With the votes now counted in Wisconsin’s April 7 election, preliminary results show that 1.55 million people voted. That’s partly due to a staggering number of absentee votes — nearly 1.1 million — which made up for much of the in-person voting that did not take place.

But what exactly should we make of the overall turnout figure? Most people expected it to be much lower than usual. Did the extraordinary conditions — fear of the virus; widespread last-minute polling place closures; an overburdened mail-in balloting system; and controversy over whether it would even be held — nevertheless affect the number of ballots that would have been cast in a normal year?

Answering that question is harder than it might seem. We explain our analysis below.

How do you know what a primary’s turnout would be under ‘normal’ circumstances?

As it turns out, overall turnout in Wisconsin’s 2020 primaries was even higher than in most Wisconsin primaries in the past 40 years. Thirty-four percent of the state’s potential voters cast a ballot last week — a slightly higher rate than the 31 percent average for all of Wisconsin’s presidential primaries since 1984.

But is 31 percent the baseline against which we should assess whether turnout was high or low? That’s not straightforward. The factors that affect voters’ participation rates in primaries can change dramatically from one election cycle to the next. Political science research finds that the closeness of the race between a party’s potential nominees is perhaps the most important influence. Idiosyncratic factors also matter, such as whether other hotly contested races are also on the ballot.

To get an appropriate measure of what Wisconsin’s 2020 turnout would have been under more normal circumstances, we used two methods that gave us remarkably similar answers.

Statistical estimation suggests this turnout was surprisingly high

First, we used statistical estimation to compare 19 Wisconsin primaries, held from 1948 to 2020. With so many, the model had to be simple. We considered the comparative competitiveness of the two parties’ presidential primaries — and whether the incumbent president was running again or at the end of his two terms. We also took into account how Wisconsin primaries’ turnout dropped dramatically beginning in 1984, when the rise of “Super Tuesday” made Wisconsin’s primary votes less influential.

Using this approach, we found that in a “normal” 2020 election, roughly 26 percent of the voting-age population would have cast ballots, for about 1.2 million voters. That is far fewer than the 1.55 million votes actually cast. This 26 percent figure is lower than the post-1984 average, for two reasons. First, on the Republican side, an incumbent president was running for reelection, more or less uncontested. Second, the Democratic race was far less contested than in past years. Indeed, the Democratic race was the least competitive for the non-incumbent party since 1964, as measured by what political scientists call “the effective number of candidates,” combined across the two parties.

More qualitative analysis also suggests surprisingly high turnout

We also examined this by looking at just the most recent presidential primaries that most resembled this one, making appropriate adjustments for obvious differences.

The 2012 Wisconsin primary most directly resembles this year’s in key ways. With President Barack Obama up for reelection in 2012, the Democratic primary was uncontested, like the Republicans’ this year. In 2012, 1,088,000 Wisconsinites voted: 788,000 in the Republican primary and 300,000 in the Democratic. In other words, 26 percent of the voting-age population cast ballots.

But that doesn’t quite capture the difference. We would expect a lower 2020 turnout than in 2012, because this year’s Democratic primary was fairly settled, while 2012’s Republican contest was still hotly contested: Mitt Romney won 44 percent of the vote, followed by Rick Santorum’s 37 percent and Ron Paul’s 11 percent.

But 2020 turnout was actually eight points higher than that in 2012.

Still, there’s another factor to take into account. In 2020, some states’ Republican voters have been turning out in higher-than-usual numbers for a noncompetitive primary. For instance, turnout in the Michigan Republican primary was only 10 percent lower than it had been in 2016, while North Carolina’s was down 33 percent. If we average the experience in Michigan and North Carolina, and “expect” that Republican turnout in Wisconsin would have dropped only 22 percent from 2016, that would predict this year’s turnout to have been about 1.4 million. But despite chaotic conditions, more Wisconsin citizens than that voted.

One caution about these findings

One thing makes us uneasy about these estimates. In 2016, Wisconsin’s primary turnout was a complete outlier. Fully 47 percent of the state’s voting-age population cast ballots — 16 points more than the average since 1984.

Why, and what should that suggest to us? It’s hard to be certain, since that was just one election. But both 2016 presidential primaries were strongly contested. This year, even though neither primary was as competitive as in 2016, turnout was only 13 points lower. On the Republican side, turnout was down 43 percent — unsurprising with an unopposed president on the ballot. In contrast, Democratic voting was down by only 7.6 percent. That’s extraordinary, given that the primary between former vice president Joe Biden and Sen. Bernie Sanders (I-Vt.) was not close.

There’s another possible reason for 2016’s exceptionally high primary turnout: a fiercely fought race for a Wisconsin Supreme Court justice, which would determine the balance on the court. But that’s unlikely; our statistical analysis finds that this would have been the first time since World War II that a judicial race dramatically affected primary turnout in Wisconsin. This year’s election did feature another hotly contested state Supreme Court seat, though not one that would control the court’s balance of power. And roughly 340,000 more votes were cast for the court race this year than a similar one in 2019, which further suggests that the presidential races, not the court ones, drive turnout.

Wisconsin’s turnout was remarkably high, especially given the chaos

Wisconsin’s primary turnout was up eight points from 2012 and down 13 points from the (possibly exceptional) 2016 race. Given the circumstances, that’s remarkable. A week ago, informed commentators were wondering whether the chaos would drive turnout down to historic lows. The opposite happened. Why?

The most likely answer is that Democrats are so mobilized in the Trump era — either for Democrats or against Trump — that they are showing up in unexpectedly high numbers, even under Wisconsin’s difficult pandemic circumstances. The 2018 midterm election in Wisconsin had the highest turnout that state has seen since World War II. And the 2019 supreme court spring election had the second-highest turnout among comparable elections over the past two decades, behind only 2011, when ideological control of the court was at stake.

In addition, allegations that the Republican legislature was trying to hold down turnout by not postponing the election might have further motivated Democrats to vote.

Still, beneath the aggregate numbers, we find some things to be concerned about. Turnout in Milwaukee County dropped much more than in most of the state, as it did in Brown County, home to Green Bay; both had difficulties keeping polling places open. Further, some voters who tried to vote absentee could not, given administrative problems with the overburdened absentee ballot process. The surprisingly high turnout, despite all of this, is a sign that we should not underestimate the commitment of those who voted — or of the poll workers who served them.

Richard H. Pildes is the Sudler Family Professor of Constitutional Law at New York University.

Charles Stewart III (@cstewartiii) is the Kenan Sahin Distinguished Professor of Political Science at MIT.