Hayes estimates that he examines about 40-50 cases annually, but files only about five per year.

He explained: You might have a good case of infringement, but the validity of the patent is suspect. Or, you might have the greatest patent, but no damages, or the damages are more speculative than not. Even if you vet them, frankly, the long-run chance of success is probably less than 50 percent. It's better than Vegas, but not much.

Finding the right formula

Each case will dictate the specifics of a contingent fee arrangement, but a few basic models exist.

One option is a straight contingent fee based on the recovery, typically 40 percent or more. A law firm may take 40 percent of the recovery and pay the expenses, or it might take 35 percent of the recovery and have the client guarantee the first $1 million in expenses.

More common, however, is a hybrid or blended fee in which the firm reduces its hourly rate in exchange for a percentage or bonus for achieving a positive result. One example: A law firm offers a 50 percent discount on fees, the client pays expenses and the firm gets 25 percent of the recovery.

The parties can also negotiate a contingent fee based on some result, either inside or outside the litigation, said Hughes.

For instance, the fee may be pegged to achieving an injunction or retaining or transferring jurisdiction to a favorable location with shorter dockets.

Sunstein emphasized that the parties must address their expectations of the litigation in advance, such as what constitutes a reasonable settlement and under what circumstances the client and law firm would accept a settlement.

He also noted that a contingent fee arrangement in patent cases can get quite complicated, such as where royalty payments over time are involved, and the sharing of settlement proceeds need to be layered - such as evenly sharing the first $10 million and splitting recovery above $10 million on a 60-40 basis.