Use of the word "opprobrium"

I have seen it maybe once every few years. Most people would have to consult a dictionary.

Very rare. In fact, I don't think I've ever heard anyone utter the word.

I've seen it only in novels set at the turn of the prior century, used in dialogue by well-educated characters.

You would only see it in scholarly writing. It's not especially rare there, I'd say.

Mr. TomI would like to know how common the word "opprobrium" is among native speakers.

On a scale from 1 to 1,000,000, it's not even as high as a 1.

CalifJimOn a scale from 1 to 1,000,000, it's not even as high as a 1.

In Google Books ( 155 billion words) opprobrium appears 13,555 times. Two books have the word in the title "The Opprobrium of Wanton Behavior" & "Opprobrium in Duluth"

That's about 13 times every 155 million words in published books
You have to discount a few of these, such as

AlpheccaStarsCJ - you were pretty close!

I'll take your word for it. I'm not up to doing the math just now.