The “paradox of luck and skill,” as explained by Pomona College economics professor Gary Smith, could be as good an explanation as any for your busted NCAA tournament bracket.

The premise is that the more skilled the athletes – and the more even the skill level between individuals or teams – the greater the influence that good (or bad) fortune will have on the outcome of a single contest. In the win-or-go-home crucible of March Madness, where every team has at least a few quality players, luck might not merely be the way the losing team and its fans explain away the result.

“You can take the four best golfers in the world – any sport, but let’s do golf because it’s head-to-head,” Smith said in a phone conversation this week. “And they play a round of golf and see who gets the lowest score, and it’s pretty much random. Nobody’s going to win every single time. One guy might win more than 25 percent of the time, but a lot of luck goes into winning. And then you take an amateur who plays a pro, and the pro wins every time.

“So the paradox of luck and skill is, the more skilled the players, the more the outcome is determined by luck. In the same way, you take two really good basketball teams, the NBA or NCAA or whatever, and the outcome is more likely to be determined by luck than by skill, whereas you take a really good team and a really bad team and skill becomes more important.”

Smith has written scholarly articles and a book on the subject: “What the Luck–The Surprising Role of Chance in Our Every Day Lives” (Abrams Press, 2016). His research into financial markets includes statistical reasoning and its anomalies, and it’s not that big a leap to apply those theories to the probabilities of winning or losing in sports.

(Especially because there are, um, investments involved there, too, be it with daily fantasy sports or straight-up wagers on outcomes. Or NCAA Tournament brackets.)

This might be as good an explanation as any for the wide-open tournament currently taking place as well as the Cinderella run of 15th seed Saint Peter’s, which knocked off No. 2 seed Kentucky and No. 7 seed Murray State and draws No. 3 Purdue on Friday night in Philadelphia. Even 15 seeds have skilled players, and sometimes they just get on a run of good luck.

“One of the many interesting things is just the way people interpret games,” Smith said. “Team A beats Team B and the people who are fans of Team A or bet on Team A are like, ‘Yeah, we’re the better team. We’ve demonstrated it. We proved it.’ And then Team A loses and it’s, ‘Those damn officials. How do they call that block a charge?’ … I was reading stories about the nefarious conspiracies, you know, how officials favor the Big Ten or they favor the (power) conferences, or they favor the name teams.”

For every possible scenario, seemingly, there is a fan rationalization. But sometimes it really does come down to one official’s unreviewable call, or whether the rims are tight or loose, or whose star is injured or ailing. Or, as might be true in that 2 vs. 15 upset, whether the higher seed takes things too casually and suddenly finds itself in a battle with a lower seed whose confidence rises the longer it stays in the game.

And sometimes maybe it really is luck, as much as we hate to acknowledge the unexplainable.

“Humans are very uncomfortable with the idea that luck or chance or randomness plays a large role in their lives,” Smith said. “They like to have explanations, theories, patterns, whatever. They like to have reasons. Team A won because they’re better. Team A lost because the referees conspired against them. It’s never, if there were a few lucky breaks, if they played again, (Team B would) probably win.

“It’s true in every sport and it’s also true in life. A lot of things that happen to us are just chance, coincidental, serendipity. Not completely random, but an element of randomness. When a basketball player shoots the ball, it’s not completely random whether it’ll go in or not. Some players will make 50 percent from a certain (spot), some make only 40 percent.”

Thus, the shooter’s creed: Shoot till you get hot, and when you get hot keep shooting. A couple of years ago, Smith wrote an article skeptical of a statistical study that equated the probability of a streak of consecutive makes with a streak of heads or tails coming up in coin flips. “Hot hands don’t happen every day, but they do happen,” he wrote.

The formula used to measure win probability at a given moment is a multiple regression model “to estimate the parameters, the coefficient,” he said. “So how important is it that a team shoots a better free-throw percentage than another? Is that important for winning games? How important is it that one team rebounds better than the other? … They’ve got all these things built into that model.

“And still, you can’t predict who’s going to win.”

Luck, good or bad, can intervene at any moment. That, along with the reality that one bad night can send a favorite home, is as good an explanation as any for the Cinderella effect.

“If they played Kentucky 10 times, how many times would Saint Peter’s win?” he asked.

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“You can’t say games are totally determined by luck. It’s like playing poker; any given hand the amateur can beat the pro, but in the long run the pro is going to take the amateur’s money. In the same way, if Kentucky were to play them a large number of times, I’m pretty sure Kentucky would win most of the time. But in that one hand, that one game, the (underdog) can win. And so it’s not total randomness. It’s just that luck has an effect on the outcome, more than we want to admit.”

And if your bracket is shredded by now, don’t feel bad. Just attribute it to bad luck.

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