Now to complete the design of my friend’s tennis league. In the first post, we’d gotten as far as showing how the partnerships should be formed. Now we need to determine who plays who in the actual matches, taking into account a preference for “interesting” matches.
In an earlier post, the quality my friend calls “interestingness” was called “competitiveness”, and discussed briefly here. In that post, I speculated that the only format that seemed particularly designed to enhance competitiveness was the Swiss system. That led me, in an effort to meet my friend’s preferences, to incorporate the pairing logic of the Swiss system into the design for his tennis league.
The usual approach in leagues like this one is to play some sort of round robin. A full round robin tends to be quite fair, as it makes all possible pairings, so that everyone’s schedule has the same opponents. But the matches are not particularly interesting because players or teams of roughly equal skill don’t play each other more often than they play everyone else.
In the case of this tennis league, a full round robin is out of the question. For each of the 11 players, there are ten possible partners, and 36 possible partnerships among the remaining nine. Thus, without even allowing for the needful byes, it would take 396 weeks to play all possible matches.
So, given that we’re not going to play all possible combinations, is there some way to choose match pairings so that there is some tendency to play the ones with small skill differentials more frequently?
There is. The pairing logic that’s needed is the one used by tournament using the Swiss system. In essence, a Swiss tourney is like an elimination tourney in which no one ever gets eliminated. In the second round, winners play winners, and losers play losers. In each successive round, matches are set so that the competitors play agains opponents with the same, or nearly the same, records as themselves.
Now, making Swiss pairings is usually rather a complicated process. In addition to setting matches between players with similar records, one usually needs to consider the allocation of byes, to avoid rematches, and sometimes to fairly distribute factors like home court advantage, or the first move in chess. Weighing these factors properly against each other is not always straightforward, and the tradeoff between one objective and another is often made by directors who know the identity of the players involved. So rather elaborate rules are needed to sort out the priority to be given to each of the objectives in order to reduce the perception that judgments might have been made to favor one competitor over another.
In this context, however, Swiss pairings can be made very simply indeed. For each week, there are only four teams to play, and so all you need to do is to set the two teams with the best record against each other, breaking ties with a coin flip. It’s true that this simple procedure will have a tendency to create a few more rematches, but rematches are not much of a problem where the partnerships themselves are constantly changing.
At the beginning of the league, the pairings will be random, but as the league progresses, the pairing logic tends to set good players against other good players (and the reverse).
In the interest of interestingness, my friend offered to provide information about the skill of each player that could be used for a kind of seeding. Unlike the usual seeding pattern, where the early rounds of a tourney are set specifically to create uneven contests that protect the better players, these seedings could be used to create more interesting matches. This might be useful to help choose interesting matches for the early rounds. But after the early rounds, it’s a good thing to base skill assessment on actual results rather than the initial seeding.