The larger the law department, the larger the law firms that receive the most payments?

Does the size of a law department correlate with the number of lawyers in the major firms that law department retains? I hypothesize that the bigger the department the larger the law firms it pays the most. In other words, for a group of law departments, find out from each of them the average number of lawyers in the five law firms the department paid the most last year. Then run a correlation of that group of averages against the number of lawyers in each department (See my post of April 5 and May 10, 2005 on correlation and Jan. 14, 2007 on the amount of variance in an independent variable explained by correlation.).

The reason for this correlation is that large law departments, who usually support large companies, are more likely to bump into big or novel legal issues. Both kinds of issues call for specialized expertise or ample boots on the ground. This is another reason why there is some turnover of law firms: companies outgrow law firms that do not match them in resources and knowledge.