Republicans routed Democrats in the midterm elections -- especially in the statehouses. The GOP now controls more than 4,100 of the nation’s 7,383 state legislative seats -- the most since 1920, according to state legislature elections expert Tim Storey.

Democratic Party leaders will almost certainly put increased money and manpower into these elections in 2016, but funding, advertising and campaigning on the local level can only do so much. The national political atmosphere will play an outsized role in determining the outcome of state legislative contests. Specifically, the outcome of the presidential race will likely shape the composition of state legislatures across the country.

In order to show this, we analyzed state-level data from every presidential election from 1956 to today. The data shows a clear, potentially problematic pattern -- that the presidential race has become increasingly important in determining the results of state legislative elections.

For each presidential election from 1956 to 2012, we compared the Republican two-party presidential vote share in each state to the results of that state’s legislative contest (or the following contest in states with off-year elections). Sometimes a clear pattern emerged.

In 2012, bigger wins for former Massachusetts Gov. Mitt Romney translated into increased success for Republican state legislative candidates. Similarly, Democratic state legislative candidates generally performed better in states where President Obama had larger margins of victory.

In other elections, no such pattern emerged.

Bigger wins for then-Vice President George H.W. Bush and Massachusetts Gov. Mike Dukakis failed to consistently translate into larger seat shares for their respective parties in state legislatures.

For each election from 1956 to 2012, we also calculated a statistic known as the “coefficient of determination” or “R-squared.” In the most basic terms, R-squared measures, on a scale from zero to one, how well you can predict or explain one thing if you know some other thing. In this case, it measures how well you can predict or explain state legislative election results using state-level presidential election results. In the first graph (2012) the R-squared was 0.67 -- which means that about two-thirds of the behavior of the state legislative data can be explained using only presidential results. In the second graph (1988) the R-squared was 0.10. In that election, the presidential results were not very helpful in explaining state legislative outcomes.

A few caveats should be noted before moving forward: Other variables -- fundraising, organizational strength of the state parties, incumbency, candidate quality and a number of other factors -- also help shape state legislative elections. We could improve the predictive ability of these simple models by adding more variables, but our aim is to see how much presidential results alone explain -- not to actually predict -- state legislative election results. Additionally, R-squared is not a perfect measure. Simple linear regression analysis should be supplemented by further testing (when applicable) and close examination of the data. Finally, not all relationships are linear. In this analysis, it made sense to use some basic linear regressions but this is not always the case.

The R-squared value for the comparison between the state legislative and presidential election results in every presidential election since 1956 is shown below:

Two important patterns jump out of this graph.

First, for most of the elections since 1956, the R-squared value is low. In other words, for most of the last six decades (excluding a small uptick in 1976 and 1980 when Jimmy Carter did well in traditional Democratic strongholds), presidential results had little influence over state legislative elections.

Second, in recent elections, presidential results have become increasingly effective predictors of state legislative election results -- especially in 2012.

One possible explanation for this trend is the distraction hypothesis -- that when federal offices are up, voters focus on those races and end up voting for the same party down-ticket without really considering how well those officials have done their jobs.

If the distraction hypothesis holds (and there’s evidence that it does), it poses a significant problem for our political system. In our federalist system, elections are the primary method of holding legislators accountable for their actions. If voters dislike how a legislator is doing his or her job, they have the option of electing someone else. But these presidential “coattails” disrupt that mechanism.

For example, suppose the Republican-controlled statehouse and Senate in Nevada govern well and pass popular laws, but the Democratic presidential nominee carries the state in 2016. If history is any guide, those Republican lawmakers would suffer electorally despite their policy successes. The same thing could happen to Democratic state legislators in a state that a Republican presidential candidate wins.

In other words, the 2016 presidential election does not just matter because a new president will take the Oval Office -- it matters because both candidates will significantly help or hurt their party’s state legislative candidates across the country.