The first-place finish in Iowa matters for the 2016 campaign cycle. So does third.

In 2004, a little more than two weeks before the Democratic caucuses, Howard Dean had a comfortable lead over Dick Gephardt. John Kerry and John Edwards were in third and fourth place, respectively, barely making double digits. Iowa Democrats were telling our interviewers, at a two-to-one ratio, that they preferred a candidate who would stand up for principle over someone who could defeat George W. Bush.

Then, something changed.

Reports started suggesting that people were getting tired of Mr. Dean’s youthful canvassers calling and coming to their door. They were tired of hearing about the Iraq war. More important, they were growing weary of Mr. Dean and Mr. Gephardt battling each other in television commercials.

My daily tracking polls–for Reuters and NBC–showed a steady transformation. As the caucuses grew closer, Iowa Democrats suddenly preferred someone who could beat Mr. Bush by a factor of two to one. The numbers for Mr. Dean and Mr. Gephardt dropped a point or two each day as Mr. Kerry and Mr. Edwards rose about the same. With about a week to go, John Kerry surpassed Mr. Dean and Mr. Gephardt. He went on to finish first. Mr. Edwards placed second.

The situation was as dramatic in 2008. About two weeks before the caucuses, Hillary Clinton had a lead over Barack Obama and John Edwards. Then, as before, the polls started to change. Mr. Obama and Mr. Edwards finished first and second as Mrs. Clinton dropped to third place.

This year, the GOP has two clear front-runners. Many Iowans who say they have never or seldom voted in the caucuses are waiting in the bitter cold and snow to see Donald Trump. He may not have the greatest ground game, but if people are braving the elements to see his rallies and campaign stops, they may also turn out to vote for him. And the Iowa GOP caucuses are practically made to order for Ted Cruz. He has the combination of Christian/social conservativism that appeals to the substantial numbers of evangelical Christians who historically have shown up, he is a tea-party favorite, and he is considered an “outsider” in Washington. He also has the political ground game and technology to win.

Iowa is a table setter: There will be an establishment candidate, someone in a position to do better in New Hampshire, where independents and moderates normally define the winner. Marco Rubio has been doing well enough in Iowa, New Hampshire, and nationally to bear close observation. Jeb Bush still has lots of money. Chris Christie and John Kasich have spent very little time and few resources in Iowa–but are both doing well in New Hampshire.

That’s why the No. 3 spot in Iowa matters. As Mr. Cruz and Mr. Trump maintain their war, a premium will be placed on the establishment winner. Voters will be watching to see who does better than expected and is considered “adult” enough to be president of the United States. It’s a mistake to think that enough Iowans don’t care about this point.

On the Democratic side, Hillary Clinton again faces a more serious challenge than she or her team anticipated. Bernie Sanders is within striking distance and has a hold on millennials who appeared energized to come out and vote–much as they did for Barack Obama in 2008. Former Maryland Gov. Martin O’Malley has low support nationally but is drawing 5% to 8% in Iowa. If his support jumps to 15% or so–it can happen; ask Gary Hart about 1984–that would be enough to position him for New Hampshire and, combined with a very good showing by Mr. Sanders, would signal that a majority of Iowa Democrats rejects the “inevitable” nomination of the party’s front-runner and best-known political name.