The "Swiss System" is designed to improve the chances of getting a clear winner in just a few rounds. However, sometimes there are still ties for first place, and there are always going to be ties for other places (multiple players who have scored 4-1, 3-2, etc.) In order to award trophies, tournament directors will rely on several tiebreak methods. Here are a few of the most commonly used methods:
This system is based on the strength of each player's opposition on that day. To figure your Solkoff tiebreak, simply add the final scores of your opponents. The player whose opponents scored higher is presumed to have had tougher competition that day. (Here's a reason to wish your opponent "Good luck" for the rest of the day - if their final score is high, your tiebreaks will be high!)
Median (also known as the Harkness System after Kenneth Harkness)
This method is the same as the Solkoff method, but you discard the highest and lowest scores of your opponents and add the rest.
Same as Median, but modified as follows: for tied players with plus scores, only the lowest-scoring opponent is discarded; for tied players with minus scores, only the highest-scoring opponent is discarded.
(There are further modifications for tournaments of 9 or more rounds and for unplayed games).
Another easy method to determine: you simply add the cumulative (running) scores for each round. So if you won your first 2 games, lost the third and fourth games, and won the fifth, your cumulative score on the wall chart was: 1 2 2 2 3. 1+2+2+2+3 = 10, which would be your Cumulative tiebreak. A player who lost their first 2 games, then won the last three would have a Cumulative tiebreak as follows: 0+0+1+2+3 = 6 tiebreak points. The reasoning behind this method is based on the Swiss System of playing an opponent with the same score as you. The assumption is that if you win early, you're playing tougher opponents (opponents who also won early and probably finished higher). If you lost in the early rounds, you played weaker opponents (who also lost early and probably didn't finish as high). This method obviously doesn't work for players who finished undefeated.
Here's an exhaustive list of tiebreak methods.