(I don’t know whether you have the makings of a viable tort action or not as you’ve neglected to explain what caused the fall, where it occurred, the nature and extent of your injuries, nor the extent of medical treatment if any.
But let’s assume that you have a worthy tort action.)
Living in New York you must be aware that “billboard” PI lawyers are as thick as flies on a bloated camel carcass and just as ravenous. Meaning they are always hungry and competitive. Which is about as “typical” as they get.
So shop around and get one to take the case on your terms.
If you truly have a provable and case of negligence and have suffered substantial injuries and the potential defendant has deep pockets, then it is likely that a liability carrier has made you an offer.
Before seeking out the attorney insist that the liability carrier put its best offer on the table. If it is not acceptable, then find a trial lawyer willing to take the case with his or her percentage fee calculated strictly on anything over and above the insurance company’s last offer.
If you can’t find a trial lawyer willing to take the case on those terms - in other words, not grabbing a percentage of what is virtually in your pocket – then consider the company’s last offer as reasonably fair.
But keep your eye on the calendar so that New York’s statute of limitations of three years (NY CVP Section 214(5) doesn’t expire before a lawsuit is filed.