Eric Helland, Daniel Klerman, Brenda Dowling, and Alexander Kappner have written Contingent Fee Litigation in New York City. The authors were able to conduct this study because, by court rule, lawyers practicing in parts of New York City must file data about contingent-fee settlements. (I wonder why other courts don't require the same.) One thing I found interesting is that almost all lawyers charged a one-third contingency — the statutory maximum. That is, there was almost no competition among lawyers below the cap. Here is the abstract:
Since 1957, New York courts have required contingent fee lawyers to file “closing statements” that disclose settlement amounts, lawyers’ fees, an accounting of expenses, and other information. This article provides preliminary analysis of these data for the period 2004-2013. Among this article’s findings are that settlement rates in New York state courts are very high (85%), that very few cases are resolved by dispositive motions, that litigated cases and settled cases have almost exactly the same average recovery, that median litigation expenses are 3% of gross recovery, that claims are disproportionately from poor neighborhoods, and that attorneys’ fees are almost always one third of net recovery, which is the maximum allowed by law.