The Dow Jones Industrial Average (^DJI 0.61%) had a banner year in 2013. The blue-chip index gained 3,473 points, or 26.5%, to close out the year at 16,567 --  an all-time high. Thirty-three tickers claimed Dow membership at some point in 2013, and all 33 pay regular dividends. Among all these high-quality dividend stocks, where did the dividends make the biggest difference?

The answer may seem simple: AT&T (T 0.86%) once again delivered the juiciest dividend yield on the Dow, followed by Verizon (VZ 3.38%) and Intel (INTC 0.10%) in a dead heat.

Reinvesting AT&T's dividends in 2013 boosted your returns from 4.3% to 9.7%, for a 5.4% spread. Verizon and Intel both saw 5% higher returns when accounting for dividend reinvestments, though Verizon only gained 13.6% in straight-up share price returns while Intel mustered 25.9% higher prices in 2013.

But that's not the only way to do this dividend math. I could also point out that AT&T's dividend-powered return was more than twice the plain share price return, for a 126% relative boost. In these terms, Caterpillar (CAT 1.86%) stock crawled so close to the breakeven line that its modest 2.1% dividend improvement represented a 155% boost.

Don't take this stunning return-booster as a massive "buy" sign on Caterpillar. The heavy-equipment maker's dividend-powered 3.4% return might be 155% higher than the plain 1.3% share price gain, but Caterpillar investors are cursing both of these numbers. Yes, it's a massive improvement in relative terms, but the stock still trailed the Dow in a big way no matter how you slice it.

Don't be afraid to double-check the math if something looks too good to be true.

A careless headline might make you think that Caterpillar's dividend made you 155% richer in 2013, when the reality is that the dividend only softened the blow of a very disappointing year by a couple of percentage points. AT&T and Verizon are still the true dividend kings of the Dow, with Intel stepping up from behind, and three of these four stocks still trailed the Dow's dividend-adjusted returns in 2013. Only Intel lost to the Dow in plain share price returns but edged out the index when accounting for dividends.

DIA Total Return Price Chart

DJIA Total Return Price data by YCharts.