During the past few weeks, Rush Limbaugh has been on the warpath, second-guessing John McCain and GOP Chairman Mike Duncan. What really seemed to set Limbaugh off is what he perceives as a Republican preoccupation with trying to “win a majority of independents.”

Rush, of course, thinks he’s top dog in conservative circles and entitled to dictate strategies and criticize everyone else. His claim to dominant status springs from his radio ratings. He’s No. 1 and good at what he does. But he only has 20 million listeners, according to his own assertions. That’s a good start in radio, but it comes up a little short when you need at least 60 million votes to get elected president.

Rush admits that he never much cared for school. I’m betting that math was not his strong subject. If Rush would do the math, he’d discover that Republicans have to get more than a simple majority of independent votes to win.

I, too, once used vague catch phrases for campaigns, imploring clients to “do well with the base” without actually doing the math behind such phrases. But someone taught me the discipline of doing a minimum winning coalition calculation to see how I get to the proverbial 50 percent-plus-one.

This mathematical exercise is eye-opening if you’ve never done it. The computation starts with the base vote for each candidate. Real-world experience suggests that each party, by Election Day, gets 90 to 95 percent of its identifiers to vote for the nominee, sometimes more. (Actually, Democrats have occasionally not done that, but Republicans have for most all recent elections.)

Given that expectation, let’s do the math. The latest Gallup Poll says that 40 percent of Americans identify with the Republicans. Let’s assume that McCain gets 90 percent of GOP votes. Multiply 40 times .90 and get 36 percent. That’s what the Republicans contribute to our quest for 50 percent-plus-one, leaving us short of our goal by 14 percentage points. Even if we get 95 percent of Republicans to vote for McCain, we only have 38 percent of the 50 percent-plus-one goal.

Now assume that Barack Obama wins the votes of 90 percent of the 52 percent of Americans that identify as Democrats, according to Gallup. Do the math again. Multiply 52 by .10 (the 10 percent McCain will get) and we add the product, 5.2 percentage points, to the 38 percent we win from Republicans. At 43.2 percent (38 from GOP plus 5.2 from Democrat voters), we are still 6.8 points short of our goal, even assuming that McCain does better among his GOP base than Obama does in his Democratic base.

Now we get to the independents. Gallup says there are only 8 percent true independents who refuse to lean R or D. McCain would have to win not just a majority of independents, but almost 90 percent of them, to achieve a minimum winning coalition.

Now do we see why Republicans have to be so concerned about independents? If we follow Rush’s advice and spend all our time trying to wrestle the last 5 percent of Republicans to the ground, we’re unlikely to win enough fence-straddlers.

Rush’s radio ratings math is irrelevant to the real world that McCain faces. Rush only has to win over 20 million listeners to take top prize. McCain probably has to attract 62-65 million votes. Limbaugh’s math might win a primary, but it can’t win a general election.

I’d love to see Rush and all the other second-guessers have to attract 65 million viewers or listeners to stay on the air after Nov. 4. If they faced a bar that high, maybe they wouldn’t be so cocky about how they are right and everyone else is wrong.

Hill is director of Hill Research Consultants, a Texas-based firm that has polled for GOP candidates and causes since 1988.