It’s so typical of the Replacements — or what’s being billed as the Replacements — to play some of the best shows in the band’s heavily mythologized history when you least expect it.

On paper, the shows certainly have not merited high expectations: a bunch of sporadically booked, high-paying, fly-in gigs at trendy music festivals months apart, all with two fill-in band members and a frontman who hasn’t toured in a decade. No wonder many altruistic ’Mats lovers have disavowed the “reunion” run, which started a year ago August in Toronto and culminates (but doesn’t end) 10 shows later with home-field advantage Saturday at Midway Stadium.

You can’t blame the naysayers. You should feel sorry for them, though.

Chicago rock critic Jim DeRogatis astutely nailed the sentiment of those who are missing the point: “[Paul] Westerberg has every right to revisit these songs, of course, whether to reap the financial rewards he never realized back then, or to revisit past glories,” he wrote. “But better the singer and songwriter tour solo acoustic, a much more honest reflection of his dad-rock Minneapolis homebody here and now.”

One of the best things about the new-era Replacements gigs — or at least the three I’ve seen — has been the sight of the Replacements playing in the thick of today’s rock ’n’ roll frontline with bigger, younger crowds; seeing fans who weren’t alive when “Tim” came out sing along loudly to “Bastards of Young” and “Left of the Dial”; seeing the band fit in easily on festival lineups with Arcade Fire, Spoon, Jack White, Best Coast, the Hold Steady and other bands that picked up where they left off; seeing them actually teeter toward rock’s mainstream after it proved so unattainable and/or undesirable 25-30 years ago.

There’s even been something unusually rewarding about seeing Westerberg and bassist Tommy Stinson cash in on the name. We don’t know for sure these shows are mostly about making money. In the spirit of finally acting like real rock stars, the two remaining Replacements aren’t talking to the press. But we can venture a guess their naysayers have that much right.

Recently divorced and without a steady income, Westerberg humorously copped to his band’s financial worth during their set at the Forecastle Festival in Louisville, Ky. After referring to his crew as “middle-age hobos,” he asked into the microphone, “Hey buddy, can you spare a quarter of a million dollars?”

They’ll make even more money at Saturday’s show, which will gross more than $600,000 in ticket sales. At least half will probably go to the band. That’s more than 10 times what they were paid at their last local shows at the Orpheum Theatre in 1991.

If Westerberg himself won’t stick up for taking the loot and running, here’s what Frank Black of the Pixies recently said to the Quietus music blog about his own band’s reformation:

“It’s not to say it’s not about art, but we made that art [expletive] 20 years ago. So forget the goddamn art. I did the arty-farty part. Now it’s time to talk about the money.”

Both the Pixies and the Replacements were part of that pre-Nirvana era when rock’s underground was just starting to trickle into the mainstream, and their influence has long exceeded their income. Their record labels hoodwinked them into making expensive videos that MTV never played (like “When It Began”) and taking opening tours that never paid well (like a Tom Petty trek) in an effort to sell more records. But the records never sold well enough to justify the investments.

For the Replacements to make big bucks long after the major record labels collapsed might actually be seen as something of a punk-rock victory worth cheering, a final kiss-off to the industry that eventually profited from them in other ways (with other bands).

Just as they were oversold as a punk band early on, though, let’s not overstate how much the money matters really matter now. That’s clearly not the reason fan after fan has come home gushing about the 10 previous reunion shows.

Well-known to be one of the most unpredictable live bands in rock three decades ago, the Replacements have returned remarkably solid. They have a gangbuster new drummer who gives them a swift kick in the plaid pants. They have a tastefully proficient new guitarist who knows the lyrics Westerberg can’t remember. They seem to be having a lot of fun, too, way more than they had toward the end of their original run.

And they have songs. Oh, those songs. Really, the best thing about these shows has simply been hearing the tunes played live again. Westerberg could be out with a band half as good this one — and the old Replacements themselves were that on many a night — and it’d still be a thrill to hear him singing his unsung classics for a new generation of fans.

Of course, it would be just like the Replacements to play 10 mostly great shows in other cities and then come home and suck. Saturday’s concert, with their biggest hometown crowd ever, is such a meaningful event it’s worrisome. But let’s hope they continue to surprise us. 612-673-4658