With this week&#8217;s Facebook IPO filing, a lot of big numbers are being bandied about:An estimated $5 billion initial offer, and perhaps between $75 and $100 billion for the total market valuation.Facebook also represents big numbers to brand marketers: An audience of nearly 1 billion consumers, and the growing legions of brand fans &#8211; often tens of millions &#8211;marketers have accumulated on Facebook. Social media pundits often liken them to an army of brand advocates, ready to engage on a moment&#8217;s notice.The only problem with this scenario is that it turns out most fans are quite unenthusiastic about playing this role. After the initial click to "like" the brand, they rarely interact again with the brand on Facebook. That's the headline finding from a new study, just released by the prestigious Ehrenberg-Bass Institute for Marketing Science in Australia. The Institute summarized the findings as follows: "Big Brands Snubbed by Fans on Facebook."According to Dr. Karen Nelson-Field, who led the study, "many brands moved quickly onto Facebook when it emerged as the new frontier for reaching an audience but it has since proved a challenge to engage with who claim to 'like' them."More specifically, the researchers looked at Facebook's "People Talking About" metric to better understand consumer involvement with brand pages for which they are considered fans. "People Talking About," which was launched in October 2011, is designed to be an engagement metric for Facebook fan pages. It measures people who contribute any type of content to a fan page, including initial liking, liking specific content on a page, posting to a wall, commenting, sharing a post or other content, answering a question, photo tagging, sharing a deal, or any other way a user can share interactions with brand pages. The Ehrenberg-Bass study analyzed these consumer interactions for the top 200 brands on Facebook during a six week period last fall.The result? Only 1.3% of fans engage with the fan pages during the course of a week. And many of these are the result of an initial "like." Among those who have already liked the brand in the past, engagement drops to a mere 0.45%.The results are consistent with research I have written about previously, which also showed "of the ten brands with the largest number of Facebook fans &#8211; 20 million fans on average &#8211; just 0.45% are active fans."As I wrote then, "Facebook has tapped into a powerful social need of consumers around the world, and has amassed an extraordinarily large audience. But it has not yet unlocked the secret to engagement with advertiser brands."Dr. Nelson-Field agrees, calling 0.45% "not a totally miserable figure," but rather, "a sobering one, particularly given engagement is supposed to be what differentiates Facebook from other mass reaching media." And, she continues, "This doesn't mean we don't think Facebook is an important part of the marketing mix &#8211; we do &#8211; we simply encourage marketers not to spend a disproportionate amount of time and money trying to facilitate engagement or drive loyalty when we know that's not going to happen with the push of the 'like' button."This is further evidence that brands must think holistically about social engagement, and consider all the media/marketing channels that drive consumer word of mouth and brand advocacy. Driving fan engagement on social networking sites is one vehicle among many. As we have said before, "all media are social," suggesting there are multiple touch points that can be deployed by marketers to unleash advocacy. And the behaviors that define engagement need to be looked for offline as well as online.Ed Keller, CEO of the Keller Fay Group, has been called "one of the most recognized names in word of mouth." The publication of Keller's book, The Influentials, has been called the "seminal moment in the development of word of mouth." Ed can be contacted at email@example.com. You can follow Ed Keller on Twitter: @kellerfay Read all Ed&#8217;s MediaBizBloggers commentaries at WOM Matters.Check us out on Facebook at MediaBizBloggers.comFollow our Twitter updates @MediaBizBloggerThe opinions and points of view expressed in this commentary are exclusively the views of the author and do not necessarily represent the views of MediaBizBloggers.com management or associated bloggers. MediaBizBloggers is an open thought leadership platform and readers may share their comments and opinions in response to all commentaries.