Home Run is Only HR for both batter and pitcher--how rare?

Recently, a friend asked me the trivia question, “What Hall of Fame player hit a HR in his first major league at-bat, and then never hit another?” I knew the answer, Hoyt Wilhelm.

When I looked up more about Wilhelm’s HR, I discovered that he hit it on April 23, 1952, against a thoroughly obscure pitcher named Dick Hoover, whose career spanned exactly two games. It was the only HR ever given up by Hoover.

This got me to wondering how rare this might be. How many home runs have been both the only HR struck by the batter and the only HR given up by the pitcher?

If no one knows, useful fallback information would be, What % of all-time HR’s have been struck by single-HR batters, and what % have been given up by single-HR pitchers? This would give an idea about how rare the confluence should be.

If there are any, I’d guess that those involved are among September callups, in the majors for a cup of coffee once the rosters expanded?

Well, one number from Baseball-Reference: they have 1,222 careers with HR = 1 since 1901.

So now who wants to go through those 1,222 players?

And only 725 pitchers with careers with 1 HR allowed.

How many home runs total since 1900?

I’m seeing 130,986 in the AL and 124,315 in the NL since 1901.

So, 255,301.

Hmm. So 0.48% of all HR’s are batter solos, and 0.28% are pitcher solos. The product of those two numbers is 0.00134%, or one in 74,000. So it looks like it might be pretty rare.

Of course HR’s were less common in the early 1900’s, so there were probably more onesies then. But still, probably not a lot.

Anti-Federal League bigot!

There is at least one more –

Hal Keller of Washington off James Atkins of Boston, Sept. 29, 1950