CHANNEL-SURFING was no escape. In late January presidential campaigns bought up almost all the advertising on every television channel in Iowa, turning everything from “Sunday Night Football” to “The Big Bang Theory” into brief intermissions between rounds of political WrestleMania. On January 29th, three days before the state’s caucus, 20 hours’ worth of election propaganda saturated Iowa’s airwaves. By January 25th campaigns had spent $53m advertising there; that number will climb once figures for the contest’s final days become available.

For all the talk of data-driven outreach and micro-targeted get-out-the-vote efforts, television advertising is still the staple on campaign shopping lists. Yet proof that candidates are getting a return on this investment has long been hard to find. Study after study has shown that few voters are motivated or persuaded by advertising—a finding political scientists have repeated so often that it is now known as the “minimal-effects hypothesis” (MEH).

To measure the impact of advertising so far in the 2016 campaign, The Economist divided the Republican field into pairs of candidates in Iowa and New Hampshire. For each of the days in which both politicians scored above 10% in either the state or national polling averages published at RealClearPolitics (RCP), we counted how many ads, both positive and negative, had been aired in that state about each candidate during the previous week. We then compared this ratio with the two contenders’ relative positions in the state’s RCP polling average. If there were any pay-off to media spending, then candidates who appeared in lots of positive ads and few negative ones should have gained ground when compared with their rivals.

Polls can be influenced by too many factors to identify the causes of their fluctuations with precision. We tried to control for the impact of news events—such as the revelation of Ted Cruz’s failure to disclose loans he received from Goldman Sachs, or Sarah Palin’s endorsement of Donald Trump—by conducting the study on the difference between each candidate’s national polling average and their polling in Iowa or New Hampshire (where the adverts aired). Even after this, however, the numbers are still affected by campaign rallies, local media coverage and a healthy dose of random variation.

We found that paid TV airtime did matter, accounting for a modest 13% of the week-to-week changes in polling. In some cases it was more significant: from January 24th to 30th, TV viewers in Iowa saw 866 more positive spots and 220 fewer attack ads about Mr Rubio than they did about Mr Trump. After adjusting for their standing in national polls, the front-runner’s advantage over the Florida senator duly shrank by 5.1 percentage points. Overall, holding nationwide polls constant, we found that candidates could expect to gain a one-point edge over their rivals in the next week’s early-state polling for roughly every 200 net positive ads about them, or every 500 net negative ones about their opponents.

So do these results vindicate the ad men after all? Not entirely. First, the effects of paid media tend to be short-lived: during the current Republican campaign, the impact of positive ads on polling has been 4.4 times greater during the week they aired than in the subsequent week. This suggests that candidates may do well to imitate Mr Trump and skimp on their media purchases until shortly before the election. Moreover, just because adverts seem to have some persuasive power doesn’t make them the best bang for a campaign’s buck. Political scientists have generally found that “ground game” investments, like knocking on doors and get-out-the-vote efforts, deliver a superior payoff. The victory in Iowa of Mr Cruz, who was heavily out-advertised there but was widely considered to have the best caucus-day operation in the state, shows that ruling the airwaves is not the only way to win.

A summary of our methodology, along with the underlying code and data, is available here.

CORRECTION: A previous version of this story mistakenly referred to a comparison of advertising totals between Marco Rubio and Donald Trump in New Hampshire. The figures were actually taken from Iowa. The article has been updated.