Closer isn’t a good buy, so time to say goodbye

He has saved day games, night games, winning streaks, road trips, confidence, face, butts and souls.

In giving the Angels the shirt off his back this season, Francisco Rodriguez has saved all but one thing.

The shirt off his back.

Yes, his major league-record 58 saves is one of the coolest things to happen in Anaheim since Darin Erstad caught that final out.

Certainly, his skyward-pointing celebrations have turned him into a sort of statue almost as enduring as the Giant Caps.

For all this, the Angels should shake his hand and tell him two things.

Good job, and goodbye.

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Francisco Rodriguez can become a free agent this winter, and he can’t wait.

He has set the price, at five years, $15 million a year. He has set the tone, breaking a saves record that stood for 18 years.

He’s so ready to put himself on the open market, sometimes it seems as if he’s already there, with post-save celebrations that highlight his individuality.

But more than any other statistic in the game, saves are a team stat. And even without their closer this season, here’s guessing the Angels would be a first-place team.

If Rodriguez doesn’t want their three-year, $34-million offer of last winter, they should politely wish him good luck in New York.

If he really believes he will be better served playing for a manager who doesn’t understand pitchers as well as Mike Scioscia, well, they should politely offer to have his head examined.

Arte Moreno, the Angels’ owner, told The Times’ Mike DiGiovanna on Tuesday that no matter what happens in the postseason, he will not substantially increase his already impressive payroll.

In this regard, what will publicly be his toughest decision should privately be his easiest.

If Rodriguez wants to leave, they should politely escort him to the door.

He is a historically incredible closer, but he’s not as important to the team as a potential Angels free-agent slugger named Mark Teixeira, or a potential free-agent starter such as the Milwaukee Brewers’ CC Sabathia.

Closers get three outs. Closers do not hit three-run homers. Closers cannot pitch three-hit shutouts. Closers will never work three scoreless innings in relief.

Closers get three outs, and only after everyone else has first done their job.

Closers work at the behest of an offense that must get them the lead, a starter who must hold that lead until the sixth inning, and a bullpen that must make it last until the ninth.

Closers, by nature of being the last man on the mound, are the centerpieces of championship celebrations, but then what do they traditionally do?

They jump into a catcher’s arms. Even in their final act, they understand that someone else must carry them.

There is a reason that, in the 51-year history of the World Series MVP award, only four traditional closers have won it.

But forget the good old days, how about the last five years?

In the St. Louis Cardinals’ 11-win run through the 2006 postseason, only four of those games required saves.

In 2004, the Dodgers’ Eric Gagne completed a record streak of 84 consecutive saves during the regular season -- yet during their first-round playoff loss to the Cardinals, he never even had a save opportunity.

In the Florida Marlins’ run to the 2003 World Series championship, their bullpen was led by . . . wait a minute. Do you even remember the name of their closer?

And that’s the position the Angels are going to fill for $75 million?

In four postseason series since becoming the closer, Rodriguez has worked a total of 10 2/3 innings.

John Lackey has pitched more than that in one series alone.

The last time the Angels made a change at closer, they successfully filled the role with a setup man. His name was Francisco Rodriguez.

If he leaves this winter, who says that couldn’t happen again? Scot Shields and Jose Arredondo could probably squeeze a season’s worth of a saves between them, and Moreno could spend his money on the meat of the lineup and rotation.

At 26, with a wicked changeup now accompanying his other dizzying pitches, Rodriguez is a brilliant young talent who will undoubtedly be highly successful for several more seasons.

But not on this team. Not at that price. Not at that position.

If you can track him down in a jail in Venezuela, just ask former Florida Marlins closer Ugueth Urbina.

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Bill Plaschke can be reached at bill.plaschke@latimes.com. To read previous columns by Plaschke, go to latimes.com/plaschke.