In the era of President Trump, it’s become fashionable to presume that politicians can do whatever they like and get away with it. But if recent elections to Congress are any guide, scandals do have large and measurable effects. So when U.S. Rep. Chris Collins, the Republican from New York’s 27th Congressional District, was arrested on insider trading charges on Wednesday morning, it took a seat that had looked to be fairly safe for Republicans and put it into the competitive category.

I’m going to be fairly circumspect in this article because I’m knee-deep in finalizing our House model, and I don’t want to scoop our own forecast. But one of the things we evaluated in designing that model is the electoral effects of scandals, based on the data set of scandals put together by my colleague Nathaniel Rakich.

Below is a list of scandal-plagued incumbents since 1998 who made it to the general election and faced an opponent from the opposite party. I’ve compared each incumbent’s actual margin of victory or defeat against a projected margin based on a “fundamentals” model that accounts for: (i) the incumbent’s previous victory margin, (ii) the partisan lean of the district, (iii) the generic ballot at the time of the election, (iv) congressional approval ratings at the time of the election (which are a good proxy for the overall mood toward incumbents), and (v) the incumbent’s congressional voting record (representatives who break with their party more often overperform on Election Day). This is a slightly pared-down version of what our House model will look at, but it should be a fairly robust and reliable model.

How much do scandals hurt incumbents? It depends on how competitive the district is Year District Incumbent Projected Margin Of Victory Actual Margin of Victory or Defeat Net Effect Of Scandal 1998 GA-6 Newt Gingrich 31.2 41.4 10.2 1998 ID-1 Helen Chenoweth 23.4 10.5 -12.9 1998 IL-6 Henry J. Hyde 32.6 37.2 4.7 1998 IN-6 Dan Burton 51.4 55.3 3.9 2000 GA-7 Bob Barr 21.0 10.5 -10.5 2004 OH-14 Steven C. LaTourette 34.0 25.5 -8.5 2006 MI-14 John Conyers, Jr. 78.1 70.6 -7.5 2006 PA-10 Donald Sherwood 25.1 -5.9 -31.0 2008 FL-16 Tim Mahoney 7.6 -20.2 -27.8 2008 NY-15 Charles B. Rangel 82.4 81.3 -1.2 2010 MA-6 John F. Tierney 22.3 13.9 -8.4 2012 FL-26 David Rivera 12.5 -10.6 -23.2 2012 NY-11 Michael G. Grimm 10.3 5.4 -4.9 2012 TN-4 Scott DesJarlais 24.8 11.5 -13.3 2016 NC-9 Robert Pittenger 27.2 16.4 -10.9 2016 NH-1 Frank C. Guinta 5.4 -1.3 -6.8 2016 TX-27 Blake Farenthold 28.5 23.4 -5.1 Overall average 30.5 21.5 -9.0 Districts less competitive than NY-27 45.7 42.0 -3.7 Districts more competitive than NY-27 19.8 7.1 -12.7 Shaded districts were more competitive than NY-27 based on their partisan lean.

On average, the scandal-ridden incumbents … won re-election by 21.5 percentage points! But that’s quite a bit worse than their projected margin of victory, which was 30.5 percentage points. The net effect of a scandal is about 9 points, therefore. (This finding is reasonably consistent with previous research on the topic.) Fourteen of the 17 incumbents underperformed their projection by at least some amount, and the three exceptions came a relatively long time ago, in 1998. (There’s no evidence of the effect of scandals decreasing in recent elections; if anything, it’s increased slightly over the course of the data.)

Moreover, the effect of scandals is potentially greater in competitive districts, where the other party has an opportunity to mobilize a real alternative. Let’s use New York’s 27th Congressional District as a dividing line, for instance. It has a FiveThirtyEight partisan lean of R +22, meaning that it’s 22 points more Republican than the country as a whole based on its voting in recent presidential and state legislative elections. That type of district is ordinarily quite safe, but is just on the fringe of what could become competitive if everything breaks right for the opposing party — for example, in an election in a wave year against a candidate who just got arrested by the FBI. In districts less competitive than NY-27, scandals cost the incumbents only 4 percentage points, on average. But in districts that were as competitive or more competitive than NY-27, candidates with scandal issues underperformed their fundamentals by an average of almost 13 points.

So does that make Collins’s race a toss-up? You could do a little mental math: If the scandal costs him 13 percentage points, and the national environment favors Democrats by 6 points, that could produce a 19-point swing toward Collins’s Democratic opponent, Nate McMurray — almost enough to offset the strong Republican lean of the district. But you’d be leaving one thing out: Collins is still an incumbent, and incumbents usually outperform the partisan lean of their districts.

In fact, the incumbency bonus in recent elections has been in the very low double digits — on the order of 12 percentage points. (It used to be quite a bit higher.) That’s just about the same as the magnitude of the scandal penalty. The typical scandal, therefore, essentially wipes out a candidate’s incumbency advantage and makes the district perform similarly to an open-seat race. But it doesn’t necessarily reverse the advantage. Republicans would be favored to win an open-seat race in NY-27, even amid a very blue national political environment, so they’re probably still favored with Collins on the ballot too.

There’s one more complication, however, which is that this data suffers from survivorship bias. The candidates with really bad scandals will often retire rather than seek re-election, or they may lose in their primary. If all scandal-plagued incumbents were forced to be renominated, we’d probably observe a scandal penalty even larger than the 10 or 12 points we’re showing here.

But in some ways, Collins and the New York GOP are in a position where their hand has been forced. New York has already held its primary and Collins is the nominee; the general election is in only three months. He seems disinclined to bow out. And it isn’t entirely clear whether it would be possible to replace Collins on the ballot even if Republicans wanted to. This is the type of scandal that might have induced a retirement if it had occurred a year ago, but the GOP may not have that choice.

The Cook Political Report moved NY-27 from noncompetitive to its “Likely Republican” category after the news on Wednesday morning. I might go one step further and put it in the “Lean Republican” category instead, even though it’s a really red district. (It went for Trump by 25 points in 2016.) Soon, we’ll be able to tell you what the FiveThirtyEight House model thinks too, so it’s back to work on that.

But in general, Republicans face a very long list of potentially competitive districts — places where Democrats aren’t necessarily favored at even odds, but have a fighting chance when they have no real business doing so. That list got one seat longer after Collins’s arrest. Cashing in a few of those lottery tickets is what might turn a near-miss for the Democrats into a narrow majority — or a narrow majority into a wave.

Check out all the polls we’ve been collecting ahead of the 2018 midterms.