Oil and vinegar. Drinking and driving. Cats and dogs.

Stanford and Cal.

Some things just don’t mix. Luckily for Stanford (15-3, 4-2 Pac-10) fans though, the Cardinal may have the upper hand in its 4 p.m. Saturday tilt with the hosting Bears (11-6, 2-4).

It’s Trent Johnson 101: when Stanford plays a lesser opponent, make sure to talk them up as much as possible, lest you come across as haughty. The only problem is when those pesky things called facts get in the way.

“When you look at the stats in conference games, you look at ours, you look at theirs,” coach Johnson said. “How is this team 2-4?”

I’m not a math major, but Stanford is holding conference opponents to 57 points per game, while Cal is allowing 78 per game. I think that might start to explain it. Teams make 38 percent of their shots against the Cardinal and 47 percent against the Bears.

Credit Stanford’s vicious inside game. Defensively, senior forward Taj Finger and sophomore centers Brook and Robin Lopez have been dominant on the inside, with seven, 15 and 37 blocks this season, respectively. Arizona State had stormed to ten straight wins and a 30-point first half last Saturday at Maples Pavilion. Then the Stanford posts built a fence around the paint and locked the gate: the Devils managed just 22 second-half points on 26.3 percent shooting, and Stanford had its third win in a row.

The Cardinal will look to lock Cal up in the paint while exploiting that same space on offense. Johnson’s philosophy has always favored an inside-out attack, but his team has never executed it as well as they have this year.

Brook Lopez is scoring 17.2 points per game and knows the offense largely revolves around him.

“[Our goal is] just asserting our presence down low, attacking the basket, then when they start respecting us inside, kicking it out more,” he said. “When we’re rolling and get our outside game rolling, it’s pretty hard to beat us that way.”

The Cardinal, just one loss behind the Arizona State, UCLA and Washington State in the Pac-10 standings, must have been looking forward to this game for months. So many teams in this league have the speed to force Stanford to go small, pushing the Cardinal away from its strength. That means playing just one Lopez at a time and giving opponents a heavy dose of the wings: Fred Washington, a senior, juniors Mitch Johnson and Anthony Goods and sophomore Landry Fields.

Oregon and its point guard Tajuan Porter beat the Cardinal with their speed and a small lineup; UCLA did the same with guards Darren Collison and Russell Westbrook; and Arizona and point guard Nic Wise gave Stanford quite the scare last Thursday.

Cal, on the other hand, is strongest exactly where Stanford would like them to be: in the post.

“You’ll see a lot of [the twins] playing together,” Trent Johnson said. “Whether our bigs are good enough to compete with theirs, that remains to be seen. Look at it on paper — it’s a pretty good matchup, quality of players, size and position and all that.”

Again, Johnson’s being polite, if not 100 percent truthful. Sure, Cal’s Ryan Anderson and Patrick Christopher are for real. It’s early, but their numbers in the meat grinder of the Pac-10 (21 and 16 points per game respectively, on 47 percent accuracy) are great. Center DeVon Hardin is also a force; he should give the Lopez twins all they can handle on the defensive side of the ball.

“To me he’s one of those players,” said Trent Johnson of the Bears’ Anderson. “He’s a three, four or a five. Put him out there and he can flat-out play.”

And, to be fair, Cal is the stronger team offensively, shooting 46 percent overall and 40 percent from three-point range for 76 points per Pac-10 game. Stanford is mired at 40 percent overall, 28 percent from long range and 62 points per game. Add in the homecourt edge and the hard-fought nature of this rivalry, and the Bears are just slight underdogs.

But that last word, underdog, is the key. Stanford should win this one on the backs of Brook and Robin inside, both throwing it in themselves, and passing out of double-teams to an open Goods or Hill on the wings. Those two juniors, Hill especially, awoke from a slumber against Arizona State, and they should get plenty of open looks against a Cal backcourt whose greatest weakness is its defense.