New poll data from NBC/WSJ shows that Hillary Clinton's lead over Donald Trump in a two-way race significantly shrank after the second presidential debate on Sunday.

This post has been updated. Please see updates at the end of the post.

A new NBC/WSJ poll shows that Democratic presidential candidate Hillary Clinton lost significant ground in post-debate surveys of likely voters. According to the survey data collected by NBC/WSJ on October 10, the only post-debate day for which data are available, Clinton’s lead in two-way race is only two percentage points. In a four-way race, the post-debate data shows a Clinton lead of five percentage points.

The October 10 survey data can be ascertained by comparing the NBC/WSJ poll data from the pre-debate surveys on October 8 and 9 to the aggregated poll results from surveys conducted on October 8, 9, and 10.

According to the poll, Hillary Clinton received 52 percent of the two-way vote in the October 8-9 likely voter survey, compared to Trump’s 38 percent. In the October 8-10 two-way survey, Clinton received 50 percent to Trump’s 40 percent among likely voters. Since we have data from the first two days (October 8-9), and the full three days (Oct. 8-10), we can ascertain the survey data from just October 10, which is the only post-debate day in the poll. Here’s the quick math on that.

We know we have three days of data. We also have data on the average of the first two days. Using simple arithmetic, we can get the Clinton number for the third day, which we’ll call x: (52% + 52% + x) / 3 = 50%. By solving for x, we get a third-day support number for Clinton of 46 percent. We’ll do the same for Trump’s numbers: (38% + 38% + y) / 3 = 40%. Solving for y gives us 44% for Trump. Therefore, the only truly post-debate data in the NBC/WSJ “post-debate” poll actually shows a 2-point two-way race between Clinton (46%) and Trump (44%).

To figure out the four-way numbers, we’ll do the exact same math. The October 8-9 poll shows Clinton with 46 percent support compared to Trump’s 35 percent in a four-way race. The October 8-10 poll shows Clinton with 46 percent support compared to 37 percent for Trump. To determine Clinton’s polling numbers on just October 10, the equation is: (46% + 46% + x) / 3 = 46%. In this case, her support on October 10 was unchanged at 46 percent. To determine Trump’s October 10 support, the equation is: (35% + 35% + y) / 3 = 37%. Based on the polling data from NBC/WSJ, Trump’s support after the debate increased to 41 percent. As a result, the only post-debate data in the NBC/WSJ survey shows Clinton with a 5-point lead in a four-way race, 46 percent to 41 percent for Trump.

Unfortunately, the headline on NBC’s news article trumpeting the new poll numbers — “Post-Debate Poll Shows Clinton Holding 9-Point Lead Over Trump” — radically mischaracterizes the results of its own poll. The post-debate poll data showed nothing of the sort. In fact, the post-debate data actually show Hillary Clinton with a mere 5-point lead in the four-way race and a 2-point lead in the two-way race. The inclusion of data from two pre-debate days is required to show a 9-point Clinton lead in the four-way race.

It is unclear why NBC not only buried the lede about its own post-debate polling showing a tight race, but why it felt compelled to mischaracterize its own mixed poll, which combined pre- and post-debate survey data, as a purely post-debate poll. The only post-debate data in the survey shows a close race and a dwindling Clinton lead. Whether that dynamic will continue is obviously yet to be seen.

The third and final presidential debate of the 2016 election season will be held on October 19 in Las Vegas.

UPDATE: A reader points out the breakdown of interviews per day which slightly impacts the arithmetic detailed above. The poll states that 500 registered voter interviews were conducted October 8-9 and 400 were conducted after the debate on October 10. For the two-way numbers, the Hillary math would then look like this: (250/900 * 52%) + (250/900 * 52%) + (400/900 * x) = 50%. Using that math, Clinton would be at 47.5 percent in the October 10 post-debate survey. For Trump, the two-way math would be: (250/900 * 38%) + (250/900 * 38%) + (400/900 * y) = 40%. That would put Trump at 42.5 percent following the debate. Those results show Clinton’s pre-debate lead of 14 percentage points shrinking to just 5 percentage points following the debate.

For the four-way numbers, the Clinton math would be: (250/900 * 46%) + (250/900 * 46%) + (400/900 * 46) = 46%. That would put Clinton’s post-debate level of support at 46%. For Trump, the equation would be: (250/900 * 35%) + (250/900 * 35%) + (400/900 * y) = 37%. That would put Trump’s support at 39.5 percent post-debate, giving Clinton a 6.5-point lead following the debate, compared to an 11-point lead before the debate.