This article aims to answer that question:

In our Article, we analyze the text of majority opinions of all Supreme Court Justices. Using a parsimonious model based on the Justices’ use of common function words (such as “the,” “also,” and “her”), we construct a variability measure for writing style. In most instances, Justices have variability scores that are distinguishable from one another. Moreover, even Justices with comparable or identical variability scores exhibit distinct writing styles based on their different use of function words. Our analysis then allows us to accurately predict authorship in pairwise comparisons of Justices.

More importantly, our model also allows us to evaluate how Justices vary in their writing over their tenure on the Court and in comparison with other Justices. We find that current and recent Justices report significantly higher variability scores than their predecessors, supporting the anecdotal evidence that Justices on average are relying more on their clerks in the opinion-writing process. Moreover, some Justices – most notably Justice Sandra Day O’Connor and Justice Anthony Kennedy – produce variability scores that are not only higher but also vary considerably from year to year, suggesting an even greater reliance on clerks. We test the validity of our model by analyzing the opinions of two judges known to write their own opinions, Richard A. Posner and Frank Easterbrook.  The variability of Judge Posner’s and Judge Easterbrook’s writing were markedly lower and more consistent than any current or recent Justices on the Court.

From the article:

We find that current and recent Justices report significantly higher variability scores than their predecessors,29 supporting the anecdotal evidence that Justices on average are relying more on their clerks in the opinion-writing process.30 Moreover, some Justices—most notably Justice Sandra Day O’Connor and Justice Anthony Kennedy—produce variability scores that are not only higher31 but also vary considerably from year to year,32 suggesting an even greater reliance on clerks. We test the validity of our model by analyzing the opinions of two judges known to write their own opinions, Richard A. Posner and Frank Easterbrook.33 The variability of Judge Posner’s and Judge Easterbrook’s writing were markedly lower and more consistent than any current or recent Justices on the Court.34

About their methodologies:

Our analysis relies upon function words, which are common words—for example, all, have, not, than—whose usage frequencies are largely independent of subject matter.42 In the words of one statisti- cian, this approach is “topic-free in the sense that the relative fre- quency with which an author uses, for example, ‘with,’ should be the same regardless of whether the author is describing cooking recipes or the latest news about the oil futures market.”43

We considered other approaches, including such larger-scale fea- tures as sentence length, paragraph length, or the frequency of mul- tiword phrases and such smaller-scale features as frequency of specific punctuation (e.g., comma, semicolon) or of particular letters. These approaches, however, did not meaningfully improve our results. Therefore, to situate our analysis within a unified methodology, we present results only from the use of function words.