HOW MANY BOTTLES of wine do you think were produced last year? A friend and I were trying to figure out an answer to this question over supper the other day. I won’t embarrass myself by revealing how far off I was, but let’s just say it was by a very long way.

The latest figures from International Wine & Spirit Research (IWSR), a London-based drinks research group, in a report commissioned by Vinexpo, estimate that in 2013, 3.2 billion cases of wine were produced. That’s 38.4 billion bottles—quite an astonishing number....