When a New York team trades for or signs a great player, the froth-to-reason ratio in the five boroughs usually goes completely out of whack, as writers and fans ignore what he’s actually likely to do and spin fanciful tales of how the new player’s presence and winning spirit will by itself change the franchise’s psychology, heal the lame, turn the useless into the useful, and so on.

None of this is any more true of newly acquired Mets ace Johan Santana than it has been of anyone else. He will not make his teammates want to win more than they otherwise would have, he will not cure Orlando Hernandez’s arthritic neck, and he will not make Angel Pagan a good hitter. Happily, he needs to do none of this. If he stays healthy and pitches well, the Mets will likely make the playoffs.

What makes Santana so valuable to the Mets is that he isn’t just the best pitcher in baseball, but he’s also effectively replacing an unbelievably terrible no. 5 starter. This second point is really important — like most teams, the Mets gain at least as much by replacing their bad players as they do by bringing in good ones. Last year, for instance, the Mets gave 23 starts to Mike Pelfrey, Chan Ho Park, Dave Williams, Brian Lawrence, and Jason Vargas, and the five pitched 116 innings with a 7.29 ERA. If those games had instead been started by a tolerably mediocre pitcher, they would have won their division.

To put the point differently, we can compare what the Mets would look like with and without Santana, using Dan Szymborski’s excellent ZiPS projections, which are available at baseballthinkfactory.org. According to Szymborski’s numbers, Pedro Martinez, John Maine, Oliver Perez, Hernandez, and Pelfrey project to pitch 796 innings this year, with a 4.10 earned run average. Swap Pelfrey out for Santana, and the rotation looks good for a 3.69 ERA in 880 innings.

For the sake of argument, let’s say that the Mets will need 950 innings from their starters this year. (The actual number has ranged from 918 to 1,022 over the last three years.) Without Santana, they would project to enter the season needing 154 innings from prospects, veteran minor leaguers, and the like to meet this threshold. With him, they’ll need just 70 innings.

If you assume that the Mets would be able to scare up a 5.00 ERA pitcher to take up the needed innings in either case — no sure bet — the Mets’ rotation ERA projects at 4.25 without Santana, and 3.79 with him. Without taking into account either the good effects of a stable rotation on the bullpen or the likelihood that the Mets would have difficulty finding a 5.00 ERA pitcher, it looks on paper as if Santana improves the Mets by about 50 runs, or five wins.

Five wins is a lot. Last year, the Mets won 88 and finished out of first place by a game. With 93 wins, they would have had the best record in the league, and fifth-best in baseball. As their other winter moves have made them, if anything, a little bit better than they were last year, and as continued decline from older players such as Carlos Delgado should be offset by continued improvement from young ones such as Jose Reyes, closer Billy Wagner was probably right when he crowed to MLB.com that “we’re back to being one of the five best teams in the game” yesterday.

This, and not any other effect he may have, whether it be improving team chemistry or offering New York’s Venezuelans a hero in the line of Victor Zambrano and Roger Cedeno, is why Santana matters so very much. A change in the barometric pressure surrounding the franchise is wonderful, and one can’t discount the possibility that Oliver Perez will study Santana’s changeup grip and work habits and turn himself into a 20-game winner, but even if we keep to the strictly tangible, it’s clear that trading for Santana improves the Mets more than anything else they could have done.

Many have said all winter that the Mets needed to trade for Santana because it was the one way they could atone for last September’s miserable collapse. This happened to be true; the Mets weren’t good enough to win a championship last year, and Santana was the one available player who, by himself, could make them good enough. They have him now. The glow won’t fade for weeks.

tmarchman@nysun.com