Baseball is a straightforward sport without much room for the grand paradox, which makes one of its great contradictions all the more intriguing: The more important something is to winning play, the less it matters.

Stated plainly like that, the idea makes no sense, but remains true. Catchers, for instance, have an incredible impact on the game, in everything from thinking for pitchers to working the umpires to arranging the defense on the field. Everyone who knows baseball knows this is true, and yet rigorous study shows that the best catchers are worth only about 10 runs above average on defense, and the very worst 10 runs below. This seems like it can’t possibly be true, until you recognize what all major league catchers have in common: They’re all excellent defenders. The position is so important that no one who doesn’t meet a certain threshold of competence even gets a chance to play. From time to time someone who can’t catch gets a shot behind the plate, and invariably shows just how good even the worst catchers really are. Last year, the Washington Nationals were shorthanded and started Matt LeCroy, a pinch hitter who caught in the minors. He allowed seven steals and had to be pulled in the middle of an inning. The Nats’ tough guy manager, Frank Robinson, cried in shame after the game for having exposed LeCroy to this humiliation.

For more evidence, watch the Chicago Cubs play a ballgame some time, if you can stomach it. I’m of the school of belief that about 99% of a manager’s contribution to team success is in making out the lineup card, and that the phases of the moon have more effect on success than does team chemistry. As with catchers, though, this is not because everyone who’s ever watched a ballgame is wrong in thinking that the manager and the team chemistry count, but because of a selection effect. It’s pretty rare to see a manager who’s genuinely unqualified to be running a major league team, or major league players who can’t abide the most basic standards of decency in dealing with their teammates. When you do see these things, you realize very quickly just how important the manager and the locker room atmosphere can be.

And this weekend, everyone in Chicago saw these things. Friday, ace Carlos Zambrano and catcher Michael Barrett, two of the scariest players in baseball, got into a fight in the dugout and carried it into the locker room, where the monstrous Zambrano essentially mugged Barrett, banging him into a locker and sending him to the hospital. The whats and whys of it, mostly having to do with Zambrano’s fiery temper, pending free agency, and wretchedly bad 2007, don’t really matter as much as the stunning violence of the scene. Teammates scrap, even in the dugout; it happens all the time. Players and coaches intercede, everyone calms down, and that’s the end of it. By the time grown men have made the majors, they’ve generally learned to keep their tempers in check at least enough to refrain from pummeling anyone in their own uniform.

In this case, not only did two teammates come to blows, and not only did one of them, Zambrano, continue to rage after being removed from the scene, but the other, Barrett, didn’t have the good sense to stay away from him and made a bad scene worse. This makes a workable definition of team chemistry: It isn’t having the sort of team on which no one fights, it’s having the sort of team where everyone has enough selfcontrol and common sense to let the fight die down after it’s first broken up. More or less every team in the majors has perfectly good chemistry by this standard, just as more or less every team has an excellent defensive catcher. It’s only when you see the absence of something that you realize its true importance.

This is doubly true of the Cubs’ management situation. Lou Piniella is a joke. Anyone who’s watched Cubs baseball this year has seen what’s happened under his watch; he simply isn’t managing the team. Utilityman Ryan Theriot regularly overslides the bag and has been called out on routine plays after not being able to scramble back to the bag in time. The Cubs have lost via the walk-off walk. Barrett and third baseman Aramis Ramirez are forever flinging the ball into the stands and the air. These sorts of things happen, but the complete and pervasive lack of discipline in the way the Cubs play is incredible. Piniella has a reputation as a firebrand, but he’s more of a windbag; he’ll whine to the press about his crummy players and their lack of pride, but he won’t make them improve.

Bad as that is, Piniella managed to make things worse on Saturday against the Braves. He warned the umpiring crew that he was going to throw a hissy fit, presumably to fire up his team, and then did so after Angel Pagan made a quintessentially Piniella-esque play, trying to advance from second on a wild pitch while down by one with none out in the eighth inning. He was thrown out fairly easily, and then Piniella, a 63-year-old man, decided to protest by kicking the umpire. (His lame defense was that he was only trying to kick dirt on him.) Major League Baseball indefinitely suspended him yesterday; the Cubs ought to just fire him. He’s irrelevant.

I’ve often written that managers generally don’t make much difference to a club unless they’re really very good, like Bobby Cox and Mike Scioscia; I hold to that. This presupposes a certain baseline level of competence, though. A manager who can’t even make sure his team can run the bases as well as a good traveling Little League team responding to his ace violently assaulting his catcher by kicking an umpire shows just how important the skipper is. It may be that most of a manager’s value is in not being an utterly clueless fool, just as most of a catcher’s value is in being good enough to prevent the other team from literally running at will, but when you see that rare truly clueless fool in charge, you realize just how good most teams have it.

Savor Willie Randolph and Joe Torre and even Alex Rodriguez; they have their quirks, but they’re not Cubs.

tmarchman@nysun.com