Every two years, the Olympics come around as a testament to good sportsmanship and lifelong dreams achieved and Cinderella stories come true and the sheer wonder of breathtaking athletic prowess.

Of course, many watching at home also delight in the great Olympic tradition of claiming bragging rights. During the Rio Games, one particular group has been vocal on this subject: Stanford grads.

Stanford athletes (incoming, current and former) have won 18 Olympic medals in Rio as of Thursday morning, the most of any American university and more medals than most of the 200 member nations competing at the Games, according to the NCAA. If Stanford were a country, it’d currently be ranked No. 10 in the total medal count.

The second and third institutions on the list are also California schools. Just behind Stanford with 16 medals is Bay Area neighbor and longtime football rival, the University of California, Berkeley. And in at No. 3 is the University of Southern California.

Stanford is so far just edging out Cal in golds and silver medals, as well, with a total of nine golds and six silvers to Cal’s eight golds and four silver medals.

USC’s eight total medals, three of which are gold, put the school far behind Stanford and Cal -- though still ahead of all but 22 countries.

No surprise, these three schools are also the top three in terms of numbers of athletes sent to the Olympics this year, competing for countries all over the world. USC has sent 42 athletes to represent the Trojans in Rio; the Cal Bears are represented by 40 athletes; and the Stanford Cardinal sent 39. However, as many Cardinal fans have no doubt pointed out, Stanford has the most athletes competing for Team USA.

Stanford, Cal, Stanford, Cal: From left to right, Simone Manuel, Abbey Weitzeil, Dana Vollmer and Kate Ledecky of Team USA after winning the Women's 4 x 100m Freestyle Relay in Rio. Manuel and Ledecky are Stanford athletes; Weitzeil and Vollmer are affiliated with Cal. Getty Images

Stanford can also take bragging rights for being more efficient than Cal in earning medals: Its 12 athletes have brought in more medals than Cal’s 13 -- though that’s in large part thanks to the record-breaking feats of swimmer and soon-to-be Stanford freshman Katie Ledecky, who won four golds and one silver.

Stanford and Cal’s top medal standings are almost entirely due to their powerhouse swimming programs -- 14 of Stanford’s medals and 15 of Berkeley’s came in that sport.

With many medals still to be awarded and over 20 track and field finals still to come, the rankings could well change before the Games are over. It seems unlikely that any school will catch up to Stanford or Cal at this point, but most of the institutions in the top 10 still have many athletes competing in the medal race.

And with Stanford and Cal essentially neck-and-neck, the Bay Area rivalry may be one to watch right up to the Closing Ceremonies on Sunday.

Related: Why America’s toughest school to get into may not be the best