You may find that an article doesn't have an Altmetric score, that is, the score is zero. Altmetric themselves say “most articles will score zero”.
The exact proportion of articles with an Altmetric score varies from journal to journal, but a mid-tier publication might expect 30 - 40% of the papers that it publishes to be mentioned at least once, with the rate dropping rapidly for smaller, niche publications. So the lack of a score should be understood in this context.
If an article doesn't have an Altmetric score - does this matter? Well, you should remember that Altmetric is aiming to track the “social web”, with the heaviest weight given to online news and blogs. So really what the score (or lack of) means will depend on the area of research and whether it is the type of research you would expect to have this kind of attention. Some research will obviously more easily create a 'social buzz'.
Like any metric, the scores have their limitations, for example, Altmetric only collects data about articles from specific supported publishers / repositories. Also, if the article was published before July 2011, Altmetric will have missed any transient mentions of it, tweets in particular. As such, its score won't be accurate, and will represent a lower bound of the attention received.
The Altmetric score cannot tell you about: the quality of the paper or the quality of the researchers or the whole story...
If you are a Dundee researcher and would like to maximise your score - see: Ensure your articles are tracked and 5 tips for improving your article’s Altmetric score.
You know an article was popular and wonder - why is the Altmetric score so low?
When was the article published?
Altmetric only collects data about articles from supported publishers / repositories. Altmetric started collecting content from most publishers during the second half of 2011.
Was the article published before 2012? If so it might be that Altmetric simply didn't support the journal it came from until more recently.
Where was the article popular?
Was it popular with bloggers? Altmetric keep a manually curated list of blogs that they track for article mentions. They add to it frequently but usually can't import more than a few weeks worth of older posts - so it could be that they just didn't track any of the relevant blogs until a little time after the paper was published.
What were the relevant posts linking to?
Altmetric only tracks direct attention: that is, links to the actual paper. Often news stories will refer to a paper e.g. "a paper by Myers' lab published in this week's Nature" but won't contain a hyperlink, which Altmetric requires.
Sometimes news stories will link to an associated editorial, perspective or research highlight instead of directly to the article. Altmetric won't pick this up (the editorial will be scored highly instead of the actual research).
Has the attention all been in the past 24h?
Altmetric captures attention in as close to real time as possible but it can sometimes take up to a day for posts to filter through to the bookmarklet or Explorer.
It was published recently and I can see links to it that haven't been picked up!