Does anyone have access to umbrella/excess liability claims distribution data? A data distribution would tell what percent of claims you would be protected against at a given policy limit. As an example, the data may show 98% of claims are below $1M and 99% are below $2M. (In reality, I suspect the difference between $1M and $2M is less than 1% and both cover way over 99% of claims. But, just a guess.)
With one exception*(that I can think of), asset levels do not impact the above. Whether you have $1M or $2M in assets, both have the same risk of being sunk by a >$3M settlement or judgement. In other words, your risk of a large event does not change with a change in net worth. (see the exception below)
*That exception, yes you are more of a target as your wealth increases. Like bank robbers, plaintiffs tend to go where the money is.