In life, possibly not; in Shakespeare, definitely so: Size does matter. This is one lesson of the Public’s new production of “Richard III,” which features the 4-and-a-half-foot-tall movie star Peter Dinklage. Mere height isn’t what’s lacking. The real gap is more elusive – call it stature.

That stature matters in Shakespeare will come as no surprise to people who have made the theatrical rounds lately. “Richard III” is the vile and bloody end to the Bard’s vile and bloody cycle of English histories. He wrote eight plays about the warring descendants of Edward III; New York has seen seven of them lately.

At every turn, outsized personalities abound, from the unhappy, poetic Richard II, who wants to “tell sad stories about the death of kings,” to Falstaff’s catechism on honor, to King Henry’s speech on St. Crispin’s Day, to Jack Cade’s mad rebellion. (“The first thing we do, let’s kill all the lawyers.”) Sometimes the characters make bold leaps across history’s chessboard; sometimes they try to swipe the whole thing clean. Either way, they make an awful racket, to audiences’ delight.

“Richard III” needs the charisma infusion at least as desperately as its predecessors. Like the “Henry VI” plays, it lives in constant danger of turning into a litany of nobles bickering with nobles. Actually, it is a litany of nobles bickering with nobles, saved only by the charming, ambitious, bloody-minded, deformed Richard. He has decided to win the crown. To get it, he’ll kill any man, woman, or child in his way, even the ones who aren’t family.

In Peter DuBois’s production, we see Richard first as a shadow – a huge shadow across the throne and the back wall of the stage. It’s a marvelous start, one that turns sour about 10 seconds later. In “The Station Agent” last year, Mr. Dinklage gave a wonderfully understated film performance; he said much without needing to say much. Richard has to say quite a bit, and from the opening soliloquy, “Now is the winter of our discontent,” the difficulties are clear.

Mr. Dinklage has a simple, direct way of speaking the verse; not overly musical, heaven knows, but he conveys the sense of the lines. Yet he lacks the extravagance, the foul relish, that the role demands. The whole guilty pleasure of this play is the way he admits us to every scheme. He has barely finished his opening soliloquy when he sets about seducing Lady Anne over the corpse of her husband – whom he murdered. “Was ever woman in this humor wooed?” he asks us after he succeeds. “Was ever woman in this humor won?”

Mr. Dinklage doesn’t convey the wicked glee that propels the play, and makes Richard one of drama’s great villains. I’m not sure Mr. Dinklage has villainy in him at all. Throughout the play, Mr. DuBois lets him err on the side of being sympathetic. When Richard’s mother curses him, he turns to mush. Up to a point, it’s in the text, but Mr. Dinklage hasn’t gone nearly far enough in his villainy to earn it.

The premise of the production hardly needs stating: As a dwarf, Mr. Dinklage might bring insight to playing a character singled out for his appearance. Mr. DuBois has cleverly spotted some ways to lash his concept to the text, as when Richard’s young nephew seems to ridicule him for being “little.” (Here again Mr. Dinklage nurses the insult.) But in some respects, Mr. Dinklage was an altogether wrong choice to play Richard. A story in the New York Post last week mentioned his irresistibility to the ladies; my companion at the show added her own urgent confirmation of his sex appeal. Yet Mr. Dinklage wears no hump, clubfoot, or dead arm onstage. Is his height alone supposed to be adequate grounds for people calling him “That bottled spider, that foul bunch-back’d toad,” and worse?

The bizarre casting continues. Isa Thomas gives the widowed Queen Margaret a haunting regal fury, and Roberta Maxwell is largely right as the widowed Queen of York. But the two younger widows, Kali Rocha as Lady Anne and Mercedes Herrero as Queen Elizabeth, are wholly inadequate. Some casting shortfalls can be tolerated. If you can’t come up with a Broadway leading man, that’s one thing – there aren’t many around. But to not find capable actresses who work Off-Broadway? The city is awash in them.

It’s a testament to Ron Cephas Jones’s talent that he succeeds as Clarence, Richard’s brother and one of his first victims. Lithe and intense, with a propensity for attacking the verse, Mr. Jones is no “simple, plain” Clarence. His scene with the two murderers is the best in the show; it has the focused energy the rest lacks.

Getting to see Mr. Jones in action is one of the chief selling points of the production, as is watching some sharp young actors make the most of their chances. In his speech before execution, Gareth Saxe (who plays Lord Rivers) confirms the impression left by his performance opposite Frances Sternhagen this summer: He may become a major presence. As Clarence’s conscience-stricken murderer, Matthew Maher gives the play much-needed relief, comic and sympathetic alike.

Riccardo Hernandez’s exquisite set uses all the available space in Martinson Hall, which before this was the Astor Library, and before that (to judge by the scenery) a prison for the Inquisition. Lurid red light shines through barred windows. Gloomy columns rise from battered rugs. A unifying touch, an old chandelier, hangs over it all. The physical aspects of the production have the vivid personality the acting mostly lacks.

In the end, Richard loses his crown, and his life, to the stripling he dismissed as “shallow Richmond.” Shakespeare’s last twist is that the future Henry VII really is shallow, making a banal promise of “smooth-faced peace” in the new Tudor dynasty. If the production works, we should miss the plantagenets, all the hours of thrills we’ve derived from their bad behavior. No such pangs strike here. A “Richard III” that can’t give guilty pleasure gives almost none at all.