Jeff Hornacek will be the 25th head coach the Knicks have hired since 1946, not counting interim placeholders. Exactly five of his 24 predecessors can be termed “successful,” by whatever parameters you choose to define the word.

This is not exactly the same kind of success ratio as, say, Trident gum, and the four out of five dentists surveyed who’ve recommended it to their patients who chew gum, and have for roughly the same amount of time as the Knicks have been trying to master the art of hiring a reasonably competent basketball coach.

Of the five success stories, just two are what you might call no-brainers. Joe Lapchick was one of pro basketball’s founding fathers, an Original Celtic, and so it was little surprise that he led the Knicks to three straight trips to the Finals and eight winning records in eight full seasons on the job. Pat Riley had won four rings coaching the Lakers — there never has been a more accomplished coach in any sport recruited to bring that hopeful mojo to the Apple.

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One might seem like a shoo-in choice but only in retrospect: Rick Pitino is in the Naismith Hall of Fame, almost entirely based on the body of work he built after getting the Knicks’ gig in 1987. Before that, he had appeared in exactly two NCAA Tournaments.

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Jeff Van Gundy and Patrick EwingPhoto: AP
Two of them were shots in the dark that, only later, we would learn were extremely smart selections since neither of their hirings created what you would call a deafening buzz. That’s what the Knicks hope they have in Jeff Hornacek, he of the 101-113 career record in two-plus years with the Phoenix Suns. And that has to be the way Knicks fans are rooting, too. They have to hope they have the long-awaited heir to Red Holzman and Jeff Van Gundy.

Holzman was 83-120 in parts of four seasons coaching the Hawks in Milwaukee and St. Louis, making the playoffs only once, 1956, which was a year when seven teams qualified for the playoffs in an eight-team NBA — and the Hawks had the seventh-best record. He spent the next decade in scouting purgatory. Anyone who would tell you they knew what Holzman would do with the Knicks was either lying or was Selma, his wife of 55 years.

Van Gundy mostly was known as the ghostly, ghastly presence sitting next to Riley and Don Nelson for 4 ½ years, and there was so little expectation when he was elevated to replace the exiled Nelson in 1996 that the day he was hired, he finished sixth in a newspaper poll asking readers who the Knicks’ next coach should be.

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Red Holzman with Earl Monroe in 1971Photo: New York Post
Both Holzman and Van Gundy serve as beacons now, proof that the right choice isn’t always the obvious choice, isn’t always the one that screams at peak volume.

We can accept that selecting a coach in any sport, with rare exception, can be a crapshoot, but lately when the Knicks have rolled the dice, they’ve been worse than Mush from “A Bronx Tale” — the gambling degenerate who was such a jinx that when he showed up at the track his crew would rip their tickets before the horses roared down the stretch, who wound up locked in the bathroom during dice games.

Since Dave Checketts went 2-for-3 in identifying Riley and Van Gundy (not realizing that Nelson planned to spend the ’95-’96 season in semi-retirement) the men who have made these decisions have tried just about everything.

There was the Riley-esque Sure Thing, Larry Brown, a Hall of Fame coach who turned into Red Klotz — the old Washington Generals boss, before our very eyes in one year. There was the Pitino-esque Scorching Hot Commodity, Mike D’Antoni — who only seemed truly happy on the job during the 10 days or so in which Jeremy Lin turned into Superman; he was out a few weeks later.

There was the Owner’s Pet (Isiah Thomas) and the President’s Pet (Derek Fisher), there was a second Hall of Famer (Lenny Wilkens), and there was a guy who had an NBA Coach of the Year trophy stashed on his mantel (Don Chaney). Judging which of these was a greater fiasco is like trying to identify your preferred natural disaster: hurricanes or typhoons or locusts.

The men in charge all have had pocketfuls of mulligans; this one is Phil Jackson’s. He couldn’t possibly have whiffed worse on Fisher. Maybe the laws of probability will tilt in his favor this time. It’s certainly one way to root.

If you happen to care about the Knicks, it is also the only way.

hilarious, can we ever get it right.....this sht is sad, funny, and true...smh