A lesson for centrist candidates: stay positive.

Given the sizeable cash advantage Majority Leader Eric Cantor, R-Va., enjoyed in his race against Dave Brat, Cantor was in the enviable position of setting the tone for the race. Unfortunately for his supporters, Cantor badly misplayed this advantage to his own detriment — by going negative early and often, he helped shape voter turnout in a way that predictably benefitted Brat.

The effects of negative ads have been examined in the political science literature, which teaches us two things: These ads tend to stay in the minds of voters (generally a good thing for the sponsoring candidate) and they tend to reduce turnout (good or bad, depending on who shows up on Election Day). Given the first finding — that negative ads stick — these spots are a common feature of modern campaigns, and are often part of a successful campaign strategy. In general elections, reductions in turnout can impact both parties, with both Republican and Democratic voters feeling disgusted and staying home.

There is another lesson from the political science literature, however, that Cantor’s team apparently overlooked: In off-year elections and primaries, the voters who show up at the polls tend to be more partisan. This makes sense, because only the most dedicated voters are likely to take the time away from their daily lives to vote. As turnout decreases, the concentration of highly partisan voters increases.

Putting these two theories together, Cantor should have realized that by going negative in his primary, he would reduce turnout and increase the percentage of voters who favor more ideologically extreme candidates. Given that he was facing a tea-party-backed candidate, this was a strategy destined to backfire.

So why did he do it? Cantor’s negative advertisements suggest that his team thought they could convince voters that Brat was a liberal, and that Brat was running to the left of Cantor. However, with Brat receiving endorsements from conservative notables (Laura Ingraham, Mark Levin, Ann Coulter) and the simple fact that all tea party candidates run from the right, this was a long-shot. While Cantor may have had reason to respond to certain attacks levied against him, his campaign strategy was deliberate in going negative when his opponent did not have the resources to shape the debate at all.

Rather than embarking on an ambitious quest to out-conservative his tea party rival, Cantor could have used his significant campaign war chest to boost his own conservative credentials, endearing himself to a wider array of Republican voters. He’d probably still be in line for speaker.

Jennifer Bachner, Ph.D., is the director of the Master of Science in Government Analytics at Johns Hopkins University.