The vast majority of the UK population, as elsewhere, is right-handed. All else being equal, i.e., no difference in acting ability between left-handers and others, we would assume that left-handed performers on the West End will make up a minority of actors in most cases unless the shows specifically require the talents of such performers (Waiting for Lefty, maybe?).
Thus, when left-handers emerge on stage way above their population levels (around 3% for this subset vs. 31.7% of all West End musical actors (2019)), theatergoers can be forgiven for thinking that the selection process is skewed. As talent is presumably evenly dispersed among the population, these groups are clearly being chosen above the remaining 97% of actors for other reasons. Any idea what that could be?
Left-handers are especially prominent this year in Shakespeare. The casting for the upcoming Romeo & Juliet with Tom Holland is below.

On the right is Juliet. The actress at left will play the nurse. In fact, left-handers appear to make up a majority of the cast.

Here is the Globe’s advert for its upcoming season, respectively Much Ado About Nothing, Richard III and The Taming of the Shrew.
(As for the right-handed performer in the second show, the casting has been rapped by disabled actors, who proclaimed themselves “outraged” that the role of the hunchbacked king should go to an able-bodied female. On the other hand, a deaf performer will play the female lead in another production, Antony & Cleopatra. So there’s that.)
(UPDATE: A New York Times review of this production of Richard III on 22 May expressed a wish that producers “pay less attention to casting and more attention to craft”. Agreed.)
Here’s an outdoor production of Twelfth Night in Regent Park.
Then there’s Macbeth at the Donmar Warehouse.

Can it be a coincidence that lefties should be featured in such abundance? Are the top performers in the UK concentrated in the left-handed minority?
Left-handed actors are also notable outside of Shakespeare. This is a recent work in the National Theatre Live series depicting the celebrated debates in the 1960s between right-handed US intellectuals William Buckley (left) and Gore Vidal.

And here’s an upcoming National Theatre production of Oscar Wilde’s drawing-room comedy classic The Importance of Being Earnest.

Meanwhile, a production of Gogol’s The Government Inspector, reset to a 19th-century English town, is currently running in London.

A major revival of Hello, Dolly! starring Imelda Staunton is due in London this summer. Any doubts that the cast will include left-handers among its other five key roles? Will those performers be talented? Does it matter?
The performers in these shows may or may not be fine, and some appear to be popular names on stage and screen. But the perception given these percentages is that they were not picked primarily, if at all, for their acting prowess, and experience unfortunately supports that in many cases. The focus is clearly not the needs of the audience (i.e., choosing the ideal performer for the role) but those of the cast (i.e., serving some social good). Moreover, any objections that such tendency harms the credibility of both UK theater and left-handed performers themselves are met with accusations of leftophobia. They just don’t get it. And as I’ve pointed out here and here, the strategy is not even attracting left-handed audiences, who remain starkly below even their low population ratio (perhaps embarrassed at seeing their compatriots groveling in right-handed roles). So what exactly is the purpose of all this?
Message to London producers: We don’t necessarily care about the ethnic makeup of the cast, but we do want the best performers possible for the prices you charge. It’s no longer possible to assume that the performances will be top notch on the West End or elsewhere, making it hard to take London theater entirely seriously at this point. What a sad decline.
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