I do New York Times Sunday crosswords. Only. If that sounds arrogant, given how difficult those monsters are, I plead guilty.

But I also readily concede that I solve one — and “solving” a crossword puzzle means 100 percent accuracy — about once out of 20 puzzles. All it takes is one wrong letter … and you have failed.

A Sunday puzzle I worked on the other day came down to one letter. I was that close to winning.

The final letter involved two clues. And one of them was: “Forerunner of baseball.” Seven letters.

I guessed … and I was wrong. But I discovered an interesting notion about a sport played in Britain which may have led to cricket as well as baseball.

Tip-a-cat.

No, really.

When I saw the “forerunner of baseball” clue, I was sure I would get the answer. After 40 years in sports journalism, and nearly six decades of deep interest in baseball, how could I not get it?

But I could not. “Cricket” didn’t jibe with any of the other letters in t-i-p-a-c-a-X, and baseball purists resist the notion that ball came from (ick) cricket. “Over-the-line” and “work-up” and “three flies up” and “broomball” didn’t fit.

But I had the first six letters, and I went back and checked them: T-I-P-A-C-A … I was sure of all of them. But the seventh letter … I didn’t know.

And what in the heck is tipaca … something? How could I not be aware of this key game that began with those six letters?

The clue intersecting with the “forerunner of baseball” was “Grammy winner Jazz drummer … Lyne Carrington”. Five letters, and I had what I believed to be the final four — ERRI.

I had no idea of this person’s first name. Not a jazz fan.

I decided this could go one of two ways. (And guessing correctly to finish a perfect puzzle most certainly counts.)

Was it TIPACAP and PERRI? Or TIPACAT and TERRI?

I sat and looked at it and sat and looked and I decided TIPACAP was more likely. Because they wear caps in baseball, and cats have never been a part of baseball’s story. And “Perri” could be a hip jazz person’s first name.

I was wrong. I lost the crossword game.

But I won some interesting info on a game at least 250 years old, once I started investigating the clue that crossed me up.

The name is usually rendered tip-a-cat or tipcat or even one-a-cat, the Encyclopedia Britannica tells us.

(The longest description I can find is given in a book entitled Encyclopedia of British Rural Sports.)

“Tip-a-cap”, apparently, is a game in which a player holding a bat or broom handle stands over a “billet” of wood (“billet” being old-fashioned English for a chunk of wood) three to six inches long, with the ends tapered.

The batter strikes one end of the billet with his bat, and when the chunk of wood spins up in the air, the batter hits it as far as possible.

The description is a bit hazy on what the point of it is, beyond “distance hit” being a deciding factor in winning.

The “Rural Sports” authors suggest other forms of the game that seem to strongly suggest it as a forerunner of cricket.

Anyway, hitting a flying object with a stick/bat/broomhandle seems to be something of a widespread human activity and tip-a-cat appears to extend back to the 16th century. Making it even older than Tommy Lasorda.

Oh, and the jazz drummer, in the crossword puzzle? Terri Lyne Covington.

I’m more likely to remember “tip-a-cat”, if I ever see it again.