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While most corporate clients seeking legal counsel are not likely to simply hire the first law firm that comes to mind, it’s not unreasonable to believe they would be inclined to hire one of the first five firms whose names they can recall.

That, at least, is among the assumptions at the heart of research company Acritas‘ third annual survey aimed at measuring the strength of U.S. law firm brands in the United States. And for the third straight year, Skadden, Arps, Slate, Meagher & Flom claims first place. Rounding out the top five finishers on this year’s law firm brand index: Jones Day, Kirkland & Ellis, Baker & McKenzie and Hogan Lovells. (Scroll to the bottom of the story to see the complete list.)

Acritas drew up the latest rankings based on interviews with 581 senior in-house counsel at companies with more than $50 million in revenue. The participating lawyers were asked to name the first five firms that came to mind, as well as the three firms they think of most favorably, the three firms they consider most often for both top-level litigation and major M&A matters, and up to five firms to which they turn for most of their companies’ high-value work. An additional 123 lawyers abroad were also asked to name the firm they most often use in the U.S. Firms earned points according to where they figured in the answers that survey respondents gave.

“An average U.S. counsel is using 34 firms in a year, and we’re capturing the first five,” says Acritas vice president Elizabeth Duffy. “In a general counsel’s day-to-day scenario, they may not think past number two on the list when they pick up the phone.”

The results show that sheer size help keep law firms top of mind with potential clients. The first seven firms on the Acritas list all have more than 1,500 lawyers, and some have double that number. Only four of the top 20 have fewer than 1,000 lawyers—Sullivan & Cromwell (No. 13), Wilmer Cutler Pickering Hale and Dorr (No. 15), Vinson & Elkins (No. 16) and Davis Polk & Wardwell (No. 20).

International reach also helps a firm increase its profile, Duffy says. “In the last five years, we’ve seen a geographic or international footprint become a stronger and more important factor of favorability,” she says. “Firms that offer that international footprint are now appealing or attractive to an increasing share of the market.”

Jolene Overbeck, chief marketing officer at Hogan Lovells, says her firm’s global presence may help explain how the firm climbed to fifth place on this year’s index from 14th last year, one of the largest jumps on the 2014 list. “I think it’s a reflection of the fact that we’ve got a good story to tell,” Overbeck says. “It’s a firm that has roughly equivalent strength in the U.S. and outside the U.S., with the same level of quality in markets around the world. It’s got tremendous government and regulatory capability, which is of increasing concern globally for businesses. … It’s a combination that clients are increasingly interested in.”

Other movers include Wilmer Cutler Pickering Hale and Dorr, which catapulted from 53rd place last year to 15th on the latest rankings. (Wilmer held the 24th spot in the survey’s first year.) Reed Smith rose eight spots, to 17th; Weil, Gotshal & Manges rose seven spots, to 10th; and Mayer Brown dropped 11 spots, to 19th. Skadden is not the only firm to hold its spot for the three consecutive years. Second-place finisher Jones Day shares that distinction. The other firms rounding out the survey’s top 10 have shuffled places from year to year.

Duffy acknowledges that the Acritas index is just one measure of a firm’s place in the marketplace. “For law firm leaders, it’s not everybody’s aspiration to be in the top 20 across the U.S.,” she says, citing West Coast–centric firms and firms that narrowly focus their practice on advising financial institutions as two examples. “It’s about, where do we want to be known and valued?”

But no matter the segment a law firm strives to be a part of, Duffy says, “having a strong brand among your clients is essential. Just because you have clients doesn’t mean they’re thinking of you.”