The first part of one of the most topsy-turvy presidential elections in modern French history will come to a head on Sunday. That’s when voters in France head to the polls for the first round of voting. The top two finishers will proceed to a runoff election unless the top vote-getter receives more than 50 percent of the vote, in which case he or she wins outright. But if the polls are to be believed, that’s not going to happen. Instead, candidates representing the far right, far left, center and center-right all have a shot at securing one of the two spots in the runoff on May 7.

In short, the French presidential election is a mess.

Through much of 2017, Sunday’s contest looked like it was going to be a race to see who was going to advance to the runoff against the far-right National Front candidate Marine Le Pen. Originally, Le Pen’s most likely opponent appeared to be center-right Republican François Fillon. Given Le Pen’s poor showing in runoff polls, this would have made Fillon a strong favorite to become president. Fillon, though, became the center of a scandal in which he was accused of using public funds to pay his wife and adult children for fictitious jobs. He refused to drop out of the race and plummeted in the polls. That’s when former left-wing Socialist and now En Marche! centrist candidate Emmanuel Macron climbed into a first-place tie with Le Pen and looked destined to end up in a runoff with her.

Over the past few weeks, though, the first-round polls have increasingly shown a jumbled pileup. An average of surveys over the last week has Macron at 24 percent, Le Pen at 22 percent, Fillon at 20 percent and far-left Unsubmissive France’s Jean-Luc Mélenchon at 19 percent. As the chart below shows, the dipping numbers for Macron and especially Le Pen allowed the scandal-plagued Fillon — whose support has been mostly steady since February — to sneak back into runoff contention. Mélenchon, meanwhile, has surged thanks to a combative personality that’s allowed him to capitalize on a populist streak in the French electorate. He has mostly coalesced lefty support, which he originally split with Socialist Party candidate Benoît Hamon. Hamon is now polling in the single digits.

The race is tight enough, and French polls are inexact enough, that any two of the top four candidates could end up in the runoff. Polls in France are pretty good (better than in the United Kingdom), but there’s still a margin of error. In the first round of the past eight presidential elections — according to data compiled by political scientists Will Jennings and Christopher Wlezien and aggregated by The Crosstab’s G. Elliott Morris — the average absolute difference in the margin between the final week’s polling average and the top two finishers’ actual results has been 3 percentage points. That’s equal to the difference between Le Pen and Mélenchon. It’s 1 point less than the difference between Le Pen and Fillon over the last week.

MARGIN BETWEEN TOP TWO FIRST-ROUND FINISHERS YEAR FINAL WEEK POLLING AVERAGE ACTUAL RESULT GAP 2012 +1.6 +1.5 0.1 2007 +4.5 +5.3 0.8 2002 +6.3 +3.0 3.3 1995 -3.5 +2.5 6.0 1988 +11.5 +14.2 2.7 1981 +5.8 +2.5 3.3 1974 +13.5 +10.7 2.8 1969 +16.0 +21.2 5.2 Average 3.0 French presidential polls are good (but not perfect) Source: Will Jennings and Christopher Wlezien, G. Elliott Morris

And that 3-point error is just the average — sometimes there are bigger misses. Indeed, the true margin of error is probably closer to 7 to 9 points in either direction, depending on how you calculate it. That’s more than enough for Mélenchon to catch Macron in round one.

In fact, there are a few reasons to think that this election will feature a bigger polling miss.

First, a lot of candidates from across the ideological spectrum are realistically in contention, increasing the likelihood that voters will cast their ballots strategically or will switch allegiances at the last minute. In the kind of two-person, left-vs.-right race that Americans are used to, voters are less likely to flip back and forth between candidates. In this election, few voters will flip from the center-right Fillon to the far-left Mélenchon, for example. But it’s easier to see some voters going from the far-right Le Pen to the center-right Fillon. Or jumping from Fillon to the centrist Macron. Or even from Macron to the far-left Mélenchon. We know from past elections in the U.S. that polls in multi-way races are the most error-prone.

Second, pollsters may be herding — putting their thumb on the scales so as not to get any result that’s too far from the consensus (by weighting their results towards the average). While herding can make any individual survey more accurate, it makes the average of polls less accurate and increases the chance of a big miss.

The polls in France have been eerily consistent. Over a recent 53-poll span in the Huffington Post/Pollster.com database, Fillon never rose above 20 percent and never fell below 17 percent. It’s a bit difficult to judge the exact statistical probability of this occurring by chance because French pollsters almost exclusively use online quota sampling. Still, we can make an educated estimate using a normal distribution.

Given Fillon’s percentage in each of these polls, his average in them (18.9 percent) and the sample size of each poll, Fillon should have received less than 17 percent or greater than 20 percent in at least four of the 53 polls during that stretch. The probability that he didn’t end up outside of this 17-to-20 range by sheer luck at least once is only between 1 and 2 percent. And because pollsters have some differences in how they weight their polls, the number of polls outside the 17-to-20 range should probably have been even higher.

Between that possible herding and the crowded field, don’t be shocked if there’s a shock.

One thing I wouldn’t count on to contribute to a polling miss: “shy” Le Pen voters. Some people have argued that survey respondents might be afraid to admit that they support a candidate who espouses what some see as politically incorrect views (i.e. a French Bradley effect). But we can test this hypothesis by looking at how Le Pen and her father Jean-Marie Le Pen (another far-right-wing candidate) have performed in previous presidential elections compared to their polls.

The Le Pens have outperformed their pre-election polling average in two of the last four rounds of presidential elections in which they ran. In the other two, they slightly underperformed. On average, there’s been basically no difference. So Marine Le Pen could still beat her polling average in this election, but there’s just as good of a chance she’ll underperform it.

The bottom line is that we don’t know what’s going to happen on Sunday. Ironically, runoff polls are far clearer. Polls show Macron would start the short runoff campaign with at least a 15-percentage-point lead against any potential foe. Mélenchon would start with a 15-point lead against anyone but Macron. Fillon would be an underdog against everyone except Le Pen. And Le Pen would start as at least a 15-point underdog against every potential foe. That’s a far worse position than Donald Trump was ever in.

The runoff, in other words, might be anticlimactic. We just have to figure out who’ll be in it.