Let’s talk about the best-case scenario as it pertains to new Yankees hitting coach Sean Casey, and if we’re being honest there’s no other way to root except the best-case scenario. Casey was a terrific player across 12 years as a big-leaguer. He made three All-Star teams, he’s a lifetime .302 hitter who kept on hitting right to the end, posting a .322 average his final year in Boston in 2008.

Casey was also the kind of guy who would visit the New York ballparks when he was in from Cleveland, or Cincinnati, or Pittsburgh, or Detroit, and he’d regularly hold court in front of his locker, in the dugout, behind the batting cage. If ever he’d played in New York the baseball writers might’ve renamed the “Good Guy Award” presented annually after him.

His nickname is “The Mayor,” for goodness sake. You root for guys like that.

So yes: let’s say Casey hits the ground running starting Friday night in the hitter’s paradise of Coors Field, and keeps it up in Anaheim after that, and for the rest of the season. Let’s say he’s as much a natural at this as he was on TV. Let’s say the players take to his advice, respect his long and meritorious career as a batsman, and he gets nothing but A-plusses at season’s end.

Even if all of that happens … what do you put the over/under on extra wins that’ll mean for the Yankees? One? Maybe 1.5? Two? Hitting coaches aren’t faith healers. Even Casey himself admitted Wednesday: “I’m not crazy enough to think that I’m gonna come in and all of a sudden all nine guys are gonna start hitting because Sean Casey has arrived.”

Let’s ask another question, then:

What do you put the over/under on extra wins it will mean for the Yankees if Aaron Judge returns from his toe injury — and, just as important, is able to play at the level to which we’ve grown accustomed?

Well, there’s no need for guesswork, we can actually figure that out. Judge has only played 49 games this year, just over half of the Yankees’ total of 91, and he has a WAR of 2.3, according to Baseball Reference. The rest of the Yankees’ regulars — all of whom, except for Harrison Bader, have played significantly more games — have a WAR of 3.8. Combined.

Now, WAR is one of those stats that make some baseball fans uncomfortable but is a generally unsparing and unsentimental look at a player’s value. The actual acronym is “wins against replacement.” Judge’s number was a stunning 10.6 last year, but even in this season, in which Judge’s pace wasn’t yet close to 2022’s, he was on pace for an 8.4. We’ve seen Judge, and we’ve seen essentially a whole team of replacements.

Which ought to explain one simple fact:

The Yankees need Judge back. They need him back quickly, but they also need him back healthy if they are going to truly wrangle free from the team-wide batting malaise that has kept the Yankees from taking full advantage of the Rays’ recent cooling off, and has actually put them in jeopardy of missing the playoffs altogether.

Was Dillon Lawson an easy scapegoat? You bet he was. The Yankees are hitting .231 as a team. There are a lot of days when Aaron Boone’s batting order includes Josh Donaldson (.152), Giancarlo Stanton (.203), Jose Trevino (.211), Anthony Volpe (.216), DJ LeMahieu (.220) and Jake Bauers (.224). Is that the hitting coach’s fault?

Well, it’s on his record.

Will Sean Casey wave a magic wand and increase every number by 40 points? He will not. And none of those players — even the ones like Donaldson and Stanton, with MVP trophies in their dens, and LeMahieu, with two batting crowns — can replicate Aaron Judge.

Which is why the Yankees yearn so desperately for the actual Judge. Now, it’s true: baseball isn’t basketball. The mathematics of baseball insist that one excellent player shouldn’t be able to move the needle as much as one can in hoops.

Except if you’ve seen Judge the past two years — and, as important, if you’ve seen the way opposing pitchers, pitching coaches and managers are forever recalibrating strategy while calculating where they’ll need to pitch Judge late in games — well, then you know how essential Judge is to what the Yankees do, and who the Yankees are.

Casey, as smart as ever, made sure Judge was his first call when he got hired. “He’s obviously the leader and I really wanted to hear what he had to say and what his thoughts were with the offense.”

All of that is nice. All of that is good. All of that is appropriate, as Judge is the team captain. But there’s really only one pertinent question Casey needed to ask Judge.

“When are you coming back, big fella?”