Going off on a tangent here, but the chances that Shakespeare truly invented any words or more than a handful of distinguishable uses is vanishingly small. What Shakespeare did was (1) be a half-educated middle class rube, (2) get popular enough that his colleagues wanted to collect his plays and a printer wanted to publish them, and (3) retained his reputation through the generations so that volume of plays wasn’t left to rot.

He was absolutely brilliant, don’t get me wrong (most Anti-Stratfordians are a weird combination of classist and ignorant), but the brilliance lies in the ways he played with the forms of poetry and drama, how he found the humanity in so many of his characters (though not all), and how he corralled all of his influences, cultural, literary, personal, and historical, into wholes that were way beyond the sum of their parts. Given the rigidity of Tudor education and expectations of the upper classes, I’d argue a unique voice like his would almost have to come from an “upstart crow.” From the perspective of linguistic novelty though, by and large his was just the first known use of words, which were likely in some degree of use in at least one of his various communities (actors, writers, Londoners, and Strafordians to name a few). The OED can only cite the earliest written sources its researchers have found. The fact that so many of “his” communities were poorly documented in the historical and literary record probably explains most of the words ascribed to him.