The candles fluttered in the slight breeze as the door opened suddenly, blinding the boy at the table with sunlight. Around him charts covered the wooden walls, and pages of calculations showed why his fingers were ink-stained. "Harry!", called the older boys as they hurried in, "Harry, it's time for dinner!" They rushed to their lockers and stripped off team practice shirts and combed wind-blown hair. Lockers slammed as brooms were locked away for the day.
Harry tucked away his calculations in a safe folder with the date of the next match on the cover, corked the ink bottles and wiped his quills clean. His lovely broom had never even left the locker, and the messy condition of his hair had nothing to do with wind. He had been running his fingers through it as he struggled to understand how the moon phases were expressed in Arithmancy. He placed the team reference book back on the shelf.
Arithmancy. Oliver had explained it to him. You could be a good Seeker with just a feeling for patterns, if you saw the snitch several times. You could not be a great Seeker unless you could predict the pattern the snitch was flying in - and that meant practical Arithmancy. The snitch did not fly at random. The pattern for each game was influenced by dozens of factors - the day, the time of day, the moon phase, month of the year (calculated in Druid months, thank you), and smaller factors such ley lines, power totem of the teams playing, or even which team won the coin toss. A great seeker calculated as many of these in advance as possible. Even a glimpse of the snitch in motion could confirm which pattern it was using and help you know what to do.
You trusted your own calculations - but you had to keep an eye on your opponant in case he had done a better job. If he spotted the snitch before you did, or you both saw it at the same time, the winner would be determined by skill and quality brooms. However, if you predicted where the snitch was going you could be there before it arrived and catch it before anyone else realized what you had done.
Seekers didn't take Arithmancy as an elective. It was independent study, though often several players on a team studied together. They took the Owl (and Newt) for it automatically. Most Seekers took high marks, which gave them highly desireable job and school interviews. Most players of other positions also took the tests by choice.
Harry hurried after the others. He was starving! Study was hard work! He knew Hermione wouldn't understand how a game could help your education, so he didn't talk to her about it. He also knew Ron didn't want to study Aritmancy for any reason, even to win. Ron had an instinctive understanding of strategy, but he would never be a great seeker.