Washington Post ombudsman Patrick B. Pexton has a flawed analysis on the logic of a possible paywall there and on the performance of the one that already exists at The New York Times.

How much revenue could charging digital readers really add to the bottom line? To find out, let’s look at the Times’ and Post’s annual reports — publicly available data.

The New York Times Media Group — the division that includes the New York Times and the International Herald Tribune — increased its circulation revenue (revenue from people buying newsstand copies, print subscriptions and digital subscriptions) from 2010 to 2011 by $21 million, or about 3 percent. It saw no growth in circulation revenue the year before. Let’s assume that most or all of that increase was from new digital subscriptions. It didn’t even cover the decline in Times advertising revenue in 2011, which was $24 million.

These numbers are bad (Adding: though technically accurate) in a couple of different ways. First, Pexton is comparing apples to oranges. The NYT’s paywall was only in place for nine months of last year, not all year, as Pexton implies. You can’t compare nine months of circulation-revenue changes to twelve months of ad-revenue changes and then say the former “didn’t even cover the decline in” the latter.” That’s like giving somebody a 100 meter headstart in the 400 meters and then talking about how the laggard couldn’t even compete, even though they ran faster than the rest of the field.

If you make this an apples-to-apples comparison by taking out first-quarter NYT ad revenue declines, which accounted for $3.5 million of that $24 million 2011 ad drop, then circulation revenue increases actually covered ad declines, by about a half a million dollars. That’s a lot different than Pexton’s “it didn’t even cover the decline,” which if fairly calculated should have been “it more than covered the decline.”

Moreover, Pexton doesn’t take the rapid growth of the NYT’s digital subscriptions into account. Advertising is a 160-year-old business at the paper, but the paywall was brand new last March. Digital subs got off to a quick start, yes, but there were many more of them at the end of the fourth quarter than there were in, say, May.

A fairer comparison would take the run rate of the fourth quarter numbers of a new business when comparing them to an old business.

When you do that, you find that circulation revenues, if they had been at a fourth-quarter level all year (and note that circ revenues aren’t cyclical like ads), would have been more than $50 million above 2010 levels. They grew faster as the year went on, and the Times projects they’ll continue to grow at a high rate in the current quarter:

This brings us to another flaw in Pexton’s analysis: He doesn’t consider what print circulation declines were doing to overall circulation-revenue numbers before the paywall went up. The NYT doesn’t break those numbers out, but you can bet that print circulation revenue was declining in the low-to-mid single digits before the paywall went up. Times circulation revenues declined an average 3.6 percent a quarter from July 2010 to March 2011 (the second quarter of 2010 benefited from favorable comps due to a price increase three quarters earlier).

The paywall changed that trajectory sharply, as you can see by combining the last two charts:

Assuming a 3 percent decline in 2011, circulation revenues would have declined roughly $21 million in 2011 without a paywall. Add that to my $50 million figure above and you’re talking about a swing of more than $70 million a year due directly to the paywall. Not all of that is directly due to digital subscriptions. Some of it comes from discouraging people from quitting the print paper to read free online. The Times’s print circulation on Sunday—far and away the most important day—actually increased for the first time in half a decade in the wake of the paywall.

Meanwhile, there’s another critical piece of information missing from Pexton’s column: A paywall doesn’t have to be an all-or-nothing affair, and the Times’s isn’t. He says this:

The other thing to consider is that if everyone else is putting up paywalls, and The Post doesn’t, it has a huge opportunity. It could be the only quality news site that remains free.

Ryan Chittum is a former Wall Street Journal reporter, and deputy editor of The Audit, CJR's business section. If you see notable business journalism, give him a heads-up at rc2538@columbia.edu. Follow him on Twitter at @ryanchittum.