There are many ways to quantify the impact of attorney involvement and social inflation (of which attorneys are a significant cause) on insurance carriers.
One of the most striking examples is featured in a report by Jim Lynch and Dave Moore of the Casualty Actuarial Society, Social Inflation and Loss Development. The report shows what they calculated as the unexpected paid losses each year.
They find "evidence that social inflation in the 2010s caused paid losses to be more than $4 billion higher than predicted with standard loss development techniques,’ including more than $1 billion of unexpected paid losses in 2016 alone.