It takes a calculator and perhaps the rigor of Sherlock Holmes to cut through the partisan rhetoric about President Obama’s first-term record on judicial nominations. But the bottom line is clear enough.

There are more vacancies on the federal courts now than when Obama took office nearly four years ago. And he is the first president in generations to fail to put a nominee on the U.S. Court of Appeals for the D.C. Circuit, the second most influential court in the land and traditionally a training ground for Supreme Court justices.

Obama has, of course, left his mark on the high court by nominating Sonia Sotomayor and Elena Kagan. Their confirmations leave those two seats for decades in liberal hands, and marked a historic diversification of the court.

But, depending on what the Senate does in these final days,Obama’s record on the rest of the federal judiciary will show one more opening on the nation’s powerful 13 courts of appeal than when he took office, and more than a dozen additional vacant district court judgeships.

Senate Judiciary Committee Chairman Patrick J. Leahy (D-Vt.) blames Senate Republicans for foot-dragging on nominees that he says are utterly uncontroversial.

“These delays mean that the Senate will, again, be needlessly forced to devote the first several months of next year confirming judges who could and should have been confirmed the previous year,” Leahy said earlier this month.

He added that the increase in vacancies “is bad for our federal courts and for the American people who depend on them for justice.”

Sen. Charles E. Grassley of Iowa, the committee’s ranking Republican, responds that the Senate has confirmed at least as many as were approved during President George W. Bush’s first term. “The continued complaints we hear about how unfairly this president has been treated are unfounded,” he said.

Russell Wheeler, a judicial scholar at the Brookings Institution, has taken a more detached look at the process. “There is so much propaganda out there,” Wheeler says. “It’s almost as if they are speaking different languages.”

Wheeler’s conclusion: “The contentiousness that affected President William Clinton’s and President George W. Bush’s efforts to appoint judges to the courts of appeals did not appear to worsen during Obama’s first term, but battles have heated up over district nominations.”

Drastically increased delays in confirming district court judges are part of the reason for the higher vacancy rates, Wheeler said, but the Obama administration is responsible for sending up fewer nominees and taking longer to do it.

District judges are at the first tier of the federal judiciary; they decide individual cases and their decisions do not create precedent for other judges. In the past, confirmation of district judges was seen as somewhat routine.

But that has changed, Wheeler said, with longer wait times and more contested votes. The average time from nomination to confirmation for a Clinton district judge was about three months. That grew to 154 days for a Bush nominee, Wheeler said, compared to 223 days for Obama’s choices.

Nominations to the appeals courts are always more controversial. Those judges hear tens of thousands of appeals each year — by comparison, the Supreme Court hears arguments in about 80 — and their judgments become precedent in the states within those circuits.

Despite some high-profile fights, however, Wheeler found that Obama’s circuit court nominees have fared about as well as those of his predecessors. Or as he put it, “That the Senate has since 1993 denied confirmation to three of every 10 circuit nominees reflects a new (and unfortunate) normal, but at least so far it has not worsened under Obama.”

Obama’s nominees, in fact, have had a shorter path from nomination to confirmation than did Bush’s — 240 days compared to 283 days, according to Wheeler’s calculations.

No court is more contested by either side than the D.C. circuit, for obvious reasons. Chief Justice John G. Roberts Jr. and Justices Antonin Scalia, Clarence Thomas and Ruth Bader Ginsburg all put in time on the court before being picked for the Supreme Court; Kagan was nominated for the D.C. circuit but was blocked by Senate Republicans.

Even though there are three vacancies on the court — there will be a fourth next year — Obama did not submit a nominee until September 2010. Then, Republicans blocked nominee Caitlin Halligan, general counsel for the New York district attorney’s office, and an additional choice, California law professor Goodwin Liu. Liu has since been appointed to the California Supreme Court, and Obama will try again on Halligan.

Last June, he picked Sri Srinivasan, deputy U.S. solicitor general and a former clerk to retired Justice Sandra Day O’Connor, for another seat on the court. Srinivasan has not had a Judiciary Committee hearing. (Lest one think it is only Republicans who do the blocking, Senate Democrats ran out the clock the first time Roberts was nominated for the court.)

While liberal groups complain about Republican obstruction, they have also been critical of the White House. The American Prospect recently featured a long piece called “The Courts: How Obama Dropped the Ball.”

But as Wheeler points out, a two-term president almost always has a major impact on the makeup of the federal judiciary.

“Democratic appointees, who in 2009 constituted about a third of active circuit judges, might constitute about two-thirds in 2017,” Wheeler wrote.