There has been extensive research published on whether film critics affect the success (on box-office or otherwise) of a film.
There is however currently no clear consensus between these published academic (or: other) studies.
Overall, it appears (from the overwhelming majority of peer-reviewed, published academic studies) that: critics do not significantly affect box office.
Favorable film reviews by critics may raise box office slightly, and similarly, unfavorable reviews may negatively impact rolling box office, often slightly more than the (usually minimal) `favorable critical review box-office-boost effect’.
(The data indicates that: bad/negative film reviews by critics in the media can make people tend to stay away from a film, with a more noticeable effect, than a good/positive review will encourage/convince them to go see it.)
Of much greater impact and influence are the story memes presented within the marketing (the story/characters/situations presented to the potential audience in the film poster and the film trailer, etc.)
When I helped to run the Newcastle Film Festival in 1996, our international guest of honor was the legendary Roger Corman, who started the film careers of: James Cameron, Martin Scorsese, Ron Howard, and countless others. I asked Roger what areas of film he researched; he said he researched exactly which Titles, Genres and Stars would make people want to go and see a movie. (And if you note the awesome titles of Roger’s movies, this research clearly paid dividends. Roger is also the author of the excellent film industry memoir: How I Made A Hundred Movies In Hollywood And Never Lost A Dime).
What is perhaps most remarkable about this StoryAlity empirical study of the Top 20 ROI Films is that:
The aggregate film quality scores/ratings awarded to them by critics (where available from Metacritic.com) and the scores awarded them by the widest and most-comprehensive sampling of Viewer Ratings to date (where available from IMDb.com) come out exactly equal at: 73%
Metacritic is: “The best critics’ reviews combined into a simple Metascore. Scores are out of 100.”  (This does not mean the best critics reviews, but rather, the best critics reviews. The reviews themselves may be unfavorable; it should also be noted that SAW only got a 46% aggregate Metacritic score, however it is still a Top 20 ROI Film.)
In other words, given the above result, Film Critics ratings – when their ratings are aggregated – appear to be an extremely-accurate barometer of public movie-going taste.
That is to say – not necessarily influencers of box office tendencies, but certainly: accurate predictors of a film’s story quality, as judged by The Field (the audience, critics, the film industry as a whole) – if the above empirical evidence is any guide.
So; Film Critics absolutely do matter.
(Though; not necessarily in the exact way that we may customarily think.)
High-RoI Story/Screenplay/Movie and Transmedia Researcher
The above is (mostly) an adapted excerpt, from my doctoral thesis: “Communication, Creativity and Consilience in Cinema”. It is presented here for the benefit of fellow screenwriting, filmmaking and creativity researchers. For more, see https://aftrs.academia.edu/JTVelikovsky
JT Velikovsky is also a produced feature film screenwriter and million-selling transmedia writer-director-producer. He has been a professional story analyst for major film studios, film funding organizations, and for the national writer’s guild. For more see: http://on-writering.blogspot.com/
NOTES / REFERENCES
 McKenzie, J (2012), ‘The Economics of Movies: A Literature Survey’, Journal of Economic Surveys, Vol 26:1, pp.42-70.
From the comprehensive literature review: `The Economics Of Movies’ – McKenzie, J (2012), University of Sydney – some key research papers on whether movie critics affect the success of a film include:
Basuroy, S., Chatterjee, S. and Ravid, S.A. (2003), ‘How Critical are Critical Reviews? The Box Office Effects of Film Critics, Star Power, and Budgets’, Journal of Marketing, 67, 103-117.
Eliashberg, J. and Shugan, S. (1997), ‘Film critics: Influencers or predictors?’, Journal of Marketing, 61(2), 68-78.
Gemser, G., Van Oostrum, M. and Leenders, M. (2007), ‘The Impact of Film Reviews on the Box Office Performance of Art House versus Mainstream Motion Pictures’, Journal of Cultural Economics, 31, 43-63.
Holbrook, M. (1999), ‘Popular Appeal Versus Expert Judgements of Motion Pictures’, Journal of Consumer Research, 26, 144-155.
Moul, C. (2007), ‘Measuring Word-of-mouth’s Impact on Theatrical Movie Admissions’, Journal of Economics & Management Strategy, 16(4), 859-892.
Prag, J. and Casavant, J.(1994), ‘An Empirical Study of the Determinants of Revenue and Marketing Expenditures in the Motion Picture Industry’, Journal of Cultural Economics, 18(3), 217-235.
Ravid, S. A., Wald, J. and Basuroy, S. (2006), ‘Distributors and Film Critics: Does it take Two to Tango?’, Journal of Cultural Economics, 30, 201-218.
Reinstein, D. and Snyder, C. (2005), ‘The Influence of Expert Reviews on Consumer Demand for Experience Goods: A Case Study of Movie Critics’, The Journal of Industrial Economics, 103(1), 27-51.
* Where available; not all Top 20 ROI Films are on both IMDb and Metacritic.
For more articles on film economics, see the excellent and comprehensive literature review: `McKenzie, J 2012, ‘The Economics of Movies: A Literature Survey’, Journal of Economic Surveys, Vol 26:1, pp.42-70.