIGHT AWAY. Please view this video as it may prove helpful when answering your question: