The biggest appeal of the show is the charming and well-developed characters, but a very common reaction among those who watch it is "wow, I can't believe that they made something so seemingly lame so exciting". Chihayafuru is proof that execution is everything. Also, it helps that the game is a bit more vigorous/physical than it might sound from reading the rules (eg: http://mizunoyukino.tumblr.com/post/42129944787), and that the show isn't afraid to have the protagonists actually lose important matches sometimes.

There's also a character who uses detailed statistics on the team and their opponents' play to improve their strategy, which may be up your alley :).