Update: Here's the podium setup, as tweeted by CNN.

As the end point of CNN's polling window for Tuesday's debate neared, Rand Paul's camp was understandably nervous about whether its candidate would make the main stage. On Friday, we noted that Paul was likely to end up on the junior stage, because he was below the 3.5 percent average he needed in national polling and below the 4 percent needed in Iowa or New Hampshire.

With the release of a few new polls over the weekend, though, his team felt confident. Paul's strategist in Iowa, Steve Grubbs, did the math:

The network was very specific about which polls it would use, and the ones Grubbs cites all came out during CNN's window and from CNN's chosen firms.

And when the network's Jake Tapper announced the final line-up during "State of the Union" on Sunday, Paul had made the cut.


We created this graphic showing all of the numbers in play. You'll notice that Paul, at the bottom of the list, has a 3.7 percent average in Iowa according to our numbers, which we'll explain below.

If you round that up to 4 percent, Paul's in. But: Why would you set a 3.5 percent average nationally and a 4 percent average in the states if you were going to round up anyway?

To be included, polls needed to be polling voters ("in the field," in the parlance) starting no earlier than Oct. 29 and released no later than 9 a.m. Sunday. The polls Grubbs point to are as follows:

- Fox News (in the field from Dec. 7 to Dec. 10): 5 percent
- Des Moines Register/Bloomberg (Dec. 7 to Dec. 10): 3 percent
- CNN (Nov. 28 to Dec. 6): 3 percent
- Monmouth University (Dec. 3 to Dec. 6): 4 percent
- Quinnipiac University (Nov. 16 to Nov. 22): 5 percent

Average those up, and you get 4 percent on the nose.

But there was another poll that was in the field from Oct. 29 — the start of the window — until Nov. 4. In that poll, Paul got a miserable 2 percent support, dragging his Iowa average down to 3.7 percent. CNN may have excluded that survey from its results, but it would be weird if it did. After all, it was a CNN poll.

What's more, the debate criteria specifically say that the numbers won't be rounded up.

It's highly unlikely that any of Paul's opponents (save one) will raise a fuss. Trying to exclude him would simply look petty, and with an already crowded stage, what's one more person.

But Paul's inclusion is certainly questionable from an objective perspective. On Friday, we noted that the network was inadvertently ensuring more moderates on the stage. Now it is doing a favor to the libertarian, too.