The Boston Celtics should cut back on the hero ball

Hero ball is giving the offense of the Boston Celtics hiccups. That should change.

Over the course of their Western Conference road trip — and briefly before, in a game against the Orlando Magic — the Boston Celtics have found themselves drawn into a frustrating pattern outlined by Celtics writer John Karalis: They miss open shots; when they miss open shots, they don’t necessarily stick to a system or start running plays or making the extra pass to get themselves shots; instead, it appears they just switch to hero ball.

That kind of choice may work if you’re Jimmy Butler seeking to prove a showy point, but in the current iteration of the NBA, it appears to be a one-way ticket for the team to spend time over the course of three different games down by 20 points.

Hero ball should not be a damagingly seductive choice. Ball movement creates open shots. You don’t need to be a deep-seated fan of Gregg Popovich’s philosophy to believe that. You can take a glimpse of the back-of-the-napkin math ESPN did in 2012. You can read this anonymous paper from the 2015 Sloan Analytics Sports Conference. You can squint at the charts.

The authors of the Sloan paper argue that a ball-handler has a high likelihood of scoring if he attempts a shot where there’s an immediate opportunity. If the offense is efficient, he should be taking those shots.

So what happens if the shots aren’t falling when there’s an opportunity? You pass until you get an opportunity. By doing this, you’re adding something unpredictable to the offense. And — if you click through to the paper — you’ll note that the data backs it up: The more you pass, the greater likelihood there will be that you’ll have a chance to take an open or guarded 3 from the top of the key, as well as baseline shots, perimeter shots and restricted area shots.

Even though ball movement doesn’t fix a player’s shooting ability, there’s a greater likelihood that you’ll make a more open shot than a contested shot. If you compare tightly guarded shots vs. uncontested shots over at NBA.com, for instance, you’ll note that even the “worst” players making uncontested shots on the first page are in the 40 percent range while the “worst” tightly guarded player might make 20 percent of their shots.

And the nice thing about this is in a world of switching, you might be able to hide an unpredictable player. Consider: The player who brought the “highest entropy situation” to a game, per the paper’s calculations, was found to be Kevin Garnett playing the center 3. I’ll bet anything that mathematical subtlety is one reason why Marcus Smart has the kind of impact on the game that he does.

But the complicating thing is hero ball is a seductive choice. It’s what happens when you figure out how to beat the odds. It can sometimes happen when you exploit a mismatch. It can happen when you want to control the clock in a high-pressure environment, like the playoffs or the Finals. You crack open the math and the joy of a job well done comes sailing through.

But if you’re averaging 0.73 points per possession while playing isolation — as Jayson Tatum is — then it might make sense to pass out of the guarded 3 in the closing moments against the Portland Trail Blazers.

Not only would the math be on his side, but we’re fast approaching a point where — as Marcus Smart put it — there are no more excuses.