And they use computers to do that analysis. There are many types of computer analysis and stylometry: verb/noun/adverb, subject-verb-object order, passive/active voice, length of words, difficulty of words/vocabulary, range of vocabulary, reading level, approximate educational level, era active, combinations of words, so on and so forth, used to break the text in to blocks by certain authors. These methods have been used to verify Pauline authorship of seven of his epistles, but they run in to major problems when the document to be analyzed is short (such as the Pastorals). The Book of Mormon has no such problem. It is long - very long. The Doctrine and Covenenants is long. The Pearl of Great Price is decently long, longer than any of Paul’s letters. There are many distinct texts known to be authored by Joseph Smith that can be analyzed and compared, something that can’t be done with Shakespeare or Paul - yet computer analysis can still determine this:
“This group of seven epistles were written by the same author”. It can’t determine who that author was. The author may not have been “Paul” - it could have been Barnabas, or Simon Magus himself. That’s outside of the realm of computer analysis without other documents in other corpi known to be written by the analyzed author.
“This Book of Mormon was written by X authors”. It can not determine who those authors were, only their numbers. However, in comparison with other texts known to be written by Joseph Smith, it can determine that he was one of the authors, as there are JS writings outside of the BoM with which to compare.
“These four plays of Shakespeare were written by one man”. It can not determine if Shakespeare wrote those plays, only that a single individual did, or the same group of individuals. If five individuals work together for an entire book, with no divisions between the authors - that every author had (name removed by moderator)ut in every sentence, and shared responsibility equally (a situation nearly impossible in reality), the book will appear to be the work of one author, a composite of the voices of five.
Even when done by primitive hand analysis (which hasn’t been used since the invention of the computer), one can’t tell who the authors are, only their number: that’s why liberal critics of Mosaic authorship call the sources “J” (Jahwist), “E” (Elohist), “D” (Deuteronomist), and “P” (Priestly source), instead of “Moses, David, Ezra, and Judas Maccabeus”. The authors are identified by characteristics of their writing (i.e. J uses YHWH, E uses Elohim, D wrote the Book of Deuteronomy and Kings, P added “Priestly” material, such as massive genealogies and rituals, and emphasized the transcendence of God), not by their actual historical existence (although they must have existed, in order to have written), or their actual personalities.
Most of those seem to indicate that the Book of Mormon was written by three or four individuals: Isaiah, Deutero-Isaiah, “Joseph Smith” (or his associate), Spaulding, and/or Rigdon.
The only ones that can be certain are Isaiah (because we have another work known to be Isaiac to be compared, namely the Book of Isaiah), and possibly Spaulding (if Manuscript Found is extant).